Prepared in cooperation with the Hawaii Institute of Geophysics of 

the University of Hawaii, Honolulu, Hawaii 
I 

L 
The Viscosity of Synthetic and Natural 

Silicate Melts and Glasses at 

High Temperatures and 1 Bar (1 05 Pascals) 

Pressure and at Higher Pressures 

By MICHAEL P. RYAN and JAMES Y.K. BLEVINS 

Prepared in cooperation with the Hawaii Institute of Geophysics of the 

University of Hawaii, Honolulu, Hawaii 

An extended compilation of viscosity 

data in tabular and graphic format 

U.S. GEOLOGICAL SURVEY BULLETIN 1764 
DEPARTMENT OF THE INTERIOR 

DONALD PAUL HODEL, Secretary 

U.S. GEOLOGICAL SURVEY 

Dallas L. Peck, Director 

UNITED STATES GOVERNMENT PRINTING OFFICE:1987 

For sale by the Books and Open-File Reports Section, U.S. Geological Survey, 

Federal Center, Box 25425, Denver, CO 80225 

Library of Congress Cataloging in Publication Data 

Ryan, Michael P., 1943-

The viscosity of synthetic and natural silicate melts and glasses at high temperatures and 1 bar (1 05 Pascals) pressure and at higher pressures. 

(U.S. Geological Survey bulletin ; 1764) 

Bibliography: p. 

Includes indexes. 

Supt. of Docs. no.: I 19.16:1353 

1. Silicates. 2. Silicate minerals. 3. Glass. 4. Viscosity. 5. Navier-Stokes 

equations. 6. Newtonian fluids. I. Title. II. Blevins, James Y. K. Ill. Series. 

QE75.B9 no. 1764 [QE389.62] 549' .6 86-600232 
CONTENTS 

Symbols VI 

Abstract 1 

Acknowledgments 1 

Introduction 1 

Organization 2 

Group I: Synthetic oxides and Si02 systems 2 

Group II: Mineral systems 2 

Group III: Rock systems 2 

Group IV: Standard glasses , 2 

Mechanics of the rotational (Couette) viscometer 2 

Melt vorticity 3 

Secondary melt motions 8 

Mechanics of the falling-sphere (Stokes flow) viscometer 10 

Descent of the sphere 13 

Flow-field visualization 14 

Direct-observation falling-sphere viscometry 16 

Attainment of terminal velocity 16 

Organization of the tables 24 

Sources of tabulated data 26 

Organization of the graphs 26 

References 27 

Two-component systems 31 

Ba0-Si02 32 

Ca0-Si02 36 

Fe0-Si02 44 K20-Si02 55 

Li

20-Si02 59 

Mg0-Si02 66 

Na

20-Si02 71 

Sr0-Si02 87 

Three-component systems 91 

Al

2

0

3-Ca0-Si02 92 

Al

2

0

3-K20-Si02 169 

Al

2

0

3-Mg0-Si02 170 

Al -Na 0~Si02 175 

Mg0-Ca0-Si02 176 

N a

20-Ca0-Si02 183 

Na

20-K20-Si02 186 

Na

20-Li

20-Si02 189 

Four-component systems 193 

Al

2

0

3-CaO-CaF2-Si02 194 

Al

2

0

3-Ca0-Fe0-Si02 197 

Al

2

0

3-Ca0-K

20-Si02 203 

Al

2

0

3-Ca0-Mn0-Si02 204 

Al

2

0

3-Ca0-Na20-Si02 207 

Al

2

0

3-Ca0-Ti02-Si02 208 

Al

2

0

3-Mg0-Ca0-Si02 212 

Al

2

0

3-K20-Na20-Si02 332 

Five-component systems 333 

Al

20

3-Ca0-Ba0-Mg0-Si02 334 

Al

2

0

3-Ca0-K

20-Na20-Si02 375 

Contents Ill 
Six-component systems 377 

Al20 3-Ca0-Mg0-Ba0-Sr0-Si02 378 

Al20 3-Mg0-Ca0-Fe0-Fe20 3-Si0z 381 

Seven-component systems 389 

Al20 3-CaO-MgO-Mn0-LFe-LS-Si02 390 

Al20 3- Fe20 3-Ca0-MgO-Na20-K20-Si02 391 

Minerals 395 

Two-component mineral systems 407 

Three-component mineral systems 429 

Basalts 435 

Andesites 467 

Rhyolites 479 

Additional igneous melts 497 

Standard glasses 513 

Commercial glasses 537 

Indexes 557 

Two-component systems 558 

Three-component systems 558 

Four-component systems 558 

Five-component systems 558 

Six-component systems 558 

Seven-component systems 559 

Oxide systems 559 

Oxides by author 561 

Minerals 561 

Two-component mineral systems 561 

Three-component mineral system 561 

Lithologic 562 

Additional igneous melts 562 

Standard glasses 562 

Commercial glasses 562 

Authors 562 

FIGURES 

1-5. Diagrams showing: 

1. Three-dimensional cutaway section of the Couette flow developed in 

the fluid-filled annulus of a concentric cylinder viscometer 3 

2. Progressive deformation of adjacent fluid elements at the inception of 

flow 4 

3. Primary and secondary melt motions induced during rotational Couette 

flow 9 

4. Falling-sphere (Stokes flow) viscometer 12 

5. Pressure distribution around a sphere descending through quiescent 

melt 13 

6. Schematic representation of melt deformation field produced by the descent of a 

sphere 15 

7. Photograph showing the creeping flow field produced by the axial passage of a 

sphere in a circular cylinder containing a viscous fluid 16 

8. Diagram showing the flow field developed around a sphere descending at 

constant velocity through a Newtonian melt 16 

9. Photograph showing the creeping flow field produced by the axial passage of a 

sphere in a circular cylinder containing a transparent viscous fluid 17 

10. Schematic diagram of a direct-observation falling-sphere viscometer for silicate 

melts 18 

IV Contents 
11, 12. X radiographs showing: 

11. Real-time 1-atm falling-sphere viscometer assembly 19 

12. Real-time descent of a sphere in Hawaiian olivine tholeiite melt at 

1,244 oc 20 

13, 14. Graphs showing: 

TABLES 

13. Drag on a sphere falling axially in a circular cylinder 24 

14. Wall-correction factors for a rigid sphere falling axially in a circular 

cylinder 24 

1. Wall-correction factors for rigid spheres translating in quiescent melt along the axis 

of a circular cylinder 23 

2. Symbols, units, and conversions used in compiling viscosity data 24 

3. Atomic weights of the elements 25 

4. Units of viscosity 26 

5. International System units having special names 26 

6. Activation energies 27 

7. Units of R 21 

Contents V 
SYMBOLS 

An First end correction function for the Couette 

viscometer 

Bn Second end correction function for the Couette viscometer 

CA Coefficient of resistance in an infinite fluid 

medium 

en Integration constant 

Cs Coefficient of Stokes resistance (drag) 

D Cylinder diameter for the falling-sphere viscometer 

E Concise prefix signifying exponentiation to a 

power of 10 

E* Activation energy for viscous flow 

F Wall proximity correction factor for the 

translation of a sphere falling axially in a 

right circular cylinder 

FP Pressure drag component of the moving 

sphere 

Fv Viscous drag component of the moving 

sphere 

FT Total drag of the moving sphere 

Fx,Fy,Fz Components of the gravitational force vector ~ 

F Body (gravitational) force vector 

G Gravitational acceleration constant 

lz Modified Bessel function of the first kind and 

of the second order 

Kn nth positive root of the equation 11 (Kb)=O 

KI Wall-correction factor for the falling-sphere 

viscometer 

L Length of the inner cylinder of the Couette 

viscometer 

La Increment of length to be added to L to account for the end effect 

Lw Length of the wetted inner cylinder of the 

Couette viscometer 

NRe The Reynolds number, based on sphere diameter for the falling-sphere viscometer 

p Pressure 

ps Pressure distribution on the surface of a descending sphere 

Poo Fluid pressure in melt before perturbation by 

~ a descending sphere 

p Vector of surface tractions 

Q Instantaneous volumetric flow rate 

R Universal gas constant 

Re Reynolds number 

R; Radius of the inner cylinder in the Couette 

configuration 

R' 0 Cylinder radius for the falling-sphere viscometer 

Ro Radius of the outer cylinder in the Couette 

configuration 

VI Symbols 

~ 

R 

T 

~ 

T 

u 

Uoo 

u 

v 

v, 

Va 

w 

w 

X 

y 

z 

a 

fij 

i 

" i 

r 

u 

u 

v 

w 

X 

y 

z 

a 

v 

~ 

v 

"' 'Y 

'Y(r) 

A 

1T 

'I'' \jJ 

p 

Pm 

nij 

~ 

n 

Position vector with respect to the solid angles internal to descending spheres 

Temperature 

Torque vector 

Cartesian velocity component in X 

Terminal velocity of a descending sphere 

Local fluid velocity vector 

Cartesian velocity component in Y 

Radial velocity component (in cylindrical coordinates) 

Tangential velocity component (in cylindrical coordinates) 

Cartesian velocity component in Z 

Velocity vector 

Cartesian coordinate 

Cartesian coordinate 

Cartesian coordinate 

Sphere radius for the falling-sphere viscometer 

Infinitesimal strain tensor 

Unit vector 

Unit vector 

Unit vector 

Radial coordinate 

Time 

Fluid velocity in the x direction 

Local (microscopic) velocity of a fluid element 

Fluid velocity in the y direction 

Fluid velocity in the z direction 

Cartesian reference direction 

Cartesian reference direction 

Cartesian reference direction 

Ratio of the outer to inner cylinder radii in the 

Couette configuration 

Del (or nabla), the gradient operator 

Hamiltonian nabla operator, t( at ax)+ }(iJt 

ay) + k( at az)' a vector quantity 

Shear strain 

Shear strain rate 

Shear strain rate as a function of radial position 

"Second" (volumetric) coefficient of viscosity, as per Stokes' (1845) hypothesis 

3.1415 ... 

Stream function 

Melt density 

Melt density (in contrast with Ps) 

Component of the vorticity tensor 

Vorticity vector 
fie Tangential vorticity vector for secondary mo- 6' Reference angle taken along a meridian plane 

tions in the Couette configuration of the sphere 

n, r component of vorticity a Vertical separation of the bottom of the inner 

nx x component of vorticity cylinder and the crucible base in the Couette 

ny y component of vorticity configuration 

nz Axial vorticity vector for primary melt mo- dij Rate-of-strain tensor 

tion in the Couette configuration X Operation of forming the cross product of 

w Angular velocity two vector quantities ~ ~ Vector quantity w Angular velocity vector 

W; Angular velocity of the inner cylinder [ ] Tensor quantity; when it encloses an array of 

Wo Angular velocity of the outer cylinder nine elements, it symbolizes a second-rank 

11 Melt (shear) viscosity tensorial quantity 

'Ylo Preexponential constant in the Arrhenius relation for the temperature dependence of viscosity Subscripts: 

Ps Sphere density in the falling-sphere configuration Directional index 

(T Stress within the melt j Directional index 

c:r, Radial component of stress 0 Initial value 

c:r(r) Stress as a function of radial position r Radial component 

(Tii Normal stress components e Tangential component 

(Tij Components of the second-rank stress tensor X Cartesian component 

6 Spatial coordinate in the Couette configura- y Cartesian component 

tion z Cartesian component 

Symbols VII 

The Viscosity of Synthetic and Natural Silicate Melts and 

Glasses at High Temperatures and 1 Bar (1 05 Pascals) 

Pressure and at Higher Pressures 

By Michael P. Ryan1 and James Y.K. Blevins2 

Abstract 

The Navier-Stokes equations of fluid motion are reviewed for 

isotropic incompressible Newtonian fluids. These equations 

have been applied to two primary viscometer configurations 

appropriate for the Earth and material sciences: the rotational 

Couette viscometer and the falling-sphere (Stokes flow) viscometer. 

Viscosity data have been collated from widely distributed 

published sources and are presented in this volume in tabular 

and graphic formats that allow direct utilization of the original 

viscosity numbers, an efficient means of data intercomparison, 

and a means of evaluating the kinetics of viscous flow. The data 

fall into four groupings: synthetic oxide and Si02 systems, 

mineral systems, rock systems, and standard glasses. 

ACKNOWLEDGMENTS 

April Kam and Laura Mackenzie of the Hawaii Institute 

of Geophysics (Honolulu) and M. Sandra Nelson of the 

U.S. Geological Survey drafted the figures. The Hawaii 

Institute of Geophysics of the University of Hawaii, Honolulu, Hawaii, defrayed a major portion of the drafting 

effort, and we thank Richard Rhodes of that institution for 

his support. Review comments by Robert B. Bird of the 

Rheology Research Center, University of Wisconsin, and 

Bruce Hemingway of the U.S. Geological Survey have improved portions of this presentation. Elizabeth Good has 

provided editorial assistance at several stages of manuscript 

preparation. The typescript has been prepared by Joan 

Masterson and Ruthie Robertson. Douglas Blackburn, 

Webster Capps, and Wolfgang Haller of the Materials Division of the National Bureau of Standards in Gaithersburg, 

Md., provided technical support during Couette viscometry 

experiments. The Hawaii Institute of Geophysics also defrayed a portion of the computing costs. Robert P. Wemple 

1

U.S. Geological Survey, 959 National Center, Reston, VA 22092. 

2Now at Mobil Oil Exploration and Producing, Inc., 1250 Poydras 

Street, New Orleans, LA 70113. 

of Sandia National Laboratories, Albuquerque, N. Mex., 

provided technical assistance with direct-observation viscometry. Financial, office, and laboratory support provided 

to M.P. Ryan by H.C. Hardee and William C. Luth during 

a visiting professorship at Sandia National Laboratories is 

gratefully acknowledged. This support was provided under 

U.S. Department of Energy contract DE-AC04-

76DP007889 to Sandia National Laboratories. Additional 

support was provided to Ryan and the U.S. Geological 

Survey by the U.S. Department of Energy through DOE-lA 

agreement DE-AI01-79RA50294 and DE-AI01-

86CE31002. Overall project support by the U.S. Geological 

Survey's Geothermal Research Program under grant 14-

08-0001-G-631 to M.P. Ryan is acknowledged with gratitude. 

INTRODUCTION 

Few physical properties of magmatic fluids play the profound role in the development of igneous systems and the 

evolution of their rocks that melt viscosity does, and few 

vary over such immense ranges in magnitude. We know 

now that 'TI varies over 13 orders of magnitude for natural 

melts and over 15 orders of magnitude for their synthetic 

analogues. 

This volume is intended as a handbook for those wishing 

essential viscosity data for multicomponent melts. It has 

been divided into two primary units: (1) introductory review 

material on the mechanics of certain classes of viscometers 

and (2) tabular material presenting viscosity-temperaturecomposition data for silicate melts. 

Source material relevant to problems concerning the mechanics of silicate melts and melt-crystal mixtures includes 

the geologic reports of Bottinga and Weill (1972), McBirney .and Murase (1984), Murase and McBirney (1973), 

Mysen (1981), Shaw and others (1968), and Shaw (1972). 

In addition, the Year Books of the Geophysical Laboratory 

of the Carnegie Institution of Washington contain regular 

reports on melt viscosity and melt density. Texts on the 

rheology of Newtonian and non-Newtonian fluids have been 

Introduction 
written by Bird and others (1977a, b) and Fredrickson 

(1964). Texts devoted exclusively to non-Newtonian flow 

are those of Coleman and others ( 1966), Harris ( 1977), and 

Schowalter ( 1978). Treatises on experimental technique and 

the theoretical analysis of experimental results have been 

presented by Bockris and others (1959), Van Wazer and 

others (1963), Walters (1975), and Whorlow (1980). In 

addition, two volumes emphasizing the particle-particle interactions of multiphase flow have been prepared by Clift 

and others (1978) and Happel and Brenner (1973). Journals 

containing regular reports on the mechanics of single-, two-, 

and three-phase flows are Computers and Fluids (John 

Wiley), Journal of Colloid and Interface Science (Academic 

Press), Journal of Fluid Mechanics (Cambridge J]niversity 

Press), Journal of Multiphase Fluids (John Wiley), Journal 

of Non-Newtonian Fluid Mechanics (Elsevier), Journal of 

Physicochemical Hydrodynamics (Pergamon Press), Journal of Rheology (Society of Rheology and John Wiley), and 

Rheologica Acta (Dietrich Steinkopff Verlag). 

ORGANIZATION 

Group I: Synthetic Oxide and Si02 Systems 

Major-element oxide and Si02 systems have been arranged in order of increasing numbers of components, from 

binary through seven-component systems. Within each system, subsystems are defined generally by sequential variations of the weight percentages (mole fractions) of the constituents. This grouping contains 25 systems, 506 

subsystems, and 2,383 discrete viscosity (TJ)-temperature 

(T)-composition (X) values. Each subsystem is represented 

by a table. Compositionally related neighboring subsystems 

are plotted on log10 TJ versus T (in degrees Celsius) and 

Arrhenius log10 TJ versus 1<r1T (per kelvin) graphs. 

Group II: Mineral Systems 

Single-component (monomineralic) and two- and threecomponent systems have been arranged in order of increasing numbers of components. This grouping contains 29 subsystems and 194 discrete TJ-T -X values. Graphs and tables 

follow the format used for group I. 

Group Ill: Rock Systems 

Basaltic, andesitic, and rhyolitic lithologies are the primary areas within this group. Subsystems are defined on the 

basis of (1) hand-sample lithology and major phenocryst 

assemblage; (2) H20 content during the experimental run (as 

appropriate); and (3) pressure (P) (where applicable). This 

group contains 41 subsystems and 193 discrete TJ-P-T -X 

entries. Tables and graphs follow the format used for 

group I. 

2 Viscosity of Synthetic and Natural Melts and Glasses 

Group IV: Standard Glasses 

National Bureau of Standards reference glasses are presented in this last grouping. The data have been evaluated at 

1 atm and comprise 189 discrete TJ-T -X entries. Tables and 

graphs follow the format used for group I. 

A guide to the use of the data, conversion factors, a list 

of data sources, symbol definitions, a number of indexes, 

and a reference list are also included in the volume. 

MECHANICS OF THE ROTATIONAL (COUETTE) 

VISCOMETER 

We begin by reviewing the relations for fluid deformation 

in terms of the spatial derivations of the (local) Cartesian 

components of velocity. The presentation draws on the work 

of Eskinazi (1967, 1975), Walters (1975), Darby (1976), 

and Bird and others (1977a). We assume the flow to be 

laminar, steady state, and Newtonian. Normal stress effects 

and transitions to Taylor flow regimes are either unwarranted or beyond the scope of this report. 

The infinitesimal strain tensor is defined (Aris, 1962) as 

(

av. av.) 

eij= a~+ a~ (1) 

relative to Cartesian coordinates. In terms of the general 

expression for the rate of strain (cast in the form of 

"covariant" derivatives), 

(2) 

where the comma signifies differentiation with respect to the 

index that follows. 

The rate of strain is 

(3) 

which, in covariant form, becomes 

a .. =av .. +av .. lJ l,J J,l (4) 

These expressions (eqs. 1-4) are generalized for melt deformation irrespective of geometry. They are now to be specialized for a specific coordinate system. 

The rotational viscometer (fig. 1) is constructed from 

coaxial cylinders that have differing radii and a continuously 

sheared fluid annulus between them. The appropriate coordinates are therefore cylindrical. Here the rate-of-strain tensor (Bird and others, 1977a) is 
1 av, ra Va av, av2 --+--

r ae ar r az+Tr 

d;j= 

1 av, ra Va 1 av6 v, --+-- 2--+- (5) r ae ar r r ae r 

avo 1 avz 

-az+;:Te 

aV2 

2-az 

Because the flow velocity varies in the radial direction 

only, all of the generally realizable terms with a e or a Z 

dependence become zero, and the new rate-of-strain tensor 

takes the following form: 

dw 

r-dr 

0 

0 

0 (6) 

0 

This equation is a result of the shear strain rate definition 

dw -y=r- dr (7) 

and the realization of the directionality of flow, which produce the conditions 

V,=V2 =0 (8) 

and 

V6(r)=rw(r) (9) 

Physically, this fluid movement in e results from a lack of 

radial or axial flow after steady-state conditions have been 

achieved. At steady state, all fluid elements follow streamlines in e only, and the velocity of these melt parcels is a 

function of r only (after the angular velocity w; has been 

established). 

Melt Vorticity 

A mutually orthogonal network of imaginary lines described on the surface of a crystal suspended in melt provides a means of monitoring the kinematics of the crystal as 

the aggregate is set in motion. If the distances between these 

lines, as well as their respective angles, do not change 

during fluid motion, the crystal behaves as a rigid body. 

Moreover, should the crystal begin to rotate, all point~ on a 

given surface would be expected to rotate at the same angular velocity-a state referred to as pure rotation. The surT 

w· l 

Figure 1. Three-dimensional cutaway section of the Couette 

flow developed in the fluid-filled annulus of a concentric 

cylinder viscometer. The inner cylinder is rotating at an angular 

velocity wi, and the outer cylinder rotates (in the most general 

treatment) at an angular velocity w0 • Typically, w0 for the outer 

cylinder is zero. The radii of the inner and outer cylinders are 

R;~d R0 , respectively. The torque on the inner cylinder axis 

is T. The vertical separation between the base of the rotating 

cylinder and the bottom of the crucible is~- The overall length 

of the rotating inner cylinder is L; its wetted length Lw is the 

vertical contact distance between the cylinder and the silicate 

melt and determines the torque. Z, r, and ·6 are cylindrical 

coordinates. 

rounding melt, however, will be expected to respond in 

quite a different way when it is set in motion, for, in general, 

the distances between initially equidistant lines in our network will change continuously during flow, as will the 

angles formed by their intersections. Moreover, the rotation 

of the melt may vary continuously from point to point, 

because neighboring parcels have different angular velocMechanics of the Rotational Viscometer 3 
ities. As a practical matter, then, the kinematic descriptions 

of the surrounding melt and the enclosed crystal proceed 

along differing lines, since melt parcels experience a progressive deformation as well as a translation and a rotation. 

y 

A X 

y 

8 X 

y 

c X 

4 Viscosity of Synthetic and Natural Melts and Glasses 

In this volume, we are .concerned solely with the flow 

behavior of Newtonian si[lgle-phase melts. The rigid body 

movements of suspended crystals then illustrate the rotational motions of the fluid elements themselves. Such rotations can be considered by examining the progressive deformation of neighboring melt parcels, schematically 

illustrated in figure 2. 

Figure 2 shows a microscopic patch of melt that has had 

its neighboring areas tagged by a superposed gridwork of 

imaginary lines forming a checkerboard pattern of alternating shaded parcels. This initial state (before motion) is indicated by the vertical sweephand of the clock at the lower 

right. The mutual boundaries of the four parcels adjacent to 

point 0 are delimited by the initially orthogonal line elements 1-0-2 and 3-0-4, respectively. 

~We now set the melt in motion by using a velocity vector 

V whose components are U (X, Y) and V (X, Y). Simultaneously, the clock is started, and the flowing melt progressively distorts the checkerboard, distending and rotating 

melt elements, as figures 2B and 2C show. To further fix 

ideas, we will assume that melt velocities increase in the 

direction of increasing coordinate directions. The rotation of 

the melt about the point 0 can then be examined by considering the motion of the line segments 1-0-2 and 3-0-4. For 

the segment 1-0-2, the endpoint velocities (Eskinazi, 1975)' 

are 

u.=uo+(a") · ay o ( -2- aLI-2) + ... (10) 

Uz=Uo+(a") · ay o ( aLl-2)- 2 ... (11) 

where (Al-1_ 2)/2 is the average distance between the element endpoint and the center of interest at point 0. 

The realization that the melt element was infinitesimally 

small permitted an evaluation of the velocity field in the 

~Figure 2. Progressive deformation of adjacent fluid elements at the inception of flow. Time progression during flow is 

shown by the clock in the lower right-hand corner of each 

figure. The rotation of reference lines 1-0-2 and 3-0-4 yields 

an averaged angular rotation rate w for the melt patch centered 

at point 0. From these averaged rates, the melt vorticitt.,can be 

evaluated; it is numerically given by TI=2"<t, where a is the 

vorticity vector that is normal to the plane of the diagram and 

centered, in this example, at 0. Whether this "spin" vector 

points up at us or down below the plane of the diagram depends on whether the net sense of me!.!..Jotation is counterclockwise or clockwise, respectively. A, V is a velocity vector 

describing the motion of the fluid parcel at point 0 and has the 

components U and V. aL12 and aL34 are initial reference 

lengths of the undistorted fluid checkerboard before the inception of flow. B and C, Progressive development of the ,flow 

field. Reference parcels are distorted by fluid shear and stretch. 
immediate neighborhood of point 0. Thus, the velocity has 

been expanded about U0 as a Taylor series, the higher order 

terms being truncated. The quantity (U1-U2) is then the 

relative velocity of point 1 with respect to point 2, and its 

positive value suggests that both 1 and 2 are in relative 

motion. The sense of melt spin is clockwise, and the angular 

velocity is 

(12) 

or 

w1-2= ( ~~) 0 (clockwise) (13) 

By the right-hand rule convention, the rotation vector is 

directed downward, below the plane of the diagram, and 

away from the observer. 

As the melt rotates and flows, the reference segment 

3-0-4 experiences a counterclockwise spin, the result of the 

differential velocities of points 3 and 4 and the continued 

diminution of angles 1-0-4 and 3-0-2 during deformation. 

The velocities of the relevant points (Eskinazi, 1975) are 

(av) (AL3-4) V3=Vo- ax o . -2- - ... (14) 

and 

(

av) (AL3-4) V4=Vo+ ax o . -2- + ... (15) 

The angular velocity for this segment is then 

(16) 

or 

w3_ 4 = ( ~_i) 0 (counterclockwise) (17) 

The realization that the rotation vector is orthogonal to the 

X-Y plane (acting in the Z direction) and the application of 

the right-hand rule yield a rotation vector pointing directly 

up at us, out of the plane of the diagram. 

The net rotation of the melt element results from the 

weighted contributions of both the spin components, due 

consideration being given to their respective magnitudes and 

signs. Melt rotation is viewed as a locally averaged phenomenon, and the rotational resultant, acting in a specific 

direction, is formed as the average of the summed contributions. Hence, for example, the Z component of rotation is 

(18) 

The melt vorticity was defined by Helmholtz3 ( 1858) as 

twice the angular velocity (for example, Batchelor, 1967): 

(19) 

so that, on a component basis, 

n =(aw- av) X ay az (20) 

n =(au _aw) 

y az ax (21) 

n =(av- au) z ax ay (22) 

Since the total vorticity vector must equal the sum of its 

components, taken along the X, Y, and Z axes, 

(23) 

or 

Q =f(aw _ av) +":(au_ aw) +k(av _au) (24) ay az J az ax ax ay 

Finally, the vorticity components developed in the more 

familiar Cartesian system above may now be specialized for 

the cylindrical system appropriate to Couette4 viscometry. 

3Hennan Von Helmholtz was born in Potsdam, Gennany, on August 31 , 

1821. Financial constraints led him to the early study of medicine at the 

Friedrich-Wilhelms-Institute in Berlin; subsequently, he applied his growing interest in physics to problems in physiology. His work in hydrodynamics appears to have grown out of interests in the energetics of mechanical 

systems as well as the use of Green's theorem. His work on vorticity, which 

appeared in 1858, presented the systematics of rotary fluid motion, including the relevant vector mechanics, the theorems of vortex motion, the 

concept of the vortex line (Wirbellinie), and the geometries of vortex tubes 

(Wirbelfaden). His writings on vorticity (Helmholtz, 1858) were translated 

into English by P.G. Tait in 1867. Helmholtz died in Berlin on September 8, 1894. 

4Maurice Frederic Alfred Couette was born on January 9, 1858, in 

Tours, France. His chief academic post was Professor of Physics in the Free 

Faculty of Sciences in Angers, Maine et Loire. His research centered on the 

viscosity of liquids, and his principal contribution was the development of 

the rotating concentric cylinder viscometer that bears his name (Couette, 

1890). 

Mechanics of the Rotational Viscometer 5 
This procedure involves taking the curl of the velocity vector and indicating the motion sense by their tangential, radial, and axial components. 

or 

~ ~ ~ ~( 1 avz ave) ~(avr avz) !l=VXU=z ---- +1 --- r a6 az az ar 

+ k --(rV8 "(1 a )--avr) r ar a6 

~,... ,... ,... 

!l=i!l,+j!l8+k!lz 

(25) 

(26) 

The general form of the vorticity tensor for the cylindrical 

configuration (Bird and others, 1977a) is 

0 !(~ (rVa)- av,) r ar aa 

ll·· = !(aV, -~(rVa)) 0 I} r aa ar 

ava _!(avz) 

az r aa 

For the Couette configuration appropriate to the rotation 

of concentric coaxial cylinders (end effects, for the moment, 

being neglected), all velocity dependence on 6 and Z vanishes (since V(r)=rw(r) only), and the vorticity distribution 

for the concentric cylinder viscometer becomes 

!(.E._ (rV >) r ar 8 . 0 

0 0 

0 0 

After differentiation of the two elements, it becomes 

!} .. = I} 

av6 V6 -+- ar r 

0 

0 

0 

0 

0 

(28) 

(29) 

Note that the vorticity consists of just two terms: a gradient 

·in tangential velocity with respect tor (aVofar) and a (V8/r) 

term. 

·The momentum equations for cylindrical coordinates for 

the three directional components in the general case are 

6 Viscosity of Synthetic and Natural Melts and Glasses 

given below. In general, the radial component r is ofthe 

·form 

(

melt ) 

density 

(

pressure) 

- changes 

or 

melt 

in r+ 

directional 

velocity 

changes 

changes in 

surface 

stresses on 

a melt element 

(

directional ) 

+ changes in . 

melt velocity 

(

the gravi- ) 

+ tational 

force 

component 

aP (1 a(rcr.,,). 1 acr, cr88 acr,z) =--+ ---+----+- +pG (30) ar r ar r a6 r az r 

The tangential component 6 is 

[

av6 av6 V6 (av. 8) V,V6 (V2 aV6)] 

p at + v, ar + r ' a6 + r az 

+ pGa (31) 

The axial component along Z is 

[

aVz (aVz) V6 aVz (aVz)] p at+V, ar +-;:-ae-+Vz az 

__ aP [! a(rcr,z) !(acraz) acrzz] - az + r ar + r az + az + pGz (32) 

Because of the restrictions on nonaxial and nonradial flow 

in the viscometer and· the radial dependence of tangential 

flow velocity-that is, 

(33) 

V,=O (34) 

V8(r)=rw(r) (35) 

the momentum equations take on a simplified forn1.4n'ttie 

simplified momentum· equations, (1) all accelerations have 
vanished (for example, iJV,I iJt), since steady-state conditions have been achieved; (2) all 6 and r components of pG 

have vanished, since the cylinders are constrained to be 

perfectly plumb; (3) all velocity components in rand Z have 

vanished, owing to the confinement of the melt at the 

crucible boundaries; and ( 4) all shear stress components in 

the Z and r directions have vanished. 

As a consequence of these simplifications, we are left 

with a considerably simplified set of relati~ns. They retain 

the following characteristics: ( 1) velocity components in the 

melt change in r only; (2) pressures in the melt retain only 

a radial dependence; and (3) both normal (66, rr) and shear 

(r6) stress components exhibit changes that depend on r 

only. The flow components during operation of the viscometer now become, for the radial component r, 

~=+ap _![a(rcr")]+cr69 

r ar r ar r (36) 

for the tangential component 6' 

(37) 

and for the axial component Z, 

iJP 

0=- az+pGz (38) 

If equation 37 is integrated, the dependence of the shear 

component cr, on r is identified as 

(39) 

where C 1 is a constant of integration. Here, shear stress is 

seen to fall off rapidly in the melt, in llr2 fashion. This fall 

off is a function of the velocity decay in the fluid as the 

distance from the moving inner cylinder increases. 

The net applied torque required for rotation at a given 

angular velocity is the product of the force multiplied by the 

length of the lever arm through which it acts. This torque 

must be balanced by the shear force produced within the 

melt when steady state is achieved: 

~ 

T =cr ,a(27rrL )r (40) 

~ 

Notice that, while torque ( T ) is directly proportional to the 

radial distance, the shear stress (r6) still falls off as llr2, so 

that most of the torque contribution comes from melt near 

the cylinder wall. Also, the term (2 'TrrL) embodies the total 

surface area of the inner cylinder, and, since equation 40 

holds for R; ~r ~R , the torque will grow in proportion to 

the surface area of the inner cylinder. This relation holds for 

all radial points within the melt annulus or at the surface of 

the inner or outer cylinder-that is, for R;~r~R • 

Equating relations 39 and 40 and eliminating cr ra define 

the dependence of the4onstant C 1 on the torque and cylinder 

length-that is, C1 = T /(27rL). The r6 component of shear 

stress falls off as llr2 within the melt (fig. 1), and its 

dependence on the torque and viscometer geometry is 

(41) 

Through the rate-of-strain tensor, the relation between the 

shear stress in the melt and the angular velocity w is linked 

by the fluid viscosity, such that 

(42) 

Combining equations 41 and 42 and integrating with respect 

to r provide the dependence of the 6 component of velocity 

on the radial position: 

(43) 

The velocity magnitudes in the melt are determined by the 

experimentalist. These magnitudes form a convenient set of 

boundary conditions on the tangential velocity component 

of the radial limits of the melt annulus. For the inner cylinder, 

(at r=R;) (44) 

and, for the outer cylinder, 

(45) 

These fixed conditions at the rotating bob and crucible allow 

the two constants to be evaluated: 

(46) 

and 

(47) 

where 

(48) 

If equations 43, 46, and 47 are combined, the velocity 

distribution within the melt is 

Mechanics of the Rotational Viscometer 7 
For the (hypothetical) case of a single cylinder rotating in a 

laterally large body of melt, R0 =oo and w0 =0, so that 

V-- -[w;R,j r (50) 

The final step is evaluating the dependence of the applied 

torque on the fluid viscosity. This torque may be related to 

the melt drag acting on both the bob and the crucible (inner 

and outer cylinders), and their respective dependences take 

the forms of: 

T =2TrR;Lrrre ' ~ ,R. 

r=R; (51) 

for the inner cylinder and 

(52) 

for the outer cylinder. 

Here, rr re can be determined by relating the tangential 

component of melt velocity (V6) to the angular velocity (w0 , 

w;), as equation 49 does, and introducing this term into 

equation 42. From the expression for torque 

and equation 41 , the expression for the shear stress is 

~ 

T rr(r)=--2

-

2Trr L 

and that for the shear rate is 

(53) 

(54) 

(55) 

The viscosity of the melt in the annulus can now be evaluated from the ratio of the shear stress to shear strain rate. 

(This relation is embodied in Newton's hypothesis: "The 

resistance which arises from the lack of slipperiness origin ating in a fluid-other things being equal-is proportional to 

the velocity by which the parts of the fluid are being separated from each other" (Motte, 1946).) 

8 Viscosity of Synthetic and Natural Melts and Glasses 

Secondary Melt Motions 

The primary flow developed in rotational Couette viscometry occurs in thee direction. Melt confinement within 

crucible walls and a finite length to the inner rotating cylinder have the potential for superposing secondary melt motions on the primary flow field. The secondary motions are 

illustrated in figure 3, which focuses attention on the lowest 

section of the viscometer, and can be divided into radial and 

vertical effects. 

Radial contribution-Frictional coupling between the 

melt and the inner cylinder wall-and the "no-slip" 

boundary condition at the outer cylinder wall-insures that 

all deformation occurs within the melt annulus itself and not 

along an interface. Vorticity is generated adjacent to the 

rotating inner cylinder by the melt-solid coupling at this 

moving interface. This primary (axial) vorticity component, 

designated 0 2 in figure 3, diffuses radially outward during 

viscometer startup owing to the viscous coupling between 

adjacent melt parcels. The rotation in e produces a tendency 

toward radial flow that must be counterbalanced by an 

inward-directed component of fluid pressure for equilibrium 

to be maintained. This component is directed back toward 

the axis of rotation, and, at equilibrium, centripetal and 

centrifugal forces just balance. 

Vertical contribution. -The adherence of melt to the 

crucible base generates a viscous basal boundary layer, in 

which centrifugal flow components die out. Since the centripetal force component is independent of Z, the inwarddirected force overbalances the outward-directed component, and an inward-directed motion results along the base. 

Conservation of mass requires that the resulting melt deficit 

be made up by downward-directed melt motion along the 

crucible wall. The result is a counterclockwise secondary 

rotation set up in a subvertical plane, as the large arrows in 

figure 3 illustrate. The resultanuecondary vorticity component in e has been designated n 6 in figure 3. 

A familiar example of these secondary fluid motions is 

the motion of tea leaves in a cup during moderate stirring. 

The leaves move radially inward along the bottom and collect in the center of the cup. Becuase they lack the neutral 

buoyancy to ride the secondary current for a full cycle, they 

are fated to lie on the bottom. In silicate melts, the strength 

of these secondary motions is expected to be a strong function of the melt viscosity and viscometer rotation ratehence, composition and temperature. As a practical note, 

nonviscometric motions may be handled by application of 

end-effect corrections, discussed below. 

The earlier discussion that led to expressing the shear rate 

as a function of the cylinder radii (R0 , R;) and the angular 

velocities (w0 , w;) (eq. 55) implicitly assumed that the end 

of the inner cylinder was at a large distance from the bottom 

of the outer cylinder. Note here that r is used as a distance 

measure and not as a radial coordinate per se. In practice, 

this separation of cylinders is rarely "large," and the proxim-
Figure 3. Primary and secondary melt motions induced during rotational Couette flow. 

Superposed on the primary viscometric flow developed in 9 is the tendency for motion to be 

developed along the path defined by the large arrows. This motion, in turn, produces a 

secondary vorticity (06) component superposed on the primary vorticity ({t). Z, r, and ·a are 

cylindrical vorticity coordinate~ The shaded section of the cylinder wall is a volume element 

of the inner rotating cylinder. u, is a relatively minor component of vorticity that may arise 

because of the viscous drag induced by the "no-slip" boundary condition associated with the 

crucible base. 

ity of the rotating bob to the base of the crucible produces an 

additional "instrumental" drag component. Physically, this 

drag arises from the immobilization of melt at the solid-liquid 

interface and the additional viscous coupling in those melt 

elements that form the fluid gap between what we think of as 

the no-slip interfaces. This drag is the "end" equivalent, in a 

broad qualitative fashion, of the wall effect experienced in 

falling-sphere viscometry, to be discussed shortly. 

Mechanics of the Rotational Viscometer 9 
Corrections for the end effect developed by Oka ( 1960) 

satisfy the Navier-Stokes5•

6 equations for flow: 

where Ri and R0 have been defined above, Ll is the clearance 

between the bottom of the inner cylinder and the crucible 

base, L0 is an extra "effective" length increment to be added 

to the inner cylinder length L to account for the lower end 

effect, An and Bn are functional forms of the viscometer 

geometry (that is, functions of R/R0 , Lw1R0 , and Ll!R0 ), h 

is a modified Bessel function (of the first kind and of the 

second order) (Van Wazer and others, 1963), and K n is the 

nth positive root of the relation p=(Kb)=O, from the 

Navier-Stokes relations. 

MECHANICS OF THE FALLING-SPHERE 

(STOKES FLOW) VISCOMETER 

Newton's Second Law assures us that the sum of the 

forces acting in and on a melt element is balanced by the 

product of the element's mass and acceleration. This state5Claude-Louis-Marie-Henri Navier was born in Dijon, France, on 

February 10, 1785. The son of a lawyer for the Legislative Assembly at 

Paris, he attended the Ecole Polytechnique, where he was influenced by 

-Fourier, his professor of analysis. From 1819, he taught analytical engineering mechanics at the Ecole des Ponts et Chaussees (The School of 

Bridges and Highways=the College of Civil Engineering). His research 

contributions include the application of analytic mechanics to bridge design, the development of the mechanical concept of work, and the development of a force-balance approach to the hydrodynamic interaction of solid 

bodies and fluids. His analyses of fluid-solid interactions, derived without 

using shear stress components, made use of his theory of "fluid" particle 

attraction-repulsion." Navier died in Paris on August 21, 1836. 

6George Gabriel Stokes was born at Skreen in County Sligo, Ireland, on 

August 13, 1819. The son of a parish rector, he attended Pembroke College, Cambridge, studying mathematics under William Hopkins. It was 

Hopkins who encouraged Stokes to pursue the study of hydrodynamics. In 

1842, he began his investigations with an analysis of the steady motion of 

an incompressible fluid in two dimensions. Stokes' hydrodynamics work in 

. the 1840's was largely given over to the study of internal friction in fluids. 

His research resulted in an 1842 report on what was later to become known 

as viscosity and culminated in his paper on the hydrodynamics of pendulums in 1850. In 1849, he was appointed to the Lucasian professorship at 

Cambridge (the chair once held by Newton). Most noted for his work in 

fluid mechanics, he also contributed to other branches of physics (the 

elasticity of solids, optics, and the defraction of light, as well as acoustics). 

Be died at Cambridge on February 1 , 1903. 

1il Viscosity of Synthetic and Natural Melts and Glasses 

ment provides the basis for developing the equations of fluid 

motion. In vector form, this equation (Schlichting, 1968) is 

(57) 

~ 

where pis the melt density ~"ti.Dt is the substantial derivative of the velocity_;rector W, F is the body (gravitational) 

force vector, and P is the vector of surface tractions. 

Surface forces can be explicitly written as the contribution of nine scalar quantities, each referenced to a local (l, 

], k) unit vector: 

(58) 

(59) 

~ A A A 

P z = irr zx + jrr zy + krr zz (60) 

These nine components then form the elements of a secondorder stress tensor: 

(J'xy rrn] (J'yy (J'yz 

(J'zy (J'zz 

(61) 

where the first component (i) of the i,j double subscript 

orients the face of a reference melt element (in a local 

Cartesian coordinate system) and the second (j) component 

orients the direction in which that stress component acts. 

If a balance of the net force components on the six sides 

of a reference elemental volume is formed, the resulting 

surface force per unit volume is 

(62) 

In terms of the nine tensor components discussed above, this 

surface traction becomes 

A[d(J'zx d(J'zy diT22 ] +k -+-·+- ax ay az 

(63) 

(64) 

(65) 

Surface tractions can now be fit into the formulation of the 

balance of forces and accelerations, to yield 
(66) 

(67) 

Dw _ (aa zx aa zy aa zz) p-D -F7 + -a-+-a-+-a- t " X y Z (68) 

Stated explicitly, these equations tell us that the following 

balance has been achieved within the melt: 

flui~ convected _ body force 

( 

local and ) ( melt ) 

(density) acceleration - components 

(

normal and) 

+ shear .stress 

gradients 

For an inviscid fluid, each shear stress component on the 

right-hand sides of equations 66, 67, and 68 would vanish 

and leave only the normal stress components. 

The relation between stress components in the melt and 

the resulting rate of strain requires three assumptions: 

1. The components of stress are linear functions of the 

components of strain rates. This assumption is reasonable for the infinitesimally small deformation increments considered. 

2. The relations established between the stress and deformation rate components must be invariant for coordinate transformations involving mirror reflections or rotations of the axes. This assumption provides for a 

physical "rule" for the flow process and a measure of 

independence about how a deforming reference melt 

element is viewed. 

3. The stresses must recover the hydrostatic pressure of the 

melt when velocity gradients go to zero. This condition 

provides for melt continuity when the fluid is at rest. 

The derivation of this relation involves expressing individual stress components in terms of linear combinations of 

component strains, defining the constant coefficients of 

these strains, introducing velocity gradients in terms of 

strain components, and then simplifying the final expressions. These involved steps have been well presented by 

Yuan (1967, p. 97-99). 

The sequence of steps relating stress and strain rate components leads to the identification of two connecting coefficients of viscosity: 11, the (shear) viscosity, and X., the 

"second" coefficient of viscosity. By Stokes' (1845) hypothesis, we assume that 

(69) 

or 

2 X.=-- TJ 3 (70) 

The second coefficient of viscosity, referred to as the dilatational viscosity, is generally associated with dilational deformation modes and, hence, with fluid compressibility. 

Although the value of X. in terms of 11 has been confirmed 

through experimentation, its theoretical justification and 

precise physical implications have been the subject of some 

debate (Rosenhead, 1954; Davies, 1954). 

The constitutive relations for an isotropic Newtonian fluid 

(recalling the assumption above of a linear relation between 

shear stress and shear strain rate components) are now 

(Schlichting, 1968, p. 58) 

2 . ~ au 

a =-P-- 11 dtv W+2TJ- (71) XX 3 ax 

2 . ~ av a =-P--TJdtvW+2TJ- (72) » 3 -~ 

2 . ~ aw a =-P-- 11 dtv W+2TJ- (73) zz 3 az 

(av au) (1 xy =ayx =TJ ax+ ay (74) 

(aw av) Uyz =azy =TJ ay-+ az (75) 

(au aw) azx=axz=TJ az +ax (76) 

Melt isotropy has been maintained by requiring the principal 

axes of the stress tensor to coincide with the principal axes 

of the rate of strain tensor. 

Note particularly that, in equations 74, 75, and 76, the 

shear stress is balanced by the shear strain rate acting 

through the coefficient of viscosity 11. This coefficient has 

been the principal object of our attention in this compilation. 

By introducing the constitutive relations (eqs. 71-76) into 

the surface force expressions ( eqs. 63-65) per unit volume 

and then using the relations for the deviatoric normal stress 

components, 

(77) 

(78) 

(79) 

non viscous pressure terms, the normal components of de vi .. 

atoric stress, and two sets of viscous pressure terms appear 

as separate groupings in the equations of motion. Thec;hydroMechanics of the Falling-Sphere Viscometer 11 
static and thermodynamic pressure is formed from the trace 

of the stress tensor and is given by 

p = -(<r_u +<ryy +<Tzz)/3 (80) 

where the minus sign denotes compression. It is appropriate 

for the melt at rest. The intermediate step is the development 

of the constitutive relations (eqs. 71-76). After simplifications generated by considering only incompressible fluids 

have been made, the equations of motion for an isotropic 

Newtonian melt become 

(

au+ uau + vau + wau) 

p at ax ay az 

(81) 

(

av + uav + vav + wav) 

p at ax ay az 

(82) 

(

aw + uaw + vaw + waw) 

p at ax ay az 

(83) 

These equations are the Navier-Stokes equations of fluid 

motion. 

The Navier-Stokes equations (developed above for Cartesian coordinates) can be generalized by writing them in 

vector form: 

(84) 

where the Laplacian operator is V2 and V2=(a2/ax2)+(a2

; 

ay 2)+(a2!az 2). 

In the falling-sphere viscometer (fig. 4), the axial motion 

of the descending sphere through the melt is expected to be 

very slow. Thus, to good approximation, the inertial terms 

can be eliminated in the Navier-Stokes equations developed 

above ( eq. 84). Thus, the further simplified relations become 

grad P = TJ vtw (85) 

and the equation of continuity for incompressible flow becomes 

div W=O (86) 

12 Viscosity of Synthetic and Natural Melts and Glasses 

I 

I 

. . . 1- . 

z 

I 

I 

..---Ro'---~ 

Figure 4. Falling-sphere (Stokes flow) viscometer. Crosssectional slices taken through the cylinder wall and descending 

sphere have a hachured pattern. The melt-solid interfacial regions are shown by stippling. Rand Z are coordinates for the 

cylinder. 

The results of Stokes' (1851) analysis of this creeping 

motion of fluid past a sphere take the form of the sphere 

velocity, plus the pressure developed at the front- and rearcenter positions (see Bird and others (1977a, ch. 1): 
U=Uoo{[ !-~(~)-±(~)'] 

-~( Uoo·8,8,) [ (~) -(~)']} 

(87) 

(88) 

where a is the radius of the sphere, r is a radial coordinate, 

r2 = x 2 + y 2 + z 2, and U oo is the terminal velocity. 

As the sphere descends, the maximum and minimum 

pressures developed on the surface are found at points 1 and 

2, respectively, on the pressure-distance graph in figure 5. 

These points correspond to the stagnation points of melt 

motion on the surface. Numerically, their values are 

(89) 

where the superscripts 1 and 2 refer to the leading and 

trailing pole positions (fig. 5), respectively, which are 

cases, specialized for the condition x/r = ± 1, of the more 

general relation for the surface pressure distribution on the 

sphere, 

(90) 

Here, the pressure P in equations 88, 89, and 90 is the 

hydrostatic pressure developed in the standing column of 

melt at rest and is formed from the trace of the stress tensor. 

Descent of the Sphere 

Consider, for a moment, the following thought experiment involving the movement of a sphere descending in a 

silicate melt that is initially at rest and free of any crystalline 

or discrete gas phase. We will position ourselves inside the 

sphere, at the origin of the coordinate system, and observe 

and record the changing flow conditions in the melt during 

this downward travel. 

During our descent, fluid adheres to the sphere surface 

and is effectively immobilized. This adherence produces, on 

the outer surface, a no-slip boundary condition that is physically equivalent to requiring that all flow must occur within 

the melt itself, not along the melt-solid interface. These 

conditions are Vn =0 and Vr =0 along the walls, where the 

subscripts n and t refer to the normal and tangential components of the velocity. Their specification is required to solve 

the Navier-Stokes equations of motion discussed above 

(eqs. 81-83). Effectively, the surface of the sphere is acting 

as a source of melt shearing motion and angular momentum. 

EXCESS 

TENSION PRESSURE COMPRESSION 

1 

u 

I 

I 

I 

I 

I 

~ z 

Figure 5. Pressure distribution around a sphere descending 

through quiescent melt. The pressure is hydrostatic and is 

formed as the average of the trace of the stress tensor. This 

hydrostatic pressure is the "zero datum" indicated by the 

asymptotes of the solid curve as they approach the long dashshort dash Z axis along the center line of descent. In the near 

field of the sphere, transient ''pressures" are built up and then 

relaxed during melt flow. These pressures have been plotted as 

"excess pressure" and can be either above mean hydrostatic 

(compressive) or below mean hydrostatic (tensile), depending 

on whether we are stationed on the front pole (1) or the rear 

pole (2) of the sphere. They contribute to the pressure component of the total drag. The downward axial velocity is U. 

We further fix ideas by noting that small, equally spaced 

spherical fluid elements have been temporarily dyed with a 

marker, so that we can monitor the kinematic effects of our 

Mechanics of the Falling-Sphere Viscometer 13 
passage by observing how these elements translate, rotate, 

and deform. Figure 6 illustrates the sphere and the flowing 

marker elements during a point frozen in time. 

Ahead of the sphere, the melt is at rest-immobile and 

undeformed. As the sphere moves closer, the elements 

begin to spread radially away from the front pole trajectory. 

In the two-dimensional section of figure 6, this spreading 

takes the form of a lateral flow away from the nose. In terms 

of the Navier-Stokes equation describing incompressible 

creeping flow (grad P =TJV2

W), the u, v, and w velocity 

components have begun to take on finite values, effectively 

"turning on" the viscous term on the right-hand side. 

As the sphere approaches close to a fluid element, the 

local pressure difference rises abruptly, reaches a maximum 

value at the sphere pole, and then declines as the melt 

element deforms, rotates, and accelerates laterally off to the 

side. Along a meridian, this local pressure reduction will 

continue in a linear fashion, as equation 89 and figure 5 

show, and reach a zero (that is, ambient hydrostatic) value 

at the equator. The minimum local differential pressure is 

achieved at the rear pole (point 2 in fig. 5) and contributes 

to the pressure component of the total drag. The pressure in 

the near-field wake is below hydrostatic, and an annular 

suction field centered at the rear pole has developed in three 

dimensions. Farther out in the wake, the pressure rises, 

climbing back to ambient hydrostatic values, given by -I/3 

the trace of the stress tensor (eq. 80) and thus signaling our 

passage farther downstream. 

In the path of advance, as melt elements are perturbed by 

the sphere's close approach and begin to move, they rotate 

as well as translate and deform. The rotation is imparted by 

the viscous coupling of adjacent fluid elements (inviscid 

fluids are irrotational). The magnitude of this rotation, as 

well as its sense, is specified by the angular velocity 

vector-; and is related to the fluid vorticity (ll) through the 

curl of the local velocity U: 

O=VXU=2-; (91) 

This equation is a measure of the instantaneous rotation of 

the orthogonal material lines that pass through the element 

center. Close to the sphere, in the disturbed adjacent layers, 

vorticity increases as the wall of the sphere is approached 

and dies out rapidly as the radial distance increases along a 

given azimuth. ~ond the disturbed near-field region, in 

the melt at rest, fl=O, and the fluid is irrotational. 

Flow-Field Visualization 

If one had the means of attaching neutrally buoyant bright 

particles to transparent fluid parcels, the flow fields set up 

in the fluid during the passage of solid objects could be 

monitored by tracking the motion of the particles themselves. This process exemplifies the flow visualization tech14 Viscosity of Synthetic and Natural Melts and Glasses 

niques that have been used for about 20 years in experimental studies of fluid motion (see Van Dyke's (1982) 

presentation for a recent compilation of studies). 

Coutanceau and Thizon ( 1981) used this technique in 

conducting a series of experiments designed to determine 

the wall effects of spherical bubbles rising axially in cylindrical tubes. Their experiments are particularly relevant to 

visualizing the flow field developed in the falling-sphere 

viscometer during the creeping passage of the sphere, and 

we will summarize certain of the points brought out by their 

work. Their focus was on rising bubbles, whereas oursis on 

descending spheres. However, the essential first-order effects of the near-field flow of one system may be applied to 

the other. (Minor differences show up in the deformation of 

the two-phase interface, such as certain inertial and surface 

tension effects as well as the value of traction components 

at the interface itself. These are not of immediate concern.) 

Coutanceau and Thizon's ( 1981, figs. 11, 12) origi~al plates 

have been modified to produce our figures 7 and 9. The 

plates have been inverted, and a circular white disk has been 

centered on the bubble. A circular, vertically ruled pattern 

has been superposed to suggest a vertical cross section 

through the descending sphere. 

Coutanceau and Thizon ( 1981) used silicone oil (300 

poise at 20°C) as the fluid medium in their experiments. 

Visualization of the flow patterns was accomplished by 

shining an electric-arc projector beam through a meridian 

section of the tube after fine ( <20 !J.m) magnesium flakes 

were uniformly dispersed within the liquid. The particle 

paths then portrayed the kinematics of flow during the moment of transit of the spherical body. Photographs . were 

taken with a fixed camera and with a traveling camera. In 

both cases, the terminal velocity of the sphere had been 

reached before exposure, to insure that the flow field developed was steady and not transient. Thus, it corresponded to 

the Stokes flow discussed in this volume. 

In the moving frame of reference (fig. 7), the trajt?ctories 

of the particles describe a pattern that closely duplicates the 

flow field calculated in figure 8, complete with stagnation 

points (very short lines) at the front and rear poles of the 

sphere. The flow is symmetrical about the equatorial plane, 

as well as being symmetrical along meridian planes. 

In the fixed frame of reference (fig. 9), the lines of magnesium particles describe a pattern of closed streamlines, 

resolving the extent of the fluid region disturbed by the 

passage of the sphere. The white lines or streaks thus track 

the fluid paths during the exposure interval. Their length, 

therefore, is directly proportional to their instantaneous velocity; this relative velocity environment can be appreciated 

by comparing the streak length as a function of .radial distance (along a given azimuth or along a given meridian, 

from pole to pole). 
Figure 6. Schematic melt deformation field produced by the descent of a sphere. Melt marker elements are arrayed on a 16 x 20 

field and are comprised of tiny spheres. Each marker sphere has three initially orthogonal references axes, two of which project 

out at us from the equatorial plane. These elements are translated, rotated, and stretched during the passage of the falling sphere. 

Their rigid body movements and their deformation track the kinematics of melt motion. Such deformation comprises the skin 

friction component of the total drag. (Not illustrated are the more subtle contributions of the axisymmetric compression and 

rarefaction fields near the front and rear poles, respectively.) 

Mechanics of the Falling-Sphere Viscometer 15 
Figure 7. Creeping flow field developed by the axial passage 

of a sphere in a circular cylinder containing a viscous fluid. The 

camera is moving downward with the sphere. (Modified after 

Coutanceau and Thizon, 1981.) 

Direct-Observation Falling-Sphere Viscometry 

Sandia National Laboratories, supported by the U.S. Department of Energy, has developed an approach for the 

direct observation of descending spheres in natural silicate 

melts (Wemple and others, 1980) that is a refinement of a 

surprisingly old technique. Hunter (1934) used stacked twocoil electromagnetic loops, in tandem with a shortwave receiver and an oscillograph, to record the time of flight of the 

descending 0.80 platinum-0.20 rhodium sphere. Figure 10 shows a generalized schematic layout of the experimental configuration. Figure 11 provides an X radiograph of 

the internal structure of the falling-sphere viscometer used, 

and figure 12 provides X radiographs of the descent of a 

sphere as recorded at temperatures just above the 1-atm 

liquidus for Hawaiian olivine tholeiite. 

16 Viscosity of Synthetic and Natural Melts and Glasses 

Figure 8. Flow field developed around a sphere descending 

at constant velocity through a Newtonian melt. The arrow at 

the center of the sphere denotes the direction of motion. 

Attainment of Terminal Velocity 

For a solid sphere moving at a constant velocity through 

an unbounded melt that is at rest, Stokes' ( 1851) stream 

function formulation can be used to evaluate the components of drag or the resistance to translation. For the axisymmetric flow under consideration, the stream function at a ~ 

radial position vector R is defined (Happel and Brenner, 

1973) by 

(92) 

where t is time, Q is the instantaneous volumetric flow rate 

and \fJ is the stream function. For a sphere of radius a and 

velocity U traveling in the + z direction, the appropriate 
Figure 9. Creeping flow field produced by the axial passage 

of a sphere in a circular cylinder containing a transparent viscous fluid. The position of the camera (observer) is stationary. 

(Modified after Coutanceau and Thizon, 1981.) 

boundary conditions on the sphere's surface (r=a) become 

\fJ = _.! Ua 2 sin2 8 

2 (93) 

r=a 

a\fl =-Ua sin2 8 1 

ar . (94) 

r=a 

where the reference angle 81 is taken along a meridian plane 

and begins at the front pole facing in the + z direction. 

The stream function is biharmonic and satisfies the differential equation 

(95) 

where, for spherical coordinates, 

£2=~+ sin 8

1 _E_(_1 _ _E_) 

ar r2 a8 1 sin 81 a8 1 (96) 

The successive use of final trial functions of the form 

\fl=sin2 81F(r) and a subsequent evaluation of the constant 

coefficients of r (Stokes, 1851; Happel and Brenner, 1973) 

by application of the boundary conditions lead to the stream 

function 

(97) 

The corresponding radial and tangential velocity components for this flow field are 

v 1 (~) r r2 sin 81 a8 1 (98) 

or 

v = --1 u cos 8 - - -- 1 (a) 2

(a 3r) ' 2 r r a (99) 

and 

v: =_1_ (alfl) 6 r sin 81 ar 

(100) 

or 

(101) 

Changes in differential pressure over small patches of the 

sphere's surface can be cast in terms of the fluid viscosity 

and the normal derivative of E2 \fJ (Happel and Brenner, 

1973). Thus, the total force exerted on the sphere by the 

fluid can be computed by integrations taken along the meridian planes. 

For the pressure drag component, this procedure leads to 

(102) 

For the viscous drag produced by the tangential stresses 

along the sphere skin, the procedure produces 

(103) 

The total drag is now formed from the sum of the pressure 

and viscous components 

(104) 

Mechanics of the Falling-Sphere Viscometer 17 
---

000 5 

~-------------------------------------------------, ~~----------~11 ~~ --~.~--~ 

16 

11 

0 17 

0 

0 13 

14 12 

Figure 10. Direct-observation falling-sphere viscometer for silicate melts. Principal components are (1) X-ray transmission unit; 

(2) traveling overhead crane for support and positioning; (3) Kanthal-wound furnace; (4) digital temperature indicator; 

· (5) temperature controller; (6) sphere-release mechanism; (7) sphere; (8) crucible; (9) fluorescent screen; (1 0) television camera; 

(11) remote-linkage sphere-release terminal; (12) X-ray generation unit; (13) image-enhancement unit; (14) video monitor; 

(15) videotape recorder; (16) lead- and concrete shielded inner laboratory; (17) videotape cartridge and drive. 

18 Viscosity of Synthetic and Natural Melts and Glasses 
Figure 11. X radiograph of a real-time 1-atm falling-sphere viscometer assembly. Kanthal windings and the vertical cylindrical 

crucible occupy the center of the field of view. (Photograph by Sandia National Laboratories.) 

Mechanics of the Falling-Sphere Viscometer 19 
Figure 12. X radiograph showing rea 1-ti me descent of a sphere in Hawaii an o/ ivi ne tho/ e i ite melt at 1 , 2 44 °C. The sphere has 

just National begun laboratories.) its downward travel; a sphere that had descended earlier rests on the crucible bottom. (Photographs by Sandia 

20 Viscosity of Synthetic and Natural Melts and Glasses 
Figure 128 

Mechanics of the Falling-Sphere Viscometer 21 
Figure 12C 

22 Viscosity of Synthetic and Natural Melts and Glasses 
or 

Ff = -6'ITTJaU (105) 

This equation is the Stokes resistance law of hydrodynamics, which has become known simply as Stokes law. The 

reader may also see Bird and others' (1977a, b) volumes for 

additional discussion. The negative sign for the pressure 

resistance component and for the viscous traction component (as well as the total Ff) suggests that the force exerted 

by the fluid opposes the motion of the sphere. Under the 

driving force of gravity, the downward-directed force on the 

sphere is 

(106) 

where the buoyancy of the surrounding melt has been considered by taking the effective density of the sphere as the 

density contrast between the sphere (p5 ) and the melt (Pm). 

Ultimately, the velocity of the sphere will approach a 

value where the downward-directed gravitational force is 

just balanced by the total resistance of the pressure drag and 

the viscous surface traction drag components of the total 

Stokes resistance. The value of U at which this balance 

occurs is referred to as the terminal velocity, U w The terminal velocity can be related to the driving and resisting force 

components of sphere motion by striking a balance between 

equations 105 and 106: 

(107) 

This important relation has been the object of our attention 

in this section, for its rearrangement leads to a means for 

evaluating melt viscosity through a knowledge of density 

contrasts, sphere sizes, and terminal velocities: 

(108) 

In practice, the presence of the cylinder walls exerts a 

retarding motion on the downward translation of the sphere. 

This retardation arises from the viscous coupling between 

melt elements and the sphere surface and wall surface and 

is a direct result of the immobility of melt at these fluid-solid 

contacts. Mathematically, it is a consequence of the condi-

. tion V=O along these boundaries, where all shear and normal velocity components must vanish. We might imagine, 

then, an additional coefficient added to the Stokes resistance 

expression (eq. 105) to suggest the retarding effect of the 

wall. Wall-correction factors appear in table 1. 

Expressions providing such "wall coefficients" are given 

by Happel and Brenner (1973) for translation along the axis 

Table 1. Wall-correction factors (K1) for rigid spheres translating in quiescent melt along the axis of a circular cylinder 

[a, sphere radius; R0 , cylinder radius;--, not determined. After Happel and Brenner (1973)) 

Haberman 

approximation 

a/R0 (Happel and Brenner, 1973) 

0.0 ................ 1.000 

.1 ................ 1.263 

.2 ................ 1.680 

.3 ................ 2.370 

.4 ................ 3.582 

.5 . . . . . . . . . . . . . . . . 5.871 

.6 ................ 10.591 

.7 ................ 21.406 

.8 ................ 48.985 

Bohlin (1960) 

approximation 

(eq. 115) 

1.000 

1.263 

1.680 

2.370 

3.588 

5.923 

11.057 

36.598 

of a cylinder. One such expression (Fayon and Happel, 

1960) is as follows: 

Here, the actual coefficient of resistance in an infinite fluid 

medium is given by Ca, and C5 is the Stokes resistance drag, 

24/NRe (based on the sphere diameter). Therefore, (CAl 

C s)- 1 is a measure of the fractional departure from the 

resistance computed by considering Stokes law alone. Figure 13 presents Fayon and Happel's (1960) curve as well as 

the comparative curves of Faxen (1923), Oseen (1927), and 

Bohlin (1960). For Reynolds numbers over the range 0.1 to 

1.0, the curves are essentially coincident. 

Another such expression is 

F 1 

6

'ITTJUa ( 1- 1

3

6 NRe) -(~)2.104+2.09(~) 3 (110) 

(Faxen (1923) cited by Oseen (1927)), where NRe is the 

Reynolds number based on the sphere diameter, d is the 

sphere diameter, and D is the cylinder diameter. (The coefficient 2.104 was evaluated for NRe=O.) 

A third expression is 

(111) 

(Bohlin, 1960), where 

K1 = v[ J-2.10443(;J +2.ossn(;J' 

-0.94813(;J -J.m(;J+3.s7(;J+ ... ] (112) 

Mechanics of the Falling-Sphere Viscometer 23 
103 

1- 102 

z Faxen ( 1923) and w 

u Oseen (1927) ii 

u. 

w 

0 ~ u ~ 

(.!) ~ 

~ <{ " r:r: 

Q 10 " ' ' ' ' ' 

Bohlin (1960) /',, 

' ' ' ' 

1 ' 

0.1 10 100 

REYNOLDS NUMBER (NRel 

Figure 13. Drag on a sphere falling axially in a circular cylinder. The convergence of computed drag at low particleReynolds number is evident. 

Figure 14 presents wall-correction factors for the axial 

motion of a rigid sphere as a function of the melt annulus 

thickness (a/R0 ), defined as the ratio of the sphere diameter 

to the cylinder diameter. It is based on the "exact" curve 

presented by Happel and Brenner (1973, p. 319). 

ORGANIZATION OF THE TABLES 

A standard format has been selected for the tabulation of 

data. Each table begins with a heading. For multicomponent 

synthetic systems, the heading is comprised of two parts: the 

system name and the subsystem number. System names are 

combinations of the first letters of each major oxide component. For example, the four-component system Al20rCaOMgO-Si02 is referenced as ACMgS. Subsystems are defined by sequential variations in the mole fractions (and 

weight percentages) of major oxides. Thus, ACMgS-147 

indicates the one hundred and forty seventh subsystem 

within this overall composition. 

For standard glasses, minerals, or rocks, the system-name 

equivalent in the table title is the standard glass number, the 

mineral name, or the lithologic name, respectively. Multicomponent mineral systems also may have subsystem divisions, which delimit the proportions of each component 

over a systematic range of compositions. For example, DiAl-An-5 is the fifth subsystem within the compositional 

group diopside-albite-anorthite. Rocks also have been divided into subsystems; the subsystem number denotes a 

restricted lithologic variant or, for that matter, a change in 

24 Viscosity of Synthetic and Natural Melts and Glasses 

100 

80 

60 

40 

a: 

0 

~ 

u 

<( 20 

LL 

z 

0 

i= 

u 10 w 

a: 8 

a: 

0 6 u I 

....J 

....J 

<( 4 

~ 

2 

a/R0 

Figure 14. Wall-correction factors for a rigid sphere falling 

axially in a circular cylinder. The ratio a/R0 is formed by the 

radius of the sphere and the cylinder. 

water pressure during the experimental run. An example of 

the latter is R-5 for rhyolithic glass at a PH2

o of 20.7 bars. 

Symbols, units, and conversions used in compiling the viscosity data are listed in table 2. 

Table 2. Symbols, units, and conversions used in compiling 

viscosity data 

Symbol Definition 

K------------ Boltzmann's constant 

P ------------ Pressure, in atmospheres (atm) and bars 

(1 bar= 106 dyn cm- 2= 105 Pa; 

1 std. atm=101,325 Pa1

). 

R ------------ Universal gas constant2 (commonly 

8.314(3)±0.0008 J·K- 1 mol- 1). 

T -- --- --- - - -- Temperature, in degrees Celsius ec) and 

kelvins (K). 

Z ------------ Function 10,000.0/T in K- 1 

Tl - - - - - - - - - - - - Apparent viscosity, in poises 

log ---------- Common (or Briggsian) logarithm, to the 

base 10. 

In --- - - --- -- - Natural (or Napierian) logarithm, to the base 

e =2.718(2). 

1 Recommended by CODATA (Committee on Data for Science and 

Technology). 2 CODATA Task Group on Key Values for Thermodynamics (1976). 
Beneath the table title, in the upper left-hand comer, are 

the weight percentages and mole fractions of each major 

oxide within a synthetic system. Mole proportions have 

been computed by using the atomic weights presented in 

table 3. For rocks and multicomponent mineral systems, this 

section of each viscosity table gives the sample locality, 

including, where possible, the district as well as the country. 

The upper right-hand comer of each table gives the 

names of the investigators and the year in which their results 

were published. Information about the original paper can be 

found in the reference list. 

The measurement method is given in the left-central portion of the table (for example, "rotating cylinder viscometer"). 

The data source within the original reference is given in 

the right-central portion of the table under the heading 

"Derived from." This source will almost always be a table 

presented in the original paper. 

Table 3. Atomic weights of the elements 

[Recommended for 1975 (Commission on Atomic Weights, 1976)] 

Element Symbol 

Actinium - - - - - - - - - - - - - - - - - - - - - - - - - - - Ac 

Silver - - -- - - - - - - - - - - - - - - -- - - - - - - -- - - Ag 

Aluminum - - - - - - - - - - - - - - - - - - - - - - - - - - AI 

Americium - - - - - - -- - - - - - - -- - - -- - - - - - - Am 

Argon - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ar 

Arsenic - - - - - - - - - - - - - - - - - - - - - - - - - - - - - As 

Astatine - - - - - - - - - - - - - - - - - - - - - - - - - - - - At 

Gold - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Au 

Boron - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - B 

Barium - - - - - - - - - - - - - -- - - - - - - - - - - - - - - Ba 

Beryllium - - - - - - - -- - - - - - - - - - - -- - -- - - - Be 

Bismuth ---------------------------- Bi 

Bromine - - - - - - - -- - - - - - - - - - - - - - - - - - - - Br 

Carbon - - - - - - - - - - - - - - - - - - - - - - - - - - - - - C 

Calcium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ca 

Cadmium --------------------------- Cd 

Cerium ----------------------------- Ce 

Chlorine - - - - - - - - - - - - - - - - - - - - - - - - - - - - Cl 

Cobalt - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Co 

Chromium - - - - - - -- - - - -- - - - - - - - - - - - - - Cr 

Cesium - -- - - - - - - - - - - -- -- - - - - - -- -- - - - Cs 

Copper - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Cu 

Dysprosium - - - - - - - - - - - - - - - - - - - - - - - - - Dy 

Erbium - - - - - - - - - -- - - - - - - - - - - -- - - - - - - Er 

Europium - - - - - - - - - - - - - - - - - - - - - - - - - - - Eu 

Fluorine - - - - - - - - - - - - - - - - - - - - - - - - - - - - F 

Iron - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Fe 

Francium - - - -- - - - - - - - - - - - - - - - - - - - - - - Fr 

Gallium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ga 

Gadolinium -- - - - - - - - - - - - -- - -- - - - -- - - Gd 

Germanium - -- - - -- - - - - - - -- - - - - - - - - - - Ge 

Hydrogen --------------------------- H 

Helium - - - - - - - - - - - - - - - - - - - - - - - - - - - - - He 

Hafnium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Hf 

Mercury - - - - - - - - - - - - - - - - - - - - - - - - - - - - Hg 

Atomic 

weight 

227.0278 

107.868 

26.9815 

(243). 

39.948 

74.9216 

(210). 

196.9665 

10.811 

137.33 

9.0121 

208.9804 

79.904 

12.0111 

40.08 

112.41 

140.12 

35.453 

58.9332 

51.996 

132.905 

63.546 

162.50 

167.26 

151.96 

18.998 

55.847 

(223). 

69.72 

157.25 

72.59 

1.0079 

4.0026 

178.49 

200.59 

Table 3. Atomic weights of the elements-Continued 

Element Symbol 

Holmium - -- - -- --- - - -- - - - --- -- - - -- - - Ho 

Iodine------------------------------ I 

Indium ----------------------------- In 

Iridium - - - - - -- - - --- - - - - --- -- -- - - - - -- Ir 

Potassium -- --- -- -- - - --- -- - - - -- - -- - - - K 

Krypton - - - - - - - - - - - - - - - - - - - - - - - - - - - - Kr 

Lanthanum - - - - - - - - - - - - - - - - - - - - - - - - - - La 

Lithium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Li 

Lutetium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Lu 

Magnesium - - - -- -- - - --- - - - - - -- --- -- - Mg 

Manganese - - - - - - - - - - - - - - - - - - - - - - - - - - Mn 

Molybdenum ------------------------ Mo 

Nitrogen - -- - -- -- - - - - - - -- --- -- -- --- - - N 

Sodium ----------------------------- Na 

Niobium ---------------------------- Nb 

Neodymium - -- - - -- -- -- -- ---- -- - - --- - Nd 

Neon - - - -- - - -- - -- -- --- - - --- - -- -- -- -- Ne 

Nickel - - - - - --- -- -- - - - -- - -- - -- - - --- - - Ni 

Neptunium - - -- - - -- -- - - - - -- - - -- - - -- -- Np237 

Oxygen - -- - - - - - - -- - - -- --- - -- -- --- - - - 0 

Osmium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Os 

Phosphorus - - - - - - - - - - - - - - - - - - - - - - - - - - P 

Protactinium --- -- -- -- --- -- - - - -- - -- -- - Pa 

Lead ------------------------------- Pb 

Palladium --------------------------- Pd 

Polonium - - --- - - -- - - - - - - -- --- - - --- - - Po 

Promethium - - - - - - - - - - - - - - - - - - - - - - - - - Pm 

Praseodymium - - - - - - - - - - - - - - - - - - - - - - - Pr 

Platinum - - - - - - - - - - - - - - - - - - - - - - - - - - - - Pt 

Plutonium --- -- -- -- - - - - - - --- -- -- - -- - - Pu 

Radium - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ra 

Rubidium - - - - - - - - - - - - - - - - - - - - - - - - - - - Rb 

Rhenium - - - - - - - - -- - - - - - - - - - - - - - - - - - - Re 

Rhodium --- ----- -- -- - -- --- - - --- -- - - Rh 

Radon - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Rn 

Ruthenium - - - - - - - - - - - - - - - - - - - - - - - - - - Ru 

Sulfur -- - - -- - -- --- - - -- -- --- - -- -- --- - S 

Antimony - - - - - - - - - - - - - - - - - - - - - - - - - - - Sb 

Scandium - - - - - - - - - - - - - - - - - - - - - - - - - - - Sc 

Selenium - - - - - - - - - - - - - - - - - - - - - - - - - - - Se 

Silicon - -- - - --- -- -- --- - - -- - - -- -- -- -- Si 

Samarium - - - - - - - - - - - - - - - - - - - - - - - - - - - S 

Tin -------------------------------- Sn 

Strontium - -- - -- --- - - -- - --- -- -- --- - - - Sr 

Tantalum - - - -- - - -- -- -- -- -- - --- - - ---- Ta 

Terbium - --- -- - -- - - - - - -- --- - - -- --- - - Tb 

Technetium --- - - --- -- - - --- -- -- - - -- -- Tc 

Tellurium - - -- - -- -- -- --- --- -- ----- - - - Te 

Thorium -- -- - - - --- -- -- -- - -- --- - - --- - Th 

Titanium -- - - --- -- -- --- -- -- - - - - -- -- -- Ti 

Thallium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tl 

Thulium - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tm 

Uranium - - --- -- --- -- -- -- - -- - -- - - --- - U 

Vanadium - - - - - - - - - - - - - - - - - - - - - - - - - - - V 

Tungsten - - - - - - - - - - - - - - - - - - - - - - - - - - - W 

Xenon - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Xe 

Yttrium ----------------------------- Y 

Ytterbium --------------------------- Yb 

Zinc - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Zn 

Atomic 

weight 

164.930 

126.904 

114.82 

192.22 

39.098 

83.80 

138.905 

6.939 

174.97 

24.305 

54.938 

95.94 

14.0067 

22.9897 

92.9064 

144.24 

20.179 

58.70 

237.0482 

15.9994 

190.2 

30.9737 

231.0359 

207.2 

106.4 

(209). 

(145). 

140.9077 

195.09 

(244). 

226.0254 

85.467 

186.207 

102.9055 

(222). 

101.07 

32.06 

121.75 

44.955 

78.96 

28.085 

150.4 

118.69 

87.62 

180.947 

158.925 

(97). 

127.60 

232.038 

47.90 

204.37 

168.934 

238.029 

50.941 

183.85 

131.30 

88.905 

173.04 

65.38 

Organization of the Tables 25 
The units of viscosity, temperature, and pressure are set 

out in the central portion of the table. 

The data have been organized in a five-column format. 

Starting on the left-hand side and moving across the table, 

the columns are temperature (in degrees Celsius), function 

[10,000/T], In (TJ), log10 (TJ), and viscosity (TJ). 

For systems having low viscosity, the TJ entry in column 

5 will be a real number (for example, TJ=277.0) (ACMgS147, at 1,250 oc and 1 atm). For systems having high 

viscosities, the entry will be cast in exponential notation (for 

example, TJ=2.04X 1010) (National Bureau of Standards reference glass no. 711, at 510 oc and 1 atm), which is read 

"2.04 * 10E10." Finally, for convenience, interconversions 

of the units of viscosity are presented in table 4, and the 

units of length, time, force, and mass are set out in table 5 

for internal consistency. 

Table 4. Units of viscosity 

[CGS unit of viscosity is poise (P), where 1 P=10- 1 Pa·s. SI unit of 

dynamic viscosity is pascal·second (Pa·s), where 1 Pa·s= 1 N·s·M- 2= 1 

kg·(m·s)- 1. Interconversions from Bird and others (1960, p. 752)] 

g·cm-l.s- 1 

g·cm-l.s- 1 ------------------- 1 

kg· m-I. s - 1 - - - - - - - - - - - - - - - - - - 10 

CP - - - - - - - - - - - - - - - - - - - - - - - - - 1 0 

kg·m-l.s- 1 

10-1 

1 

10 

CP 

102 

103 

1 

Table 5. International System (51) units having special names 

[From McGlashan (1973, p. 62)) 

Physical quantity Unit 

Length - - - - - - - - - - - - - meter 

Mass - - - - - - - - - - - - - - - kilogram 

Time - - - - - - - - - - - - - - - second 

Thermodynamic 

temperature. ------- kelvin 

Amount of substance - - mole 

Frequency - - - - - - - - - - hertz 

Energy - - - - - - - - - - - - - joule 

Force - - - - - - - - - - - - - - newton 

Pressure - - - - - - - - - - - - pascal 

Symbol 

m 

kg 

s 

K 

mol 

Definition 

Hz s-1 

J m2·kg·s-2 

N m·kg·s-2=J·m-I 

Pa m- 1·kg·s-2=N·m-2 

=J·m-3 

SOURCES OF TABULATED DATA 

Data have been compiled from the following sources: 

Carnegie Institution of Washington (Geophysical Laboratory) Year Book 

Faraday Society of London Transactions 

Geological Society of America Bulletin 

Geological Society of America Special Papers 

Glastechnische Berichte 

Imperial Academy of Japan Proceedings 

Journal of the American Ceramic Society 

Journal of Geophysical Research 

26 Viscosity of Synthetic and Natural Melts and Glasses 

Journal of the Iron and Steel Institute (London) 

Journal of Petrology 

Journal of Research of the U.S. National Bureau of 

Standards, Series A-Physics and Chemistry 

Proceedings of the Royal Society of London 

Revue Internationale des Hautes Temperatures et des 

Refractories 

Revue de Metallurgie 

Science 

Society of Glass Technology Journal (London) 

Stahl und Eisen 

Tectonophysics 

Transactions of the American Geophysical Union 

U.S. National Bureau of Standards Miscellaneous Publications 

U.S. National Bureau of Standards Publications Series 

U.S. National Bureau of Standards Special Publications 

Zeitschrift fiir Erzbergbau and Metallhiittenwesen 

ORGANIZATION OF THE GRAPHS 

Two types of graphs are presented: plots oflog10 TJ (poise) 

versus temperature (degrees Celsius) and plots of log10 TJ 

versus 10,000/T (per kelvin). The graphs are presented in 

pairs, the log10 TJ x T plot appearing first. Both graphs immediately follow the tabulated data on which they are based 

and provide a rapid means of summarizing the trends within 

a subsystem as well as of making comparisons between 

neighboring subsystems. 

The primary purpose of the log 10 TJ versus T graphs is the 

assessment of the temperature dependence of the data. The 

log10 TJ versus 10,000/T plots provide a graphic means of 

evaluating the activation energy for viscous flow. 

Within an individual graph, the data have been organized 

on the basis of compositionally neighboring subsystems; 

this method of presentation reflects the subsystem ordering 

within the tables, especially for the multicomponent synthetic systems. Individual graphs, then, typically contain 

multiple plots; each suite of data points represents one subsystem and is labeled within its subsystem number. 

The temperature dependence of the viscosity of silicate 

melts is adequately decribed by the Arrhenius relation 

log TJ=TJo +E*/2.302RT 

where TJo is a (preexponential) constant, E* is the activation 

energy for viscous flow, R is the gas constant, and T is the 

absolute temperature. 

Activation energies are frequently presented in two formats; for convenience, both have been incorporated in table 

6. In addition, it is not uncommon to find viscosity values 

cast in terms of natural logarithms to the base e (in addition 
Table 6. Activation energies 

Variable Definition 

Format 1 (in electron volts per atom): TJ=TJo exp-(E*/KT) 

K - - - - - - - - - - - - - - - - - - - - - Boltzmann's constant 

E* -------------------- Activation energy for viscous flow 

(in electron volts per atom). 

T --------------------- Temperature (in kelvins) 

'Y'Jo - - - - - - - - - - - - - - - - - - - - Preexponential constant 

Format 2 (in calories per mole): TJ=TJ exp-(E*/RT) 

R - - - - - - - - - - - - - - - - - - - - - Gas constant 

E - - - - - - - - - - - - - - - - - - - - - Activation energy for viscous flow 

(in calories per mole). 

T --------------------- Temperature (in kelvins) 

to the base 10). A summary for conversions from one system to another follows. The relations between the logarithms of a number N to different bases a and b are given by 

so that 

loge N=1n N=2.302585 log 10 N 

and 

log10 N=log N=0.434 loge N 

(Selby and Girling, 1965, p. 14). 

Finally, interconversions in the units of energy (calories, 

joules, ergs, and electron volts) alter the numerical value of 

the gas constant; these conversions are considered in table 7. 

Activation energies for given subsystems can be conveniently estimated by evaluating the line slopes in the log 11 

versus 104/T plot series. 

Table 7. Units of R 

[R=energy/(temperaturexmole). All temperatures in kelvins, all moles in 

grams. Conversions from Rosenberger (1979, p. 494)] 

Energy R 

Calories - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1. 987 

Joules---------------------------------- 8.314(3) 

Ergs ----------------------------------- 8 .314(3) x 107 

Electron volts---------------------------- 5.189(2)X1019 

REFERENCES 

Aris, R., 1962, Vectors, tensors, and the basic equations of fluid 

mechanics: Englewood Cliffs, N.J. , Prentice-Hall, 286 p. 

Batchelor, G.K., 1967, An introduction to fluid dynamics: London, Cambridge University Press, 615 p. 

Bills, P.M., 1963, Viscosities in silicate slag systems: Journal of 

the Iron and Steel Institute, v. 201, p. 133-140. 

Birch, F., and Dane, E.B., 1942, Viscosity, in Handbook of 

physical constants: Geological Society of America Special 

Paper 36, p. 131-137. 

Bird, R.B., Stewart, W.E., and Lightfoot, E.N., 1960, Transport 

phenomena: New York, John Wiley, 780 p. 

Bird, R.B., Armstrong, R.C., and Hassager, 0., 1977a, Dynamics of polymeric liquids, v. 1, Fluid mechanics: New York, 

John Wiley, p. 1-470. 

Bird, R.B., Hassager, 0., Armstrong, R.C., and Curtiss, C.F., 

1977b, Dynamics of polymeric liquids, v. 2, Kinetic theory: 

New York, John Wiley, p. 471-727. 

Bockris, J.O., and Lowe, D.C., 1954, Viscosity and structure of 

molten silicates: Proceedings of the Royal Society of London, 

v. A226, p. 423-435. 

Bockris, J.O., Mackenzie, J.D., and Kitchener, J.A., 1955, Viscous flow in silica and binary liquid silicates: Faraday Society 

of London Transactions, v. 51, p. 1734-1748. 

Bockris, J.O., White, J.L., and MacKenzie, J.D., 1959, Physicochemical measurements at high temperatures: London, Butterworths, 394 p. 

Bohlin, T., 1960, On the drag on a rigid sphere moving in a 

viscous liquid inside a cylindrical tube: Transactions of the 

Royal Institute of Technology (Stockholm), no. 155, p. 1-63. 

Bottinga, Y., and Weill, D.F., 1972, The viscosity of magmatic 

silicate liquids: A model for calculations: American Journal of 

Science, v. 272, p. 438-475. 

Burnham, C.W., 1963, Viscosity of a water rich pegmatite melt at 

high pressure [abs.]: Geological Society of America Special 

Paper 76, p. 26. 

Clift, R., Grace, J.R., and Weber, M.E., 1978, Bubbles, drops 

and particles: New York, Academic, 380 p. 

COD AT A Task Group on Key Values for Thermodynamics, 1976, 

CODATA recommended key values for thermodynamics, 

1975: Journal of Chemical Thermodynamics, v. 8, p. 603-

605. 

Coleman, B.D., Markovitz, H., and Noll, W., 1966, Viscometric 

flows of non-Newtonian fluids: Berlin, Springer-Verlag, 

130p. 

Commision on Atomic Weights (International Union of Pure and 

Applied Chemistry), 1976, Atomic weights of the elements, 

1975: Pure and Applied Chemistry, v. 47, p. 75-95. 

Couette, M.F.A., 1890, Etudes sur le frottement des liquides: 

Annales de Chimie et de Physique, v. 21, p. 433-510. 

Coutanceau, M., and Thizon, P., 1981, Wall effect on the bubble 

behaviour in highly viscous liquids: Journal of Fluid Mechanics, v. 107, p. 339-373. 

Darby, R., 1976, Viscoelastic fluids: New York, Marcel Dekker, 

638 p. 

Davies, R.O., 1954, Kinetic and thermodynamic aspects of the 

second coefficient of viscosity: Proceedings of the Royal Society of London, v. A226, p. 24-33. 

Eskinazi, S., 1967, Vector mechanics of fluids and magnetofluids: 

New York, Academic, 499 p. 

---1975, Fluid mechanics and thermodynamics of our environment: New York, Academic, 422 p. 

Organization of th~ Graphs 27 
Euler, R., and Winkler, H.G.F., 1957, Uber die Viskositaten von 

Gesteinsund Silikatschmelzen: Glastechnische Berichte, 

V. 30, p. 325-332. 

Faxen, Hilding, 1923, Die bewegung einer starren kugellangs der 

Achse eines mit zaher flussigkeit gefiillten Rohres: Arkiv for 

Matematik, Astronomi och Fysik, v. 17, no. 27, p. 1-28. 

Fayon, A.M., and Happel, J., 1960, Effects of cylindrical 

boundary on fixed rigid sphere in moving viscous fluid: 

American Institute of Chemical Engineers Journal, v. 6, 

p. 55. 

Fredrickson, A.G., 1964, Principles and applications of rheology: 

Englewood Cliffs, N.J., Prentice-Hall, 326 p. 

Friedman, 1., Long, W., and Smith, R.L., 1963, Viscosity and 

water content of rhyolite glass: Journal of Geophysical Research, v. 68, p. 6523-6535. 

Fujii, T., and Kushiro, I., 1977a, Density, viscosity and compressibility of basaltic liquid at high pressures: Carnegie Institution 

of Washington Year Book, v. 76, p. 419-424. 

---1977b, Melting relations and viscosity of an abyssal tholeiite: Carnegie Institution of Washington Year Book, v. 76, 

p. 461-465. 

Happel, J., and Brenner, H., 1973, Low Reynolds number hydrodynamics: Leyden, Noordhoff, 553 p. 

Harris, J., 1977, Rheology and non-Newtonian flow: London, 

Longmans, 338 p. 

Helmholtz, H.V., 1858, Ueber Integrate der hydrodynamischen 

Gleichungen welche den Wirbelbewegungen entsprechen: 

Journal fur die Reine und Angewandte Methematik, v. 55, 

p. 25-55. (Translated into English by Tait, P.G., 1867, On 

integrals of the hydrodynamical equations, which express 

vortex motion: Philosophical Magazine (and Journal of Science), 4th ser., no. 226, suppl. to v. 33, p. 485-512.) 

Hofmaier, G., 1968, Viskositat und struktur fliissiger Silikate: 

Berg- und Hiittenmannische Monatshefte, v. 113, p. 270-

281. 

Hofmann, E.E., 1959, Viskositatsverhalten von synthetischen 

Schlacken in Abhangigkeit von der Zusammensetzung und 

der Temperatur: Stahl und Eisen, v. 79, p. 846-854. 

Hunter, R.G., 1934, Application of Stokes' law in the determination of the absolute viscosity of glass: Journal of the American 

Ceramic Society, v. 17, p. 121-127. 

Johannsen, F., and Brunion, H., 1959, Untersuchungen zur 

Viskositat von Rennschlaken: Zeitschrift fiir Erzbergbau und 

Metallhiittenwesen, v. 12, p. 211-279. 

Kani, K., 1934a, The measurement of the viscosity of basalt glass 

at high temperatures, pt. 1: Imperial Academy of Japan Proceedings, v. 10, p. 29-32. 

---1934b, The measurement of the viscosity of basalt glass at 

high temperatures, pt. II: Imperial Academy of Japan Proceedings v. 10, p. 79-82. 

Kozakevitch, P., 1960, Viscosite et elements structuraux des aluminosilicates fondus: Laitiers CaO-Al20rSi02 entre 1600 et 

2100° C: Revue de Metallurgie, v. 57, p. 149-160. 

Kozu, S., and Kani, K., 1934, Viscosity measurements of the 

ternary system diopside-albite-anorthite at high temperatures: 

Imperial Academy of Japan Proceedings, v. 10, p. 29-32. 

Kushiro, 1., 1976a, Decrease in viscosity of some synthetic melts 

at high pressures: Carnegie Institution of Washington Year 

Book, v. 75, p. 611-614. 

28 Viscosity of Synthetic and Natural Melts and Glasses 

---1976b, Changes in viscosity and structure of melt of 

NaA1Si20 6 composition at high pressures: Journal of 

Geophysical Research, v. 81, p. 6347-6350. 

---1981 , Change in viscosity with pressure of melts in the 

system Ca0-Al20 3-Si02: Carnegie Institution of Washington Year Book, v. 80, p. 339-341. 

Kushiro, I. Yoder, H.S., and Mysen, B.O., 1976a, Viscosity of 

basaltic and andesitic liquids at high pressures: Carnegie Institution of Washington Year Book, v. 75, p. 615-618. 

---1976b, Viscosities of basalt and andesite melts at high 

pressures: Journal of Geophysical Research, v. 81, p. 6351-

6356. 

Lillie, H.R., 1929, Viscosity measurements in glass: Journal of the 

American Ceramic Society, v. 12, p. 516-529. 

---1931, Viscosity of glass between the strain point and melting temperature: Journal of the American Ceramic Society, 

v. 14, p. 502-511. 

---1939, High-temperature viscosities of soda-silica glasses: 

Journal of the American Ceramic Society, v. 22, p. 367-374. 

Machin, J. S., and Hanna, D. L., 1945, Viscosity studies of system 

CaO-MgO-Alz03-SiOz, pt. I, 40% Si02: Journal of the 

American Ceramic Society, v. 28, p. 310-316. 

Machin, J. S. , and Y ee, T. B. , 1948, Viscosity studies of system 

Ca0-Mg0-Al20 3-Si02, pt. II, CaO-Al20rSi02: Journal 

of the American Ceramic Society, v. 31, p. 200-204. 

---1954, Viscosity studies of system Ca0-Mg0-Al20r 

Si02, pt. IV, 60 and 65% Si02: Journal of the American 

Ceramic Society, v. 37, p. 177-186. 

Machin, J.S., Yee, T.B., and Hanna, D.L., 1952, Viscosity studies of system Ca0-Mg0-Al20 3-Si02, pt. III, 35, 45 and 

50% Si02: Journal of the American Ceramic Society, v. 35, 

p. 322-325. 

Mackenzie, J.D., 1957, The discrete ion theory and viscous flow 

in liquid silicates: Faraday Society of London Transactions, 

v. 58, p. 1488-1493. 

McBimey, A.R., and Murase, T., 1984, Rheological properties of 

magmas: Annual Review of Earth and Planetary Sciences, 

v. 12, p. 337-357. 

McCaffery, R.S., Lorig, C.H., Goff, I.N., Oesterle, J.F., and 

Fritsche, 0.0., 1931, Determination of viscosity of blast 

furnace slags: American Institute of Mining and Metallurgical 

Engineers Technical Publication 383, p. 27-140. 

McGlashan, M.L., 1973, Internationally recommended names and 

symbols for physicochemical quantities and units, in Eyring, 

H., Chris, C.J., and Johnston, H.S., eds., Annual review of 

physical chemistry, v. 20: Palo Alto, Calif., Annual Reviews, 

546 p. 

Motte, A., trans., 1946, Mathematical principles of natural philosophy and his system of the world (Newton, I.S., 1687): 

Berkeley, Calif., University of California Press, 680 p. 

Murase, T., and McBirney, A.R., 1970, Viscosity of lunar 

lavas: Science,v.167,p.l491-1493. 

---1973 , Properties of some i common, igneous rocks and 

their melts at high temperatures: Geological Society of America Bulletin, v. 84, p. 3563-3592. 

Mysen, B.O., 1981, Melting curves of rocks and viscosity of 

rock-forming minerals, in Touloukian, Y.S., Judd, W.R., 

and Roy, R.F., eds., Physical properties of rocks and miner-
als: McGraw-Hill-CINDAS Data Series on Material Properties, v. 11-2, 548 p. 

Napolitano, A., and Hawkins, E.G., 1964, Viscosity of a standard 

soda-lime-silica glass: Journal of Research of the U.S. National Bureau of Standards, v. 68A, p. 439-448. 

---1966, Viscosity of a standard lead-silica glass: U.S. 

Naitonal Bureau of Standards Miscellaneous Publication 

260-11, p. 1-23. 

---1970, Viscosity of a standard borosilicate glass (standard 

reference material no. 717): U.S. National Bureau of Standards Special Publication 260-23, p. 1-8. 

Napolitano, A., Simmons, J.H., Blackburn, D.H., and Chidester, 

R.E., 1974, Analysis of low temperature viscosity data for 

three NBS standard glasses: Journal of Research of the U.S. 

National Bureau of Standards, v. 78A, 323-329. 

N'Dala, 1., Cambier, F., Anseau, M.R., and Urbain, G., 1984, 

Viscosity of liquid feldspars, pt. I, Viscosity measurements: 

British Ceramic Society Transactions, v. 83, p. 105-107. 

Oka, S., 1960, The principles of rheometry, in Eirich, F.R., ed., 

Rheology: Theory and applications: New York, Academic, 

v. 3, p. 17-80. 

Oseen, C., 1927, Neuere Methoden und Ergebnisse in der Hydrodynamik: Leipzig, Akademische Verlagsgesellschaft. 

Riebling, E. F., 1964, Structure of magnesium aluminosilicate liquids at 1700° C: Canadian Journal of Chemistry, v. 42, 

p. 2811-2821. 

Roentgen, P., Winterhager, H., and Kammel, R., 1956, Struktur 

und Eigenschaften von Schlacken der Metallhi.itten-prozesse, 

pt. I, ViscosiHitsmessungen an Schlaken des systems 

Eisen ox ydul-Tonerde-Kieselsauer: Zeitschrift fi.ir Erzbergbau 

and Metallhi.ittenwesen, v. 9, p. 207-214. 

Rosenberger, F., 1979, Fundamentals of crystal growth, v. 1: 

Berlin, Springer-Verlag, 530 p. 

Rosenhead, L., 1954, The second coefficient of viscosity: A brief 

review of fundamentals: Proceedings of the Royal Society of 

London, v. A226, p. 1-6. 

Rossin, R. , Bersan, J. , and Urbain, G. , 1964, Etude de Ia viscosite 

de laitiers liquides appartenant au systeme ternaire: Si0zAI203-Ca0: Revue Internationale des Hautes Temperatures 

et des Refractories, v. 1, p. 159-170. 

Scarfe, C. M. , 1981 , The pressure dependence of the viscosity of 

some basic melts: Carnegie Institution of Washington Year 

Book, v. 80, p. 336-339. 

Searle, C.M., Cronin, D.J., Wenzel, J.T., and Kauffman, D.A., 

1983, Viscosity-temperature relationships at 1 atm. in the 

system diopside-anorthite: American Mineralogist, v. 68, 

p. 1083-1088. 

Schlichting, H., 1968, Boundary-layer theory: New York, 

McGraw-Hill, 748 p. 

Schowalter, W.R., 1978, Mechanics of non-Newtonian fluids: 

New York, Pergamon, 300 p. 

Selby, S.M., and Girting, B., eds., 1965, Standard mathematical 

tables (14th ed.): Cleveland, Chemical Rubber Co., 632 p. 

Shartsis, L., Spinner, S., and Capps, W., 1952, Density, expansivity and viscosity of molten alkali silicates: Journal of the 

American Ceramic Society, v. 35, p. 155-160. 

Shaw, H.R., 1963, Obsidian-H20 viscosities at 1000 and 2000 

bars in the temperature range 700° to 900° C: Journal of 

Geophysical Research, v. 68, p. 6337-6343. 

---1969, Rheology of basalt in the melting range: Journal of 

Petrology, v. 10, p. 510-535. 

---1972, Viscosities of magmatic silicate liquids: An empirical method of prediction: American Journal of Science, 

V. 272, p. 870-893. 

Shaw, H.R., Peck, D.L., Wright, T.L., and Okamura, R.T., 

1968, The viscosity of basaltic magma: An analysis of field 

measurements in Makaopuhi lava lake, Hawaii: American 

Journal of Science, v. 266, p. 225-264. 

Stokes, G.G., 1845, On the theories of internal friction of fluids 

in motion: Transactions of the Cambridge Philosophical Society, v. 8, p. 287-305. 

---1851 , On the effect of the internal friction of fluids on the 

motion of pendulums, pt. II: Transactions of the Cambridge 

Philosophical Society, v. 9, p. 8-106. 

Van Dyke, M., 1982, An album of fluid motions: Stanford, Calif., 

Parabolic Press, 176 p. 

Van Wazer, J.R., Lyons, J.W., Kim, K.Y., and Colwell, R.E., 

1963, Viscosity and flow measurement: New York, Interscience, 406 p. 

Volarovich, M.P., and Tolstoi, D.M., 1936, The simultaneous 

measurement of viscosity and electrical conductivity of some 

fused silicates at temperatures up to 1400°: Society of Glass 

Technology Journal (London), v. 20, p. 54-60. 

Walters, K., 1975, Rheometry: New York, Chapman and HallJohn Wiley, 278 p. 

Wemple, R.P., Hammeter, W.F., and Greenholt, C.J., 1980, 

Development of high temperature viscosity measurement 

technique: Albuquerque, N. Mex., Report SAND8-0641, 

Sandia National Laboratories, 27 p. 

Whorlow, R.W., 1980, Rheological techniques: Ellis Horwood 

Ltd./J. Wiley-Halsted Press, 447 p. 

Yuan, S.W., 1967, Foundations of fluid mechanics: Englewood 

Cliffs, N.J., Prentice-Hall, 608 p. 

References 29 

Two-Component Systems 

Two-Component Systems 31 
SYSTEM 

BAO (15. 4), SI02 (84. 6) (X) 

BA0(31.7) ,SI02(68.3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

5.700 

5.273 

4.905 

4.605 

BAO (25 .1) , SI02 (74. 9) (X) 

BA0(46.1) ,SI02(53.9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN (N) 

4.701 

4.191 

3.777 

3.408 

3.063 

2.773 

2.526 

BAO (30. 7) , SI02 (69. 3) (X) 

BA0(53.1),SI02(46.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

3.478 

3.110 

2.766 

2.468 

2.141 

1.899 

1.670 

BAO ( 33. 5) , SI02 (66. 5) (X) 

BA0(56.3),SI02(43.7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

3.270 

2.901 

2.559 

2.268 

1.974 

1.758 

1.504 

LOG(N) 

2.476 

2.290 

2.130 

2.000 

LOG(N) 

2.041 

1.820 

1.641 

1.480 

1.330 

1.204 

1.097 

LOG(N) 

1.511 

1.350 

1.201 

1.072 

0.930 

0.825 

0.725 

LOG(N) 

1.420 

1.260 

1.111 

0.985 

0.857 

0.763 

0.653 

32 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 1000.0. 0/T (K) (1/K) 8 S- 1 

N 

299. 

195. 

135. 

100. 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 8 S- 2 

N 

110. 

66.1 

43.7 

30.2 

21.4 

16.0 

12.5 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 8 S- 3 

N 

32.4 

22.4 

15.9 

11.8 

8.51 

6.68 

5.31 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 8 S- 4 

N 

26.3 

18.2 

12.9 

9.66 

7.20 

5.80 

4.50 
SYSTEM 

BA0~40.2~,SI02~59.8~ BAO 63.2 ,SI02 36.8 ~~~ MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T z LN(N) 1500.00 5.640 2.833 

1550.00 5.485 2.468 

1600.00 5.339 2.180 

1650.00 5.200 1.900 

1700.00 5.068 1.681 

1750.00 4.943 1.520 

1800.00 4.824 1.381 

SYSTEM 

BAO (42. 0), SI02 (58. 0) (X) 

BA0(65.0),SI02(35.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

2.072 

1.726 

1.447 

1.197 

0.963 

0.766 

BAO (49. 8) , SI02 (50. 2) (X) 

BA0(71.7),SI02(28.3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

1. 030 

0.798 

0.621 

0.495 

0.406 

LOG(N) 

1.231 

1.071 

0.947 

0.825 

0.730 

0.660 

0.600 

LOG(N) 

0.900 

0.725 

0.628 

0.529 

0.418 

0.332 

LOG(N) 

0.447 

0.346 

0.270 

0.215 

0.176 

p = 

z = 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

1.0 A1M. 

10000.0/T(K) (1/K) 85-5 

N 

17.0 

11.8 

8.85 

6.68 

5.37 

4.57 

3.92 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 A1M. 

Z = 10000. 0/T (K) (1/K) 8 S- 6 

N 

7.94 

5.62 

4.25 

3.31 

2.62 

2.15 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 8 S -7 

N 

2.80 

2.22 

1.86 

1.64 

1.50 

Two-Component Systems 33 
4 ~----~------~------~------~------.------, 

Ba0-Si02 

IJOCKRIS, MACKENZIE and KITCHENER (1955/ 

3 

.-..._ 

w 

<.I) 

0 BS-1 

a.. 

---

>-

t-

-

<.I) 2 0 

u 

<.I) 

-

> 

() 

0 

-I 

1 

0 ~----~------~------~------~------~----~ 

1500 1600 1700 1800 

TEMPERATURE (°C) 

34 Viscosity of Synthetic and Natural Melts and Glasses 
4~----~------~------~----~------~----~ 

Ba0-Si02 

BOCKHIS, MACKENZIE and KITCHENER (1955) 

3 

~ 

LU 

V') 

- BS-1 0 

a.. 

......__.. 

>- 1-

V') - BS-2 2 0 

u 

V') 

-

> 

<-' BS-3 

0 BS-4 

_,J 

BS-5 

1 

0 ~----~------~------~----~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS-1

) 

Two-Component Systems 35 
SYSTEM 

CAO (30. 5) , SI02 (69. 5) (X) 

CA0(29.0),SI02(71.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1700.00 5.068 2.610 

1750.00 4.943 2.342 

1800.00 4.824 2.140 

SYSTEM 

CA0(34.6),SI02(65.4) (X) 

CA0(33.0),SI02(67.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

2.303 

2.054 

1.800 

1.504 

CAO ( 38. 8) , SI02 (61. 2) (X) 

CA0(37.2),SI02(62.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

SYSTEM 

LN(N) 

3.049 

2.667 

2.322 

1.988 

1.658 

1.366 

1.131 

CAO (38. 8) , SI02 (61. 2) (X) 

CA0(37.2),SI02(62.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1450.00 5,804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

3.039 

2.639 

2.282 

1.960 

1.635 

1.369 

1.099 

0.916 

LOG(N) 

1.134 

1.017 

0.929 

LOG(N) 

1.000 

0.892 

0.782 

0.653 

LOG(N) 

1.324 

1.158 

1.009 

0.863 

0.720 

0.593 

0.491 

LOG(N) 

1.316 

1.146 

0.991 

0.851 

0.710 

0.594 

0.477 

0.398 

36 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

13.4 

10.4 

8.5 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.0 

7.8 

6.05 

4.5 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

21.1 

14.4 

10.2 

7.30 

5.25 

3.92 

3.10 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

20.7 

14.0 

9.8 

7.10 

5.13 

3.93 

3.00 

2.5 

CS-1 

CS-2 

cs- 3 

CS-4 
SYSTEM 

CAO (38. 8), SI02 (61. 2) (X) 

CA0(37.2),SI02(62.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N JPOISES) T DEGREES c

2

) 

LN(N) 

1450.00 5.804 3.054 

1500.00 5.640 2.639 

1550.00 5.485 2.272 

1600.00 5.339 1.960 

1650.00 5.200 1.658 

1700.00 5.068 1.361 

1750.00 4.943 1.147 

SYSTEM 

CA0(41.6) ,SI02 (58.4) (X) 

CA0(40.0),SI02(60.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

2.235 

1.869 

1.543 

1.273 

1.012 

0.770 

0.588 

CAO (43. 7), SI02 (56. 3) (X) 

CA0(47.0),SI02(53.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

2.035 

1.723 

1.399 

1.082 

0.854 

0.668 

0.405 

LOG(N) 

1.326 

1.146 

0.987 

0.851 

0.720 

0.591 

0.498 

LOG(N) 

0.971 

0.812 

0.670 

0.553 

0.439 

0.334 

0.255 

LOG(N) 

0.884 

0.748 

0.607 

0.470 

0.371 

0.290 

0.176 

/ 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P == 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

21.2 

14.0 

9.7 

7.10 

5.25 

3.90 

3.15 

AU'IHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P == 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.35 

6.48 

4.68 

3.57 

2.75 

2.16 

1.8 

AU'IHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

7.65 

5.60 

4.05 

2.95 

2.35 

1.95 

1.5 

(1/K) 

CS-5 

CS-6 

CS-7 

Two-Component Systems 37 
SYSTEM 

CAO (48. 7l, SI02 (51. 3) (X) CA0(47.0 ,SI02(53.0) (%) 

MEASUR MENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

17oo.oo· 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.470 

1.154 

0.880 

0.642 

0.405 

0.182 

-0.010 

CAO (49 o 7~, SI02 (50. 3) (X) 

CA0(48.0 ,SI02(52.0) (%) 

MEASUR MENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750o00 4.943 

1800.00 4o824 

SYSTEM 

LN(N) 

1.058 

0.779 

0.519 

0.285 

0.058 

-0.128 

CAO (50. 7) , SI02 (49. 3) (X) 

CA0(49oO),SI02(51.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 - -~~ 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

0.993 

0.703 

0.419 

0.174 

-0.030 

-0.223 

CAO (51. 7) , SI02 (48. 3) (X) 

CA0(50.0),SI02(50.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550o00 5o485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4o943 

1800.00 4.824 

LN(N) 

0.888 

0.593 

0.329 

0.104 

-0.105 

-0.208 

LOG(N) 

0.638 

0.501 

0.382 

Oo279 

0.176 

0.079 

-0.004 

LOG(N) 

0.459 

0.338 

0.225 

0.124 

0.025 

-0.056 

LOG(N) 

0.431 

0.301 

0.182 

0.076 

-0.013 

-0.097 

LOG(N) 

Oo386 

0.258 

0.143 

0.045 

-Oo046 

-0.125 

38 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000 o 0/T (K) (1/K) 

N 

4.35 

3.17 

2.41 

1.90 

1o50 

1o20 

0.99 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.88 

2.18 

1.68 

1.33 

1.06 

0.88 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATH. 

Z = 10000. 0/T (K) (1/K) 

N 

2.70 

2.00 

1.52 

1.19 

0.97 

0.8 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.43 

1.81 

1.39 

1.11 

0.90 

Oo75 

CS-8 

cs- s 

cs -10 

CS-11 
SYSTEM 

CAO (52. 7) I SI02 (47. 3) (X) CA0(51.0)~SI02(49.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.109 

0.788 

0.507 

0.247 

0.010 

-0.186 

-0.329 

CAO (53. 7) I SI02 (46. 3) (X) 

CA0(52.0) 1 SI02(48.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.058 

0.747 

0.451 

0.182 

-0.041 

-0.236 

-0.416 

CAO (54. 7) I SI02 (45. 3) (X) 

CA0(53.0) 1 SI02(47.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

0.944 

0.329 

0.336 

0.095 

-0.105 

-0.288 

-0.416 

LOG(N) 

0.481 

0.342 

0.220 

0.107 

0.004 

-0.081 

-0.143 

LOG(N) 

0.459 

0.324 

0.196 

0.079 

-0.018 

-0.102 

-0.180 

LOG(N) 

0.410 

0.143 

0.146 

0.041 

-0.046 

-0.125 

-0.180 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3.03 

2.20 

1.66 

1.28 

1.01 

0.83 

0.72 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.88 

2.11 

1.57 

1.20 

0.96 

0.79 

0.66 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

2.57 

1.39 

1.40 

1.10 

0.90 

0.75 

0.66 

(1/K) 

c s- 1 2 

C S-13 

CS-14 

Two-Component Systems 39 
SYSTEM 

CAO (56 .1), SI02 (43. 9) (X) 

CA0(54.5),SI02(45.5) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.197 

0.871 

0.588 

0.329 

0.049 

-0.211 

-0.386 

-0.511 

CAO (57. 6) , SI02 (42. 4) (X) 

CA0(56.0),SI02(44.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

0.122 

-0.105 

-0.301 

-0.478 

-0.616 

LOG(N) 

0.529 

0.378 

0.255 

0.143 

0.021 

-0.092 

-0.167 

-0.222 

LOG(N) 

0.053 

-0.046 

-0.131 

-0.208 

-0.268 

40 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.31 

2.39 

1.80 

1.39 

1.05 

0.81 

0.68 

0.60 

AUTHOR 

BOCKRIS AND LOWE (1954) 

DERIVED FROM 

TABLE . 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.13 

0.90 

0.74 

0.62 

0.54 

CS-15 

cs -16 
..--..... 

w 

c.l) 

-

0 

a.. 

._,__. 

>-

1-

-

0 

u 

c.l) 

-

> 

~ 

g 

3 ------~----------~----~----~----~----~ 

2 

1 

0 

Ca0-Si02 

BOCKRIS and LOWE I 1954) 

-1 ~----~----~----~----~----~----~~--~ 

1450 1550 1650 

TEMPERATURE (°C) 

1750 

I 

Two-Component 54 41 

I 

! 
.......... 

w 

(./') 

-

0 

a.. 

........... 

>- 1-

-(./') 

0 

u 

(./') 

-

> 

() 

0 

__, 

3~----~--------------~------~------~------~ 

2· 

1 

0 

Ca0-Si02 

BOCKRIS and LOWE (1954} 

CS-5 

-1 ~------L-----~~----~~----~------~------~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

42 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

CAO (36. 58) , SI02 (63. 42) (X) 

CAO (35. 0) , SI02 (65. 0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1500.00 5.640 3.063 1.330 

SYSTEM 

CAO (42. 0) , SI02 (58. 0) (X) 

CA0(40.0),SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 1450.00 5.804 2.667 1.158 

1500.00 5.640 2.196 0.954 

SYSTEM 

CAO (56. 71) , SI02 (43. 29) (X) 

CAO (55. 0), SI02 (45. 0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1500.00 5.640 0.846 0.367 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

21.4 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

14.4 

8.99 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

C S-17 

CS-18 

Z = 1 0 0 0 0 . 0 /T (K) ( 1 /K) C S - 1 9 

N 

2.33 

Two-Component Systems 43 
SYSTEM 

fEO (55. 5) , SI02 ( 44. 5) (X) 

fE0(59.9),SI02(40.1) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

1.649 

1.065 

0.405 

0.336 

0.262 

0.182 

fEO (56. 9) , SI02 ( 43 .1) (X) 

fE0(61.2),SI02(38.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

SYSTEM 

LN(N) 

1.308 

0.742 

-0.105 

-1.609 

fEO (59 .4), SI02 (40. 6) (X) 

fE0(63.6),SI02(36.4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1250.00 6.566 0.642 

1300.00 6.357 0.095 

SYSTEM 

fEO (60. 8) , SI02 ( 39. 2) (X) 

fE0(65.0),SI02(35.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1200.00 6.789 1.749 

1250.00 6.566 0.588 

1300.00 6.357 0.470 

1350.00 6.161 0.336 

LOG(N) 

0.716 

0.462 

0.176 

0.146 

0.114 

0.079 

LOG(N) 

0.568 

0.322 

-0.046 

-0.699 

LOG(N) 

0.279 

0.041 

LOG(N) 

0.760 

0.255 

0.204 

0.146 

44 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED fROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.2 

2.9 

1.5 

1.4 

1.3 

1.2 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED fROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.7 

2.1 

0.9 

0.2 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.9 

1.1 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL ( 1956) 

DERIVED FROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.75 

1.8 

1.6 

1.4 

FS-1 

FS-2 

F S-3 

FS-4 
SYSTEM 

FEO (61. 0) , SI02 (39. 0) (X) 

FE0(65.2),SI02(34.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1400.00 5.977 

LN(N) 

0.405 

0.000 

LOG(N) 

0.176 

0.000 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.5 

1.0 

FS-5 

------------------------------------------------------------------------------ SYSTEM 

FEO (61. 0) , SI02 (39. 0) (X) 

FE0(65.2),SI02(34.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

0.182 

0.095 

0.095 

0.000 

-0.105 

FEO (62. 0) , SI02 (38. 0) (X) 

FE0(66.1),SI02(33.9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

0.405 

0.262 

0.182 

0.000 

-0.105 

-0.223 

FEO (63. 0) , SI02 (37. 0) (X) 

FE0(67.1),SI02(32.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1200.00 6.789 -0.223 

1250.00 6.566 -0.357 

1300.00 

1350.00 

1400.00 

1450.00 

6.357 

6.161 

5.977 

5.804 

-0.511 

-0.511 

-0.693 

-0.916 

LOG(N) 

0.079 

0.041 

0.041 

0.000 

-0.046 

LOG(N) 

0.176 

0.114 

0.079 

0.000 

-0.046 

-0.097 

LOG(N) 

-0.097 

-0.155 

-0.222 

-0.222 

-0.301 

-0.398 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.2 

1.1 

1.1 

1.0 

0.9 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.5 

1.3 

1.2 

1.0 

0.9 

0.8 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL ( 1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

0.8 

0.7 

0.6 

0.6 

0.5 

0.4 

F S-6 

FS-7 

FS-8 

Two-Component Systems 45 
SYSTEM 

FEO (65. 5) , SI02 (34. 5) (X) 

FE0(69.6),SI02(30.4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1300.00 6.357 -0.357 

1400.00 5.977 -0.916 

SYSTEM 

FEO (65. 5) , SI02 (34. 5) (X) 

FE0(69.6),SI02(30.4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

-0.105 

-0.223 

-0.357 

-0.511 

-0.511 

-0.693 

FEO (66 .1) , SI02 ( 33. 9) (X) 

FE0(70.0),SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1200.00 6.789 0.875 

1250.00 6.566 0.668 

1300.00 6.357 0.262 

LOG(N) 

-0.155 

-0.398 

LOG(N) 

-0.046 

-0.097 

-0.155 

-0.222 

-0.222 

-0.301 

LOG(N) 

0.380 

0.290 

0.114 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

0.7 

0.4 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

0.9 

0.8 

0.7 

0.6 

0.6 

0.5 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.4 

1.95 

1.3 

FS-9 

FS-10 

F S- 1 1 

------------------------------------------------------------------------------

SYSTEM 

FEO (66. 8) , SI02 ( 33. 2) (X) 

FE0(70.6),SI02(29.4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

LN(N) 

1.856 

0.916 

0.742 

0.588 

LOG(N) 

0.806 

0.398 

0.322 

0.255 

46 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.4 

2.5 

2.1 

1.8 

FS-12 
•SYSTEM 

FEO (68. 5) , SI02 (31. 5) (X) 

FE0(72.2),SI02(27.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

-0.105 

-0.105 

-0.223 

-0.357 

-0.357 

LOG(N) 

-0.046 

-0.046 

-0.097 

-0.155 

-0.155 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z ~ 10000. 0/T (K) (1/K) 

N 

0.9 

0.9 

0.8 

0.7 

0.7 

FS-13 

-----~------------------------------------------------------------------------

.SYSTEM 

FEO (70. 0) , SI02 (30. 0) (X) 

FE0(73.6),SI02(26.4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1300.00 6.357 0.336 

1400.00 5.977 -0.357 

SYSTEM 

FEO (71. 5) , SI02 (28. 5) (X) 

FE0(75.0),SI02(25.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

12.50.00 6.566 

1300.00 6.357 

13.50.00 6.161 

LN(N) 

0.113 

0.000 

-0.357 

-0.799 

SYSTEM 

FE0(71.5),SI02(28.5) (X) 

FE0(75.0),SI02(25.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

12.50.00 6.566 

1300.00 6.357 

13.50.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

-0.105 

-0.223 

-0.511 

-0.693 

-0.916 

-1.204 

LOG (N) 

0.146 

-0.155 

LOG(N) 

0.049 

0.000 

-0.155 

-0.347 

LOG(N) 

-0.046 

-0.097 

-0.222 

-0.301 

-0.398 

-0.523 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.4 

0.7 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL ( 1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.12 

1.00 

0.7 

0.45 

AUTHOR 

ROENTGEN I WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

0.9 

0.8 

0.6 

0.5 

0.4 

0.3 

(1/K) 

FS-14 

FS-15 

FS-16 

Two-Component Systems 47 
SYSTEM 

FEO (7 3. 0) , SI02 (27. 0) (X) 

FE0(76.4),SI02(23.6) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1300.00 6.357 -0.223 

1400.00 5.977 -0.511 

SYSTEM 

FEO (77. 5) , SI02 {22. 5) (X) 

FE0(80.5),SI02(19.5) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1300.00 6.357 -0.693 

1400.00 5.977 -0.916 

LOG(N) 

-0.097 

-0.222 

LOG(N) 

-0.301 

-0.398 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

0.8 

0.6 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

0.5 

0.4 

FS-17 

FS-18 

·-----------------------------------------------------------------------------

SYSTEM 

FEO (79. 5) , SI02 (20. 5) (X) 

FE0(82.3),SI02(17.7) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

-0.693 

-0.916 

-0.916 

-1.204 

-1.609 

FEO (91. 0) , SI02 (9. 0) (X) 

FE0(92.4),SI02(7.6) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

2.477 

-0.916 

-0.916 

-1.204 

-1.609 

-2.303 

LOG(N) 

-0.301 

-0.398 

-0.398 

-0.523 

-0.699 

LOG(N) 

1.076 

-0.398 

-0.398 

-0.523 

-0.699 

-1.000 

48 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL (1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

0.5 

0.4 

0.4 

0.3 

0.2 

AUTHOR 

ROENTGEN, WINTERHAGER AND 

KAMMEL ( 1956) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

11.9 

0.4 

0.4 

0.3 

0.2 

0.1 

FS-19 

F S-20 
3~----~--------------~----~------------~ 

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956) 

2 

.......... 

UJ 

V) 

0 

a.. 

........, 

..,_ 

>-

-

V) 1 0 

u 

V) 

-

> 

0 

0 

__. FS-4 

I 

FS-1 

0 FS-6 

FS-7 

FS-2 

-1 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Two-Component Systems 49 
3 ~----~~----~--------------~------~-------

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956) 

2 

~ 

UJ 

V') 

-

0 

a_ 

---

>- IV') - 1 0 

u 

c./) 

- FS-1 

> 

l? 

0 

....J 

FS-7 

0 FS-6 

-1 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

50 Viscosity of Synthetic and Natural Melts and Glasses 
.....--.. 

UJ 

V') 

0 

a... 

........... 

>- 1-

-

V') 

0 

u 

V') 

-

> 

~ 

0 

__. 

3~----~------~------~----~------~----~ 

2 

1 

0 

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956} 

f=::=-=-::..=iE-=-==-=-=-=-:::-----...._::::::::::::::::=-,... __ __. FS -13 

FS-10 

FS-8 

-1 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Two-Component Systems 51 
3~----~------~------~-------.------~~------. 

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956) 

2 

.--... 

UJ 

V) 

0 

a.. 

___.. 

>- 1-

-

V) 1 0 

u FS-12 V) 

-

> 

0 

0 FS-11 

_J 

0 

-1 ~------~------~----~~----------------------

4.5 5.5 6.5 7.5 

10 000/T KELVINS- 1) 

52 Viscosity of Synthetic and Natural Melts and Glasses 
3 .-----~------~------~------~----~------~ 

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956) 

2 

.---

UJ 

V') 

0 

a.. 

____.. 

>- 1-

-

V') 1 0 

u 

V') 

-

> 

~ 

0 

_,J 

0 ,_ ____ _ 

FS-16 

FS-20 

-1 ~------~------~--------~------~----~--------~ 

1200 1300 1400 1500 

TEMPERATURE (°C} 

Two-Component Systems 53 
....--.. 

LU 

V") 

-

0 

a... 

......__. 

>-

~ 

V") -

0 

u 

V") 

-

> 

~ 

0 

_, 

3 ~----~------~------~------~------~------~ 

2 

1 

0 

Fe0-Si02 

ROENTGEN, WINTERHAGER and KAMMEL (1956) 

FS-16 

FS-18 

-1 ~----~------~----~~------~------~------~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

54 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

K20 (2. 5) , SI02 (97. 5) (X) 

K20(3.9),SI02(96.1) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

SYSTEM 

LN(N) 

8.451 

7.897 

7.484 

7.140 

K20 (6. 3) , SI02 (93. 7) (X) 

K20(9.5),SI02(90.5) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

SYSTEM 

LN(N) 

8.152 

7.438 

6.976 

6.585 

6.286 

K20 (10. 8) , SI02 (89. 2) (X) 

K20(15.9),SI02(84.1) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.604 

1550.00 5.485 

1600.00 5.339 

SYSTEM 

LN(N) 

7.528 

7.073 

6.632 

6.263 

5.849 

5.481 

K20 (16. 9) , SI02 (83 .1) (X) 

K20(24.2),SI02(75.8) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

8.865 

8.474 

7.714 

7.230 

6.724 

6.562 

5.872 

LOG(N) 

3.670 

3.430 

3.250 

3.100 

LOG(N) 

3.540 

3.230 

3.029 

2.860 

2.730 

LOG(N) 

3.270 

3.072 

2.880 

2.720 

2.540 

2.380 

LOG(N) 

3.850 

3.680 

3.350 

3.140 

2.92 

2.850 

2.550 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000 0 0/T (K) (1/K) K s- 1 

N 

4680. 

2690. 

1780. 

1260. 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

, DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000 0 0/T (K) (1/K) K s - 2 

N 

3470. 

1700. 

1070. 

724. 

537. 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000.0/T(K) (1/K) K s- 3 

N 

1860. 

1180. 

759. 

525. 

347. 

240. 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000 0 0/T (K) (1/K) K s- 4 

N 

7080. 

4790. 

2240. 

1380. 

832. 

708. 

355. 

Two-Component Systems 55 
SYSTEM 

K20 {22. 3) , SI02 (77. 7) (X) 

K20(31.1),SI02(68.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1100.00 7.293 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

8.383 

7.808 

7.251 

6.746 

6.286 

5.826 

5.434 

K20 {25. 6) , SI02 (74. 4) (X) 

K20(35.2),SI02{64.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

7.692 

7.115 

6.562 

5.781 

5.595 

5.136 

4.745 

K20(33.4) ,SI02 (66.6) (X) 

K20(48.0),SI02(56.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

7.139 

6.516 

5.966 

5.412 

4.077 

4.421 

4.099 

LOG(N) 

3.641 

3.391 

3.149 

2.930 

2.730 

2.530 

2.360 

LOG(N) 

3.340 

3.090 

2.850 

2.511 

2.430 

2.231 

2.061 

LOG(N) 

3.100 

2.830 

2o591 

2.350 

2.161 

1.920 

1.780 

56 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 A'IMo 

z = 10000. 0/T (K) (1/K) K s- 5 

N 

4370. 

24600 

1410. 

851. 

537. 

339o 

229o 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

z = 10000 0 0/T (K) (1/K) K s- 6 

N 

2190. 

12300 

708. 

324o 

269. 

1700 

1150 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

z = 10000 0 0/T (K) (1/K) K s -7 

N 

1260o 

676. 

390. 

224. 

145. 

83.2 

60o3 
N 

I 

(/') 

~ ~ 

~ ......... ' 

~ 

~ 

K ~ 

N ~ 

0 ~ 

c: V) C) 

I 

0 ~ 

~ 

N ~ 

\.j ~ 

~ 

~ 

~ .. ......,.; 

~ '-J 

C) 

~ 

r--

(3SIOd) A!ISO)SIA ~01 

0 

0 

~ r--

0 

0 

1.1") 

r--

0 

0 

~ r--

0 

0 

M 

r--

0 

0 

N 

r--

0 

0 

r-- or--

............ 

u 

0 

.......... 

w 

~ 

::::> 

~ 0:: 

w 

0... 

~ w 

~ 

Two-Component Systems 57 
4 ~----~------~------~------~------r-----~ 

KS-1 

3 

.....--.. 

UJ 

tl) 

-

0 

a.. 

__.. 

.,_ >-

- KS-6 tl) 2 0 

u 

tl) KS-7 

-

> 

(j 

0 

-I 

1 

K20-Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955) 

0 ~----~~----~------_.------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1) 

58 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUIHOR 

LI20~20.0~,SI02~80.0~ 

~~~ BOCKRIS, MACKENZIE AND KITCHENER 

LI20 11.0 ,SI02 89.0 (1955) MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 

N ~POISES) p = 1.0 ATM. 

T DEGREES C) z = 10000.0/T(K) (1/K) LS-1 

T z LN(N) LOG(N) N 

1400.00 5.977 5.25 2.28 191. 

1450.00 5.804 4.88 2.12 132. 

1500.00 5.640 4.54 1.97 93.3 

1550.00 5.485 4.28 1.86 72.4 

1600.00 5.339 3.89 1.69 49.0 

1650.00 5.200 3.59 1.56 36.3 

1700.00 5.068 3.31 1.44 27.3 ---------------------------------------------------------------------------- SYSTEM 

LI20(25.0),SI02(75.0) (X) 

LI20(14.2),SI02(85.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

LN(N) 

4.77 

4.40 

4. 03 

3.68 

3.36 

3.06 

SYSTEM 

LI20(30.0),SI02(70.0) (X) 

LI20(17.6),SI02(82.4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.745 

4.352 

4.007 

3.661 

3.339 

3.040 

2.766 

SYSTEM 

LI20(33.0),SI02(67.0) (X) 

LI20(19.1),SI02(80.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

4.812 

4.398 

4.007 

3.661 

3.314 

2.996 

2.715 

LOG(N) 

2.07 

1.91 

1.75 

1.60 

1.47 

1.33 

LOG(N) 

2.061 

1.890 

1.740 

1.590 

1.450 

1.320 

1.201 

LOG(N) 

2.090 

1.910 

1.740 

1.590 

1.439 

1.301 

1.179 

AUIHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) L s- 2 

N 

118. 

81.3 

56.2 

39.8 

28.8 

21.4 

AUIHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) L s- 3 

N 

115. 

77.6 

55.0 

38.9 

28.2 

20.9 

15.9 

AUIHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) L s- 4 

N 

123. 

81.3 

55. 

38.9 

27.5 

20.0 

15.1 

Two-Component Systems 59 
SYSTEM 

LI20 (35. 0), SI02 (65. 0) (X) 

LI20(21.1),SI02(78.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.282 

3.892 

3.523 

3.203 

2.901 

2.603 

2.322 

2.063 

SYSTEM 

LI20(40.0),SI02(60.0) (X) 

LI20(25.0) ,SI02(75.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.028 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.570 

3.292 

2.996 

2.741 

2.510 

2.257 

2.049 

1.866 

LI20 (45. 0), SI02 (55. 0) (X) 

LI20(28.9),SI02(71.1) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.187 

1.889 

1.635 

1.381 

1.128 

0.920 

0.693 

SYSTEM 

LI20(50.0),SI02(50.0) (X) 

LI20(33.2) ,SI02(66.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

1.058 

0.807 

0.577 

0.344 

0.140 

-0.041 

LOG(N) 

1.860 

1.690 

1.530 

1.391 

1.260 

1.130 

1.009 

0.896 

LOG(N) 

1.550 

1.430 

1.301 

1.190 

1.090 

0.980 

0.890 

0.810 

LOG(N) 

0.950 

0.820 

0.710 

0.600 

0.490 

0.400 

0.301 

LOG(N) 

0.459 

0.350 

0.250 

0.149 

0.061 

-0.018 

60 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) l S- 5 

N 

72.4 

49.0 

33.9 

24.6 

18.2 

13.5 

10.2 

7.87 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

35.5 

26.9 

20.0 

15.5 

12.3 

9.55 

7.76 

6.46 

AUTHOR 

LS -6 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) l S- 7 

N 

8.91 

6.61 

5.13 

3.98 

3.09 

2.51 

2.00 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) l S -8 

N 

2.88 

2.24 

1.78 

1.41 

1.15 

0.96 
SYSTEM AUTIIOR 

LI20~55.0~ ,SI02~45.0~ 

~~~ BOCKRIS, MACKENZIE AND KITCHENER 

LI20 37.9 ,SI02 62.1 (1955) 

MEASUREMENT ME'IHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 

N ~POISES) p = 1.0 ATM. 

T DEGREES C) z = 10000.0/T(K) (1/K) LS-9 

T z LN(N) LOG(N) N 

1250.00 6.566 -0.083 -0.036 0.92 

1300.00 6.357 -0.288 -0.125 0.75 

1350.00 6.161 -0.462 -0.201 0.63 

1400.00 5.977 -0.635 -0.276 0.53 

1450.00 5.804 -0.799 -0.347 0.45 

Two-Component Systems 61 
a'> 

N 

~ <ll 

1"1 

Q 

<ll 

~ 

s. 

VI 

-< 

a 

::r 

~. 1"1 

1)1 

:I 

Q. 

z .......... a w c 

.. 

e!.. (./') ~ 

0 <ll 

~ 

1)1 

:I a... Q. 

~ ---

>- DT 

<ll 

~ <ll ...... 

c./") 

0 

u 

(./') 

> 

0 

g 

3~--~--~--~----~--~--~--~----~------~----

li20- Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955} 

LS -1 

2 

LS- 2 

1 

0 

LS-5 

LS-6 

LS-7 

LS-8 

-1~--~--~----~--~--~----~--~--~----~--~--~ 

1150 1250 1350 1450 1550 1650 

TEMPERATURE (°C) 
3 ------~--------------~----~~----~------· 

li20-Si02 

BOCKRIS, MACKENZIE and KITCHENER (19.55) 

LS-4 

2 

LS-5 

..---..-

UJ 

V) LS-6 

0 LS -1 

a.. 

---

>- LS-3 

.,_ 

-

V) 1 0 

u 

V") 

-

> 

0 

0 

___. LS-7 

0 LS-8 

LS-9 

-1 ~----~------_.------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS-1

) 

Two-Component Systems 63 
SYSTEM 

LI20!21.5) - N POISES) 

T DEGREES 

SI02 (78. 5) 

C) 

T Z LN (N) 1390.00 

1347.00 

6.013 5.245 

6.173 5.600 

SYSTEM 

LI20!22.9) - SI02(77.1) N POISES) 

T DEGREES C) 

T Z LN(N) 

1403.00 5.967 4.769 

1300.00 6.238 5.588 

SYSTEM 

LI 20 (28. 6) , SI02 (71. 4) (X) 

LI20(12.0),SI02(88.0) (%) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1099.00 7.289 

1200.00 6.789 

1296.00 6.373 

1400.00 5.977 

LN(N) 

6.203 

5.305 

4.442 

3.652 

SYSTEM 

LI20(30.3),SI02{69.7) (X) 

LI20(17.8) ,SI02(82.2) (%) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1000.00 7.856 

1048.00 7.570 

1094.00 7.315 

1143.00 7.062 

1242.00 6.601 

1288.00 6.406 

1391.00 6.010 

LN(N) 

6.754 

6.208 

5.809 

5.420 

4.479 

4.066 

3.293 

SYSTEM 

LI20{32.6),SI02(67.4) (X) 

LI20(19.4),SI02(80.6) (%) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1102.00 7.273 5.358 

1202.00 6.780 4.419 

1302.00 6.350 3.675 

1402.00 5.970 2.991 

LOG(N) 

2.278 

2.431 

LOG(N) 

2.071 

2.427 

LOG(N) 

2.694 

2.304 

1.929 

1.586 

LOG(N) 

2.933 

2.696 

2.523 

2.354 

1.945 

1.766 

1.430 

LOG(N) 

2.327 

1.919 

1.596 

1.299 

64 Viscosity of Synthetic and Natural Melts and Glasses 

A UTI! OR 

SHARTSIS, SPINNER AND CAPPS(1952) 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

189.7 

269.8 

A UTI! OR 

SHARTSIS, SPINNER AND CAPPS(1952) 

P = 1. 0 A'IM. 

LS-10 

z = 10 0 0 0 0 0 /T (K) ( 1 /K) L s - 1 1 

N 

117.8 

267.3 

AUTHOR 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

494.3 

201.4 

84.92 

38.55 

A UTI! OR 

LS- 12 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

857.0 

496.6 

333.4 

225.9 

88.11 

58.35 

26.92 

A UTI! OR 

L S-13 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

212.3 

82.99 

39.45 

19.91 

LS-14 
SYSTEM 

LI20(33.4) ,SI02 (66.6) (X) 

LI20(20.0),SI02(80.0) (%) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1109.00 7.236 

1193.00 6.821 

1290.00 6.398 

1390.00 6.013 

SYSTEM 

LN(N) 

5.181 

4.444 

3.643 

3.095 

LI20(35.9) ,SI02(64.1) 

LI20(21.8) ,SI02(78.2) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

(X) 

(%() 

N (POISES) 

T (DEGREES C) T Z 

1110.00 7.231 

1204.00 6.771 

1307.00 6.329 

1401.00 5.074 

SYSTEM 

LN(N) 

4.679 

3.827 

3.019 

2.480 

LI 20 (38. 7) , SI02 (61. 3) (X) 

LI20(23.9),SI02(76.1) (%) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1099.00 7.310 

1195.00 6.812 

1295.00 6.378 

1386.00 6.028 

SYSTEM 

LN(N) 

3.832 

3.581 

3.081 

2.056 

LI20 (41. 3), SI02 (58. 7) (X) 

LI20(27.8),SI02(72.2) (%) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1095.00 7.310 

1200.00 6.789 

1296.00 6.374 

1393.00 6.002 

LN(N) 

3.832 

2.991 

2.342 

1.826 

LOG(N) 

2.250 

1.930 

1.582 

1.344 

LOG(N) 

2.032 

1.662 

1.311 

1.077 

LOG(N) 

1.664 

1.555 

1.338 

0.893 

LOG(N) 

1.664 

1.299 

1.017 

0.793 

AUTHOR 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

177.8 

85.11 

38.19 

22.08 

AUTHOR 

LS-15 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

107.7 

45.92 

20.46 

11.94 

AUTHOR 

L S-16 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

65.77 

35.89 

21.78 

7.816 

AUTHOR 

LS-17 

SHARTSIS, SPINNER AND CAPPS (1952) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

46.13 

19.91 

10.40 

6.209 

LS-18 

Two-Component Systems 65 
SYSTEM AUTHOR 

MG0~44.3~ ,SI02~55.7~ ~~~ BOCKRIS, MACKENZIE AND 

MGO 34.8 ,SI02 65.2 (1955) MEASUREMENT METHOD DERIVED FROM 

KITCHENER 

ROTATIONAL VISCOMETER TABLE 

N ~POISES) p = 1.0 ATM. 

T DEGREES C) z = 10000. 0/T (K) (1/K) T Z LN(N) LOG(N) N 

1650.00 5.200 1.805 0.784 6.08 

M gS-1 

1700.00 5.068 1.533 0.666 4.63 

1750.00 4.943 1.281 0.556 3.60 

1800.00 4.824 1.040 0.452 2.83 ----------------------------------------------------------------------------- SYSTEM 

MG0(45.1) ,SI02 (54.9) (X) 

MG0(35.5),SI02(64.5) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

2.119 

1.780 

1.520 

1.308 

0.990 

0.737 

MGO (45. 8) , SI02 (54. 2) (X) 

MG0(36.2),SI02(63.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

1.866 

1.558 

1.267 

0.967 

0.718 

0.588 

SYSTEM 

MG0(50.0),SI02(50.0) (X) 

MG0(40.1),SI02(59.9) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

1.151 

0.900 

0.582 

0.399 

0.166 

LOG(N) 

0.920 

0.780 

0.660 

0.568 

0.430 

0.320 

LOG(N) 

0.810 

0.677 

0.550 

0.420 

0.312 

0.255 

LOG(N) 

0.509 

0.391 

0.253 

0.173 

0.072 

66 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8.32 

6.03 

4.57 

3.7 

2.69 

2.09 

AUTHOR 

M gS-2 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) M g s - 3 

N 

6.46 

4.75 

3.55 

2.63 

2.05 

1.80 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 1oooo. o;T (K) (1/K) M 9 s- 4 

N 

3.16 

2.46 

1.79 

1.49 

1.18 
SYSTEM AUTHOR 

MG0~51.4~ ,SI02~48.6~ ~~~ BOCKRIS, MACKENZIE AND KITCHENER 

MGO 41.4 ,SI02 58.6 (1955) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 

N ~POISES) p = 1.0 ATM. 

T DEGREES C) z = 10000.0/T(K) (1/K) MgS-5 

T z LN(N) LOG(N) N 

1650.00 5.200 0.631 0.274 1.88 

1700.00 5.068 0.412 0.179 1.51 

1750.00 4.943 0.215 0.093 1.24 

1800.00 4.824 0.068 0.024 1.07 

Two-Component Systems 67 
..--.. 

UJ 

V') 

0 

a.. 

......... 

.,..._ 

>-

-

V') 

0 

u 

V') 

-

> 

l? 

g 

4 ~----~------~------~------~----~------~ 

3 

2 

1 

Mg0-Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955} 

MS-2 

MS-3 

0 ~----~------~------~------~------~----~ 

1500 1600 1700 1800 

TEMPERATURE (°C) 

68 Viscosity of Synthetic and Natural Melts and Glasses 
..---. 

UJ 

(./) 

0 

a.. 

-....-

._ >-

-(./) 

0 

u 

(./) 

-

> 

l? 

0 

__. 

4 ~----~------~------~----~------~----~ 

3 

2 

1 

Mg0-Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955) 

MS-2 

MS-3 

MS-4 

0 ~----~--~--~------~----~------~----~ 

4 5 6 7 

10 000/T (KELVINS- 1) 

Two-Component Systems 69 
SYSTEM 

MG0(50.0),SI02(50.0) (X) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1600.00 5.339 1.154 

AUTHOR 

RIEBLING (1964) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) LOG(N) N 

0.501 3.17 

70 Viscosity of Synthetic and Natural Melts and Glasses 

MgS-6 
SYSTEM 

NA20(10.0),SI02(90.0) (X) 

NA20 (10. 3) , SI02 (89. 7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

LN(N) 

6.06 

5.62 

5.20 

4.81 

4.44 

SYSTEM 

NA20(15.0),SI02(85.0) (X) 

NA20(15.4),SI02(84.6) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

SYSTEM 

LN(N) 

6.35 

5.89 

5.48 

5.09 

4.79 

4.35 

NA20 (20 o 0) , SI02 (80 o 0) (X) 

NA20(20o5),SI02(79o5) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250o00 6o566 

1300o00 6o357 

1350o00 6o161 

1400o00 5o977 

1450o00 5o804 

1500o00 5o640 

SYSTEM 

LN(N) 

5.87 

5o41 

5.02 

4.61 

4.26 

3o89 

NA20 (25. 0) , SI02 (75. 0) (X) 

NA20(25.6),SI02(74.4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250o00 6.566 

1300.00 6.357 

1350.00 6.161 

1400o00 

1450o00 

1500.00 

5o977 

5.804 

5.680 

LN(N) 

6o38 

5.919 

5.481 

5.069 

4.673 

4.352 

3.983 

3.661 

LOG(N) 

2.63 

2o44 

2.26 

2.10 

1.93 

LOG(N) 

2.76 

2.56 

2.38 

2.21 

2o08 

1.89 

LOG(N) 

2.55 

2o35 

2.18 

2.00 

1o85 

1.69 

LOG(N) 

2.77 

2.571 

2o380 

2.201 

2.029 

1.890 

1o730 

1.590 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

427. 

275. 

1820 

123. 

85.1 

AUTHOR 

NS-1 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) N s- 2 

N 

575. 

363. 

240o 

162. 

120. 

77.6 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1o0 ATM. 

z = 10000. 0/T (K) (1/K) N s- 3 

N 

355. 

224. 

151. 

100. 

70o8 

49.0 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

5890 

372. 

240o 

159. 

107. 

77.6 

53.7 

38.9 

N S-4 

Two-Component Systems 71 
SYSTEM 

NA20 (27 o 0), SI02 (73 o 0) (X) 

NA20(27o6),SI02(72o4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150o00 7o027 

1200o00 6o789 

1250o00 6o566 

1300o00 6o357 

1350o00 6o161 

1400o00 5o977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6o080 

5.617 

5o226 

4o836 

4.490 

4.122 

3o822 

3.523 

SYSTEM 

NA20(30oO),SI02(70.0) (X) 

NA20(30o7) ,SI02(69o3) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

6.240 

5.756 

5.298 

4.860 

4.467 

4.076 

3.731 

3.384 

NA20 (33. 0) , SI02 (67. 0) (X) 

NA20(33.7),SI02(66.3) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

5.869 

5.389 

4.905 

4.467 

4.099 

3.706 

3.339 

1.310 

LOG(N) 

2.641 

2o439 

2.270 

2.100 

1.950 

1.790 

1.660 

1.530 

LOG(N) 

2.710 

2.500 

2.301 

2.111 

1.940 

1.770 

1.620 

1.470 

LOG(N) 

2.549 

2.340 

2.130 

1.940 

1.780 

1.610 

1.450 

3.016 

72 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) N s- 5 

N 

437. 

275. 

186. 

126. 

89o1 

61.7 

45o7 

33.9 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) N s -6 

N 

513. 

316. 

200. 

129. 

87.1 

58.9 

41.7 

29.5 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) N s- 7 

N 

354. 

219. 

135. 

87.1 

60.3 

40.7 

28.2 

20.4 
SYSTEM AUTHOR 

NA20~35.0~,SI02~65.0~ ~~~ BOCKRIS, MACKENZIE AND KITCHENER 

NA20 35.8 ,SI02 64.2 (1955) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 

N ~POISES) p = 1.0 A'IM. 

T DEGREES C) z = 10000. 0/T (K) (1/K) N S-8 

T z LN(N) LOG(N) N 

1100.00 7.283 5.572 2.420 263. 

1150.00 7.027 5.088 2.210 162. 

1200.00 6.789 4.625 2.009 102. 

1250.00 6.566 4.237 1.840 69.2 

1300.00 6.357 3.846 1.670 46.8 

1350.00 6.161 3.478 1.511 32.4 

1400.00 5.977 3.131 1.360 22.9 

1450.00 5.804 2.809 1.220 16.6 

1500.00 5.640 2.485 1.079 12.0 

Two-Component Systems 73 
M~IJ") ao I I I I 

V')V')t/') V') 

zzz z 

N 

0 

(./') 

I 

0 

N 

0 

z 

M N ~ 

(3SIOd) A!ISO)SI/\ ~01 

74 Viscosity of Synthetic and Natural Melts and Glasses 

~ 

....... 

~ 

'-

~ 

~ 

~ " ~ 

"' c: 

~ 

~ 

~ 

~ '-' 

~ ~ ... 

~ 

~ C) 

~ 

0 

0 

..0 

~ 

0 

0 

1.1') 

~ 

0 

0 

~ ~ 

0 

0 

M 

~ 

0 

0 

N 

~ 

0 

0 

~ 

a~ 

__...,. 

u 

0 

.......... 

w 

~ 

:::> 

~ ~ 

w 

a.. 

~ w 

t-
4~----~------~------~----~------~------~ 

Na20-Si02 

BOCKHIS, MACKENZIE and KITCHENER (1955) 

3 

__....... 

UJ 

V') 

-

0 

a.. 

...__..... 

...._ >-

-

V') 2 0 NS-1 

u 

V') 

- NS-3 > 

(j 

0 

_,J 

NS-8 

1 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1) 

Two-Component Systems 75 
SYSTEM 

NA20 (21. 38) I SI02 (78. 62) (X) 

NA20(21.91) 1 SI02(78.09) (%) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

850.00 8.905 

927.00 8.333 

1003.00 7.837 

1078.00 7.402 

1155.00 7.003 

1207.00 6.757 

1258.00 6.532 

1309.00 6.321 

1360.00 6.124 

1406.00 5.956 

SYSTEM 

LN(N) 

11.439 

9.991 

8.777 

7.794 

6.942 

6.417 

5.966 

5.540 

5.158 

4.817 

NA20 (24 0 31) I SI02 (75 0 69) (X) 

NA20(24.89),SI02(75.11) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

820.00 9.149 

893.00 8.576 

970.00 8.045 

1046.00 7.582 

1119.00 7.184 

1206.00 6.761 

1256.00 6.540 

1305.00 6.337 

1357.00 6.135 

LN(N) 

11.453 

10.014 

8.752 

7.730 

6.876 

6.017 

5.586 

5.183 

4.805 

1404.00 5.963 4.476 

SYSTEM 

NA20 (25 .19) I SI02 (74 0 81) (X) 

NA20(25.78) 1 SI02(74.22) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

800.00 9.320 

904.00 8.496 

1003.00 7.837 

1104.00 7.262 

1152.00 7.018 

1201.00 6.784 

1254.00 6.549 

1307.00 6.329 

1356.00 6.139 

1403.00 5.967 

LN(N) 

11.762 

9.664 

8.140 

6.915 

6.397 

5.922 

5.496 

5.070 

4.688 

4.380 

LOG(N) 

4.968 

4.339 

3.812 

3.385 

3.015 

2.787 

2.591 

2.406 

2.240 

2.092 

LOG(N) 

4.974 

4.349 

3.801 

3.357 

2.986 

2.613 

2.426 

2.251 

2.087 

1.944 

LOG(N) 

5.108 

4.197 

3.535 

3.003 

2.778 

2.572 

2.387 

2.202 

2.036 

1.902 

76 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

92900. 

21800. 

6486.34 

2426.61 

1035.14 

612.35 

389.94 

254.68 

173.78 

123.59 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

94200. 

22300. 

6324.12 

2275.10 

968.28 

410.20 

266.69 

178.24 

122.18 

87.90 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.28*10E 5 

1.57*10E 4 

3427.68 

1006.93 

599.79 

373.25 

243.78 

159.22 

108.64 

79.80 

NS-9 

NS-10 

NS-11 
SYSTEM 

NA20 (25. 97) , SI02 (74. 03) (X) 

NA20(26.57),SI02(73.43) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

800.00 9.320 

840.00 8.985 

910.00 8.453 

990.00 7.918 

1091.00 7.331 

1189.00 6.840 

1230.00 6.653 

1270.00 6.481 

1311.00 6.313 

1354.00 6.146 

1395.00 5.995 

SYSTEM 

LN(N) 

11.709 

10.818 

9.507 

8.248 

6.986 

5.996 

5.616 

5.287 

4.962 

4.665 

4.375 

NA20~26.18~,SI02~73.82~ 

NA20 26.79 ,SI02 73.21 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N ~POISES) T DEGREES C) 

T z LN(N) 

802.00 9.302 11.561 

903.00 8.503 9.537 

1002.00 7.843 8.004 

1102.00 7.273 6.816 

1180.00 6.882 6.024 

1232.00 6.645 5.554 

1282.00 6.431 5.135 

1324.00 6.262 4.817 

1361.00 6.120 4.545 

1403.00 5.967 4.264 

SYSTEM 

~~~ 

NA20 (27. 83) , SI02 (72 .17) (X) 

NA20(28.46),SI02(71.54) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

801.00 9.311 

903.00 8.503 

1003.00 7.837 

1103.00 7.267 

1152.00 7.018 

1201.00 6.784 

1253.00 6.553 

1302.00 6.349 

1354.00 6.146 

1403.00 5.967 

LN(N) 

13.343 

9.307 

7.808 

6.641 

6.123 

5.653 

5.172 

4.849 

4.444 

4.103 

LOG(N) 

5.085 

4.698 

4.129 

3.582 

3.034 

2.604 

2.439 

2.296 

2.155 

2.026 

1.900 

LOG(N) 

5.021 

4.142 

3.476 

2.960 

2.616 

2.412 

2.230 

2.092 

1.974 

1.852 

LOG(N) 

4.926 

4.042 

3.391 

2.884 

2.659 

2.455 

2.246 

2.106 

1.930 

1.782 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.22*10E 5 

4.99*10E 4 

1.35*10E 4 

3819.44 

1081.43 

401.79 

274.79 

197.70 

142.89 

106.17 

79.43 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

p = 1.0 ATM. 

z = 10000.0/T(K) (1/K) 

N 

1.05*10E5 

1.39*10E4 

2992.26 

912.01 

413.05 

258.23 

169.82 

123.59 

94.19 

71.12 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8.43*10E4 

1.10*10E4 

2460.37 

765.60 

456.04 

285.10 

176.20 

127.64 

85.11 

60.53 

NS-12 

NS-13 

NS-14 

Two-Component Systems 77 
5.5 .-----.----,----r-----,r-----r--.--~~r----,---.--..--r----r-1 

~ 

~ 4.5 

0 

o_ 

-

>- ......_ 

V) 3.5 

0 

u 

V) 

> 

<J 

0 2.5 

_J Na20-Si02 

LILLIE (1939) 

1.5 L____l _ __L_--l,_ _ _J_ _ _j__.J...____JL------l.---L.----L...--'---L---......____. 

750 850 950 1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
-

>-

1--

4.5 

()3.5 

u 

(/) 

> 

<-? 

0 

._J 

2.5 

NS-13 

Na20 -Si02 

LILLIE (1939) 

1.5 ...__--~------~--~-----1-----L--~------~---~ 

5.5 6.5 7.5 8.5 9.5 

10 000/T (KELVINS- 1

) 

Two-Component Systems 79 
SYSTEM 

NA20 (29 .14) I SI02 (70. 86) (X) 

NA20(29.79),SI02(70.21) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

851.00 8.897 

899.00 8.532 

951.00 8.170 

1001.00 7.849 

1098.00 7.294 

1199.00 6.793 

1240.00 6.609 

1282.00 6.431 

1317.00 6.289 

1361.00 6.120 

1402.00 5.970 

SYSTEM 

LN(N) 

10.065 

9.176 

8.356 

7.633 

6.498 

5.515 

5.162 

4.829 

4.515 

4.241 

3.958 

NA20 (31. 07) I SI02 (68. 93) (X) 

NA20(31.74),SI02(68.26) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

848.00 8.921 

889.00 8.606 

949.00 8.183 

1009.00 7.800 

1079.00 7.396 

1176.00 6.901 

1220.00 6.698 

1260.00 6.523 

1301.00 6.353 

1399.00 5.981 

LN(N) 

9.770 

9.017 

8.084 

7.262 

6.459 

5.466 

5.096 

4.757 

4.444 

3.744 

SYSTEM 

NA20(32.23),SI02(67.77) (X) 

NA20(32.91),SI02(67.09) (%) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES· C) T Z 

785.00 9.452 

824.00 9.116 

866.00 8.780 

908.00 8.467 

989.00 7.924 

1091.00 7.331 

1096.00 7.305 

1197.00 6.803 

1239.00 6.614 

1280.00 6.439 

1320.00 6.277 

1362.00 6.116 

1401.00 5.974 

LN(N) 

10.926 

10.074 

9.236 

8.573 

7.375 

6.157 

6.123 

5.149 

4.801 

4.476 

4.181 

3.887 

3.622 

LOG(N) 

4.371 

3.985 

3.629 

3.315 

2.822 

2.395 

2.242 

2.097 

1.961 

1.842 

1.719 

LOG(N) 

4.243 

3.916 

3.511 

3.154 

2.805 

2.374 

2.213 

2.066 

1.930 

1.626 

LOG(N) 

4.745 

4.375 

4.011 

3.723 

3.203 

2.674 

2.659 

2.236 

2.085 

1.944 

1.816 

1.688 

1.573 

80 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z. = 10000. 0/T (K) (1/K) 

N 

23500. 

9660.51 

4255.98 

2065.38 

663.74 

248.31 

174.58 

125.03 

91.41 

69.50 

52.36 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17500. 

8241.38 

3243.40 

1425.61 

638.26 

236.59 

163.31 

116.41 

85.11 

42.27 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

55600. 

23700. 

10300. 

5284.45 

1595.88 

472.06 

456.04 

172.19 

121.19 

87.90 

65.46 

48.75 

37.41 

NS-15 

NS-16 

NS-17 
5 ~~--~----------~--~~~~--~--~--~--~--~~ 

_.......... 4 

w 

(./') 

-

0 

a.. 

...__.. 

~ 

I- 3 

V) -

0 

u 

V) 

-

> 

~ 

0 

__. 

21 Na20-Si02 

LILLIE (1939) 

1 ~~----------~--~--~--~~--~--~--~--~--~~" 

~0 850 950 1050 1150 1250 1350 1450 

TEMPERATURE {°C) 
..---.. 

w 

c.l) 

-

0 

.....,_ 

~ 

>- 1-

c.l) 

0 

u 

c.l) 

-

> 

~ 

g 

4 

3 

2 

1 

5.5 6.5 

NS-14 

Na20-Si02 

LILLIE /1939) 

7.5 8.5 

10 000/T {KELVINS-1) 

82 Viscosity of Synthetic and Natural Melts and Glasses 

9.5 
SYSTEM 

NA20 (32 .55), SI02 (67 .45) (X) 

NA20(33.24) ,SI02(66.76) (%) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

888.00 8.613 

988.00 7.930 

1084.00 7.369 

1188.00 6.845 

1290.00 6.398 

1392.00 6.006 

SYSTEM 

LN(N) 

8.805 

7.345 

6.192 

5.188 

4.386 

3.650 

NA20~33.08~ ,SI02~66.92~ NA20 33.77 ,SI02 66.23 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N fPOISES) T DEGREES C) 

T z LN(N) 

787.00 9.434 10.705 

827.00 9.091 9.853 

869.00 8.757 9.054 

911.00 8.446 8.372 

992.00 7.905 7.200 

1094.00 7.315 6.024 

1199.00 6.793 5.024 

1240.00 6.609 4.681 

1282.00 6.431 4.361 

1323.00 6.266 4.094 

1365.00 6.105 3.760 

1404.00 5.963 3.484 

SYSTEM 

~~~ 

NA20 (33. 57) , SI02 (66. 43) (X) 

NA20(34.27),SI02(65.73) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

831.00 9.058 

871.00 8.741 

912.00 8.439 

992.00 7.905 

1092.00 7.326 

1192.00 6.826 

1231.00 6.649 

1269.00 6.485 

1312.00 6.309 

1352.00 6.154 

1393.00 6.002 

LN(N) 

9.735 

9.001 

8.340 

7.200 

6.028 

5.061 

4.711 

4.430 

4.115 

3.829 

3.557 

LOG(N) 

3.824 

3.190 

2.689 

2.253 

1.905 

1.585 

LOG(N) 

4.649 

4.279 

3.932 

3.636 

3.127 

2.616 

2.182 

2.033 

1.894 

1.778 

1.633 

1.513 

LOG(N) 

4.228 

3.909 

3.622 

3.127 

2.618 

2.198 

2.046 

1.924 

1.787 

1.663 

1.545 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

6668.07 

1548.82 

488.65 

179.06 

80.35 

38.46 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

p = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

44600. 

19000. 

8550.67 

4325.14 

1339.68 

413.05 

152.05 

107.89 

78.34 

59.98 

42.95 

32.58 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

16900. 

8109.61 

4187.94 

1339.68 

414.95 

157.76 

111.17 

83.95 

61.24 

46.03 

35.08 

NS-18 

NS-19 

NS-20 

Two-Component Systems 83 
SYSTEM 

NA20 (34. 22) , SI02 (65. 78) (X) 

NA20(34.92),SI02(65.08) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

785.00 9.452 

828.00 9.083 

867.00 8,772 

911.00 8.446 

1044.00 7.593 

1157.00 6.993 

1197.00 6.803 

1236.00 6.627 

1281.00 6.435 

1322.00 6.270 

1363.00 6.112 

1405.00 5.959 

SYSTEM 

LN(N) 

10.682 

9.733 

8.989 

8.275 

6.479 

5.296 

4.930 

4.589 

4.285 

3.963 

3.675 

3.401 

NA20 (36. 01) , SI02 (63. 99) (X) 

NA20(36.73),SI02(63.27) (%) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

831.00 9.058 

907.00 8.475 

983.00 7.962 

1058.00 7.513 

1132.00 7.117 

1209.00 6.748 

1259.00 6.527 

1311.00 6.313 

1361,00 I 6,120 

1410.00 5.942 

LN(N) 

9.429 

8.096 

7.000 

6.120 

5.333 

4.628 

4.241 

3.852 

3.491 

3.136 

LOG(N) 

4.639 

4.227 

3.904 

3.594 

2.814 

2.300 

2.141 

1.993 

1.861 

1.721 

1.596 

1.477 

LOG(N) 

4.095 

3.516 

3.040 

2.658 

2.316 

2.010 

1.842 

1.673 

1.516 

1.362 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

43600. 

16900. 

8016.78 

3926.45 

651.63 

199.53 

138.36 

98.40 

72.61 

52.60 

39.45 

29.99 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12400. 

3280.95 

1096.48 

454.99 

207.01 

102.33 

69.50 

47.10 

32.81 

23.01 

NS-21 

NS-22 

-----------------------------------------------------------------------------~ 

SYSTEM 

NA20 (39. 00), SI02 (61. 00) (X) 

NA20(39.74),SI02(60.26) (%) MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

793.00 9.381 

891.00 8.591 

992.00 7.905 

1096.00 7.305 

1194.00 6.817 

1246.00 6.583 

1297.00 6.369 

1346.00 6.177 

1397.00 5.988 

LN(N) 

9.643 

7.833 

6.431 

5.250 

4.322 

3.889 

3.484 

3.122 

2.768 

LOG(N) 

4.188 

3.402 

2.793 

2.280 

1.877 

1.689 

1.513 

1.356 

1.202 

84 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

LILLIE (1939) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

15400. 

2523.48 

620.87 

190.55 

75.34 

48.87 

32.58 

22.70 

15.92 

NS-23 
.......... 

w 

V') -

0 

o_ 

......... 

>- 1-

V') -

0 

u 

V') -

> 

~ 

g 

5~----~------~--~--~~--~------~--------~~~ 

4 

31 

I 

I 

I 

21 

1 

750 

Na20-Si02 

lilliE (1939) 

850 

~ "-~ .NS-19 

~~~ I NS-20 

~ ~~ I I NS-21 

~ ~~ I I I .NS-22 

950 1050 1150 1250 1350 1450 

TEMPERATURE {°C) 
_.... 

UJ 

(./) 

0 

a... 

-

>-

I--

(./) 

0 

u 

(./) 

-

> 

0 

0 

__J 

4 

3 

2 

1 

5.5 

Na20-Si02 

LILLIE I 19.39) 

6.5 7.5 8.5 

10 000/T (KELVINS-1) 

86 Viscosity of Synthetic and Natural Melts and Glasses 

9.5 
SYSTEM 

SRO (20 .1) I SI02 (79. 9) (X) 

SR0(30.3) 1 SI02(69.7) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

4.387 

4.064 

3.764 

SRO (25. 4) I SI02 (74. 6) (X) 

SR0(37.1) 1 SI02(62.9) (%0) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

4.127 

3.742 

3.332 

3.109 

2.809 

SRO (29. 7) I SI02 (70. 3) (X) 

SR0(42.2) 1 SI02(57.8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

3.292 

2.923 

2.625 

2.322 

2.049 

1.754 

SYSTEM SR0(40.5)~SI02(59.5) (X) 

SR0(54.0) 1 SI02(46.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

2.443 

2.086 

1.823 

1.567 

1.316 

1.082 

LOG(N) 

1.905 

1.765 

1.634 

LOG(N) 

1.792 

1.625 

1.447 

1.350 

1.220 

LOG(N) 

1.430 

1.270 

1.140 

1.009 

0.890 

0.762 

LOG(N) 

1.061 

0.906 

0.792 

0.680 

0.572 

0.470 

AUTHOR 

BOCKRIS 1 MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) 

N 

80.4 

58.2 

43.1 

AUTHOR 

(1/K) SS-1 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) S S- 2 

N 

62.0 

42.2 

28.0 

22.4 

16.6 

AUTHOR 

BOCKRIS 1 MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) S S- 3 

N 

26.9 

18.6 

13.8 

10.2 

7.76 

5.78 

AUTHOR 

BOCKRIS 1 MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) S S- 4 

N 

11.5 

8.05 

6.19 

4.79 

3.73 

2.95 

Two-Component Systems 87 
SYSTEM 

SR0(44.4),SI02(55.6) (X) 

SR0(58.0),SI02(42.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.841 

1.585 

1.275 

1.033 

0.761 

0.599 

SRO (50. 3), SI02 (49. 7) (X) 

SR0(63.6),SI02(36.4) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

1.157 

-0.755 

0.668 

0.451 

0.262 

LOG(N) 

0.799 

0.688 

0.554 

0.449 

0.330 

0.260 

LOG(N) 

0.502 

-0.328 

0.290 

0.196 

0.134 

88 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000.0/T(K) 

N 

6.30 

4.88 

3.58 

2.81 

2.14 

1.82 

AUTHOR 

(1/K) SS-5 

BOCKRIS, MACKENZIE AND KITCHENER 

(1955) 

DERIVED FROM 

TABLE 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 8 8- 6 

N 

3.18 

0.47 

1.95 

1.57 

1.30 
4------~------~------~----~------~----~ 

Sr0-Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955) 

3 

__....._ 

UJ 

V') 

0 

a.. 

..__.. 

>- 1-

-

V') 2 0 

u 

V') 

-

> 

<-' 0 SS-3 

__, 

1 SS-4 

SS-5 

0 ~----~------~------~----~------~----~ 

1500 1600 1700 1800 

TEMPERATURE {°C) 

Two-Component Systems 89 
,....... 

UJ 

ll') 

0 

a.. 

>- 1-

4 ~------~--------------------~------~------~ 

Sr0-Si02 

BOCKRIS, MACKENZIE and KITCHENER (1955) 

3 

ll') 2 

0 

/

SS-1 

u 

ll') SS-2 

> 

{) 

0 

......J 

1 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

90 Viscosity of Synthetic and Natural Melts and Glasses 
Three-Component Systems 

Three-Component Systems 91 
SYSTEM AUTHOR 

AL203(9.1),CA0(38.9),SI02(52.0) (X) 

MEASUREMENT METHOD 

BILLS (1963) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.641 

4.835 

4.329 

3.753 

3.224 

2.878 

LOG(N) 

2.45 

2.10 

1.88 

1.63 

1.40 

1.25 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

281.8 

125.9 

75.86 

42.66 

25.12 

17.78 

ACS -1 

--------------------------------------------------------------------------- SYSTEM 

AL203(12.4) ,CA0(45.2),SI02(42.3) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N ~POISES) T DEGREES C) 

T Z LN(N) 1250.00 6.566 4.971 

1300.00 6.357 4.122 

1350.00 6.161 3.569 

1400.00 5.977 3.062 

1450.00 5.804 2.613 

1500.00 5.640 2.118 

SYSTEM 

AL203(10.96),CA0(18.12), 

SI02 (70. 92) (X) 

AL203(17.6),CA0(16.0), 

SI02 (67 .1) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

9.582 

8.941 

8.232 

7.512 

AL203(15.43) ,CA0(18.31), 

SI02 (66. 27) (X) 

AL203(23.9) ,CA0(15.6), 

SI02 (60. 5) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

9.547 

8.759 

8.016 

7.272 

LOG(N) 

2.17 

1.79 

1.55 

1.33 

1.135 

0.92 

LOG(N) 

4.161 

3.883 

3.575 

3.262 

LOG(N) 

4.146 

3.804 

3.481 

3.158 

92 Viscosity of Synthetic and Natural Melts and Glasses 

(X) 

p 

z 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

TABLE = 1.0 ATM. = 10000.0/T(K) (1/K) 

N 

147.9 

61.66 

35.48 

21.38 

13.65 

8.318 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

AC S -2 

z = 10000. 0/T (K) (1/K) A c S-3 

N 

14500. 

7640. 

3760. 

1830. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

14000. 

6370. 

3030. 

1440. 

{1/K) ACS-4 
SYSTEM 

AL203(17.78) ,CA0(18.57), 

SI02 (63. 64) (X) 

AL203(27.5) ,CA0(15.8), 

SI02 (58. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1400.00 5.977 7.601 

1450.00 5.804 6.846 

SYSTEM 

AL203(12.65) ,CA0(20.94), 

SI02 (66. 42) (X) 

AL203(20.1) ,CA0(18.3), 

SI02 (62. 2) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

9.629 

8.825 

8.036 

7.320 

6.659 

LOG(N) 

3.301 

2.973 

LOG(N) 

4.182 

3.833 

3.490 

3.179 

2.892 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

z = 10000.0/T(K) (1/K) ACS-5 

N 

2000. 

940. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1 /K) A c s - 6 

N 

15200. 

6800. 

3090. 

1510. 

780. 

------------------------------------------------------------------------------ SYSTEM 

AL203(17.74) ,CA0(22.81), 

SI02 (59. 45) (X) 

AL203(27.3) ,CA0(19.3), 

SI02 (53.9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1400.00 5.977 6.721 

1450.00 5.804 5.858 

SYSTEM 

AL203(14.16) ,CA0(24.26), 

SI02 (61. 58) (X) 

AL203(22.4) ,CA0(21.1), 

SI02 (57. 4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

8.810 

7.886 

7.107 

6.380 

LOG(N) 

2.919 

2.544 

LOG (N) 

3.826 

3.425 

3.086 

2.771 

1450.00 5.804 5.753 2.498 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

830. 

350. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

ACS-7 

z = 10000.0/T(K) (1/K) ACS-8 

N 

6700. 

2660. 

1220. 

590. 

315. 

Three-Component Systems 93 
SYSTEM 

AL203(10.43},CA0(24.63), 

SI02 (64. 94) (X) 

AL203(16.7),CA0(21.7), 

SI02 (61. 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

9.449 

8.560 

7.701 

6.947 

6.273 

5.670 

AL203(7.54l,CA0(26.11), 

SI02(66.35 (X) 

AL203(12.5 ,CA0(23.8), 

SI02 (64. 8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

9.185 

8.221 

7.384 

6.659 

6.040 

5.481 

AL203(13.80) ,CA0(37.49), 

SI02 ( 48. 71) (X) 

AL203(25.1) ,CA0(23.7), 

SI02 (52. 2) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1300.00 

1350.00 

1400.00 

1450.00 

6.357 

6.161 

5.977 

5.804 

7.056 

6.254 

5.598 

4.977 

LOG(N) 

4.104 

3.718 

3.344 

3.017 

2.724 

2.462 

LOG(N) 

3.989 

3.571 

3.207 

2.892 

2.623 

2.380 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 A'IM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A c s - 9 

N 

12700. 

5220. 

2210. 

1040. 

530. 

290. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 A'IM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A c s - 1 0 

N 

9750. 

3720. 

1610. 

780. 

420. 

240. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 A'IM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A c s - 1 1 

LOG(N) N 

3.064 

2.716 

2.431 

2.161 

1160. 

520. 

270. 

145. 

94 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(10.57) ,CA0(29.05), 

SI02 (60. 38) (X) 

AL203(17.2) ,CA0(26.0), 

SI02 (57. 9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

8.366 

7.450 

6.579 

5.829 

5.193 

4.787 

SYSTEM 

AL203(11.77),CA0(37.43), 

SI02 (50. 80) (X) 

AL203(21.2),CA0(25.4), 

SI02 (53.9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

8.319 

7.320 

6.492 

5.814 

5.273 

4.745 

AL203(6.75l ,CA0(34.31), SI02 (58. 94 (X) 

AL203(11.2 ,CA0(31.3), 

SI02(57.6) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

5.598 

5.011 

4.605 

3.912 

SYSTEM 

AL203(12.40),CA0(34.32), 

SI02 (53. 28) (X) 

AL203(19.9) ,CA0(30.3), 

SI02 (50. 4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.293 

6.346 

5.521 

4.868 

4.382 

4.007 

LOG(N) 

3.633 

3.236 

2.857 

2.531 

2.255 

2.079 

LOG(N) 

3.613 

3.179 

2.820 

2.525 

2.290 

2.061 

LOG(N) 

2.431 

2.176 

2.000 

1.699 

LOG(N) 

3.167 

2.756 

2.398 

2.114 

1.903 

1.740 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) A c S-1 2 

N 

4300. 

1720. 

720. 

340. 

180. 

120. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

ACS-13 

4100. 

1510. 

660. 

335. 

195. 

115. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) A c S-14 

N 

270. 

150. 

100. 

50.0 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1470. 

570. 

250. 

130. 

80. 

55. 

ACS-15 
-UJ 

(./') 

0 

a... 

-

>-

I5 

4 

(./') 3 

0 

u 

(./') 

> 

l') 

0 

.....J 

2 

1 

1150 

ACS-9 

ACS -12-.. 

Al 20 3- CoO -Si02 

JOHANNSEN and BRUNION (1959) 

1250 1350 

TEMPERATURE (°C) 

96 Viscosity of Synthetic and Natural Melts and Glasses 

ACS-10 

ACS-11 

ACS-13 

ACS-15 

ACS-14 

1450 
............ 

w 

lf) 

-

0 

a.. 

~ 

>-

..... 

lf) -

0 

u 

lf) 

-

> 

<-' 0 

__, 

5 ~----~~----~----------------------~------~ 

4 

3 

2 

1 

5 

ACS-7 

ACS-8 

ACS-9 

ACS-11 

ACS-12 

ACS-13 

ACS-15 

ACS-10 

ACS-14 

Al20 3- CoO- Si02 

JOHANNSEN and BRUNION (1959) 

6 7 

10 000/T (KELVINS-1

) 

8 

Three-Component Systems 97 
SYSTEM 

AL203(26.83),CA0(73.17), 

SI02 (0. 0) (X) 

AL203(40.0),CA0(60.0), 

SI02(0.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1900.00 4.602 

SYSTEM 

LN(N) 

0.095 

-0.223 

-0.357 

-0.511 

-0.693 

AL203(35.48) ,CA0(64.52), 

SI02 (0. 0) (X) 

AL203(50.0) ,CA0(50.0), 

SI02 (0. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

2.163 

1.740 

1.253 

0.833 

0.470 

0.182 

0.953 

0.000 

LOG(N) 

0.041 

-0.097 

-0.155 

-0.222 

-0.301 

LOG(N) 

0.940 

0.756 

0.544 

0.362 

0.204 

0.079 

0.041 

0.000 

AL203(39.23) ,CA0(60.77) (X) 

SI02 (0. 0) (X) 

AL203(54.0) ,CA0(46.0), 

SI02(0.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

LN(N) 

1.792 

1.386 

0.993 

0.693 

0.405 

0.182 

LOG (N) 

0.778 

0.602 

0.431 

0.301 

0.176 

0.079 

98 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.1 

0.8 

0.7 

0.6 

0.5 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) 

N 

8.7 

5.7 

3.5 

2.3 

1.6 

1.2 

1.1 

1.0 

(1/K) 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.0 

4.0 

2.7 

2.0 

1.5 

1.2 

A c s- 1 a 

ACS-17 

ACS-18 
SYSTEM 

AL203(45.21),CA0(54.79), 

SI02 (0. 0) (X) 

AL203(60.0) ,CA0(40.0), 

SI02 (0. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

LN(N) 

1.629 

1.194 

0.833 

0.531 

0.262 

0.095 

LOG(N) 

0.708 

0.519 

0.362 

0.230 

0.114 

0.041 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

5.1 

3.3 

2.3 

1.7 

1.3 

1.1 

ACS-19 

------------------------------------------------------------------------------

SYSTEM 

AL203(56.20) ,CA0(43.80), 

SI02 (0. 0) (X) 

AL203(70.0) ,CA0(30.0), 

SI02(0.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

0.588 

0.336 

0.095 

AL203(68.75) ,CA0(31.25), 

SI02 (0. 0) (X) 

AL203(80.0),CA0(20.0), 

SI02 (0. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

0.095 

-0.105 

-0.357 

-0.511 

-0.511 

SYSTEM 

AL203(100.0),CAO(O.O), 

SI02 (0. 0) (X) 

AL203(100.0),CAO(O.O), 

SI02 (0. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

2050.00 4.305 -0.511 

2100.00 4.214 -0.693 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

LOG(N) N 

0.255 1.8 

0.146 1.4 

0.041 1.1 

LOG(N) 

0.041 

-0.046 

-0.155 

-0.222 

-0.222 

LOG(N) 

-0.222 

-0.301 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED E'ROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.1 

0.9 

0.7 

0.6 

0.6 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

0.6 

0.5 

ACS-20 

ACS-21 

ACS-22 

Three-Component Systems 99 
SYSTEM 

AL203(19.22) 1 CA0(69.91), 

SI02 (10. 87) (X) 

AL203(30.0) ,CA0(60.0), 

SI02(10.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

0.788 

0.262 

0.000 

-0.223 

-0.357 

-0.511 

-0.693 

-0.916 

LOG(N) 

0.342 

0.114 

0.000 

-0.097 

-0.155 

-0.222 

-0.301 

-0.398 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.2 

1.3 

1.0 

0.8 

0.7 

0.6 

0.5 

0.4 

ACS-23 

------------------------------------------------------------------------------

SYSTEM 

AL203(27.05),CA0(61.48), 

SI02 (11. 47) (X) 

AL203(40.0) ,CA0(50.0), 

SI02(10.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

SYSTEM 

LN(N) 

2.041 

1.609 

1.194 

0.833 

0.531 

0.405 

0.182 

0.000 

-0.105 

-0.223 

AL203(35.79) ICA0(52.06) I 

SI02 (12 .15) (X) 

AL203(50.0) ICA0(40.0) I 

SI02 (10. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

1.649 

1.224 

0.833 

0.531 

0.336 

0.182 

0.000 

0.000 

LOG(N) 

0.886 

0.699 

0.519 

0.362 

0.230 

0.176 

0.079 

0.000 

-0.046 

-0.097 

LOG(N) 

0.716 

0.531 

0.362 

0.230 

0.146 

0.079 

0.000 

0.000 

1 00 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

7.7 

5.0 

3.3 

2.3 

1.7 

1.5 

1.2 

1.0 

0.9 

0.8 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.2 

3.4 

2.3 

1.7 

1.4 

1.2 

1.0 

1.0 

ACS-24 

ACS-25 
SYSTEM 

AL203(40.56),CA0(46.93), 

SI02 (12. 51) (X) 

AL203(55.0) ,CA0(35.0), 

SI02 (10. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

1.361 

0.956 

0.642 

0.470 

0.336 

AL203(51.01) ,CA0(35.67), 

SI02 (13. 32) (X) 

AL203(65.0) ,CA0(25.0), 

SI02 (10. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

0.788 

0.531 

0.336 

0.182 

AL203{19.37) ,CA0(58.71), 

SI02 (21. 92) (X) 

AL203{30.0) ,CAO(SO.O), 

SI02 (20. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

2000.00 4.399 

LN(N) 

0.875 

0.588 

0.336 

0.182 

0.000 

-0.223 

-0.357 

-0.511 

LOG(N) 

0.591 

0.415 

0.279 

0.204 

0.146 

LOG(N) 

0.342 

0.230 

0.146 

0.079 

LOG(N) 

0.380 

0.255 

0.146 

0.079 

0.000 

-0.097 

-0.155 

-0.222 

AUTHOR 

KOZAKEVITCH {1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.9 

2.6 

1.9 

1.6 

1.4 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.2 

1.7 

1.4 

1.2 

AUTHOR 

KOZAKEVITCH {1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.4 

1.8 

1.4 

1.2 

1.0 

0.8 

0.7 

0.6 

ACS-26 

A CS-2 7 

ACS-28 

Three-Component Systems 101 
SYSTEM 

AL203(27.27) ,CA0(49.59), 

SI02 (23 .14) (X) 

AL203(40.0),CA0(40.0), 

SI02(20.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

1.841 

1.386 

0.993 

0.693 

0.405 

0.262 

0.095 

-0.105 

SYSTEM 

AL203(36.10),CA0(39.39), 

SI02 (24. 51) (X) 

AL203(50.0) ,CA0(30.0), 

SI02 (20. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

SYSTEM 

LN(N) 

2.442 

2.001 

1.548 

1.194 

0.916 

0.642 

0.405 

0.262 

0.182 

0.095 

0.000 

AL203(46.05) ,CA0(27.90), 

SI02 (26. 05) (X) 

AL203(60.0) ,CA0(20.0), 

SI02 (20. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

0.993 

0.693 

0.470 

0.336 

0.262 

LOG(N) 

0.799 

0.602 

0.431 

0.301 

0.176 

0.114 

0.041 

-0.046 

LOG(N) 

1.061 

0.869 

0.672 

0.519 

0.398 

0.279 

0.176 

0.114 

0.079 

0.041 

0.000 

LOG(N) 

0.431 

0.301 

0.204 

0.146 

0.114 

102 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.3 

4.0 

2.7 

2.0 

1.5 

1.3 

1.1 

0.9 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.5 

7.4 

4.7 

3.3 

2.5 

1.9 

1.5 

1.3 

1.2 

1.1 

1.0 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.7 

2.0 

1.6 

1.4 

1.3 

ACS-29 

ACS-30 

ACS-31 
SYSTEM 

AL203(70.21) ICAO(O.O) I 

SI02 (29. 79) (X) 

AL203(80.0) ICAO(O.O) I 

SI02 (20. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1950.00 4.498 

2000.00 4.399 

2050.00 4.305 

2100.00 4.214 

SYSTEM 

LN(N) 

-0.105 

-0.223 

-0.357 

-0.511 

AL203(12.36) ICA0(56.18) I 

SI02(31.46) (X) 

AL203(20.0),CA0(50.0), 

SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

2000.00 4.399 

SYSTEM 

LN(N) 

o·. 916 

0.588 

0.336 

0.095 

-0.105 

-0.223 

-0.357 

-0.511 

AL203(19.52) ICA0(47.34) I 

SI02 (33 .14) (X) 

AL203(30.0) ,CA0(40.0), 

SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

2.219 

1.808 

1.482 

1.194 

0.875 

0.642 

0.405 

0.336 

0.262 

0.182 

0.095 

LOG(N) 

-0.046 

-0.097 

-0.155 

-0.222 

LOG(N) 

0.398 

0.255 

0.146 

0.041 

-0.046 

-0.097 

-0.155 

-0.222 

LOG(N) 

0.964 

0.785 

0.643 

0.519 

0.380 

0.279 

0.176 

0.146 

0.114 

0.079 

0.041 

AU'IHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

0.9 

0.8 

0.7 

0.6 

AU'IHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.5 

1.8 

1.4 

1.1 

0.9 

0.8 

0.7 

0.6 

AU'IHOR 

ACS-32 

ACS-33 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.2 

6.1 

4.4 

3.3 

2.4 

1.9 

1.5 

1.4 

1.3 

1.2 

1.1 

ACS-34 

Three-Component Systems 1 03 
SYSTEM 

AL203(27.50),CA0(37.50), 

SI02 (35. 0) (X) 

AL203(40.0) ,CA0(30.0), 

SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 

1900.00 

1950.00 

2000.00 

4.710 

4.602 

4.498 

4.399 

LN(N) 

3.408 

2.890 

2.434 

2.054 

1.758 

1.482 

1.163 

0.875 

0.642 

0.531 

0.336 

0.182 

LOG(N) 

1.480 

1.255 

1.057 

0.892 

0.763 

0.643 

0.505 

0.380 

0.279 

0.230 

0.146 

0.079 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

30.2 

18.0 

11.4 

7.8 

5.8 

4.4 

3.2 

2.4 

1.9 

1.7 

1.4 

1.2 

AC S-35 

----------------------------------------------------------------------------- ·sYSTEM 

AL203(36.43),CA0(26.49), 

SI02(37.09) (X) 

AL203(50.0) ,CA0(20.0), 

SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

1.887 

1.609 

1.361 

1.099 

0.833 

0.588 

0.405 

0.182 

SYSTEM 

AL203(46.48)1CA0(14.08) I 

SI02 ( 39. 44) (X) 

AL203(60.0) ICA0(10.0) I 

SI02(30.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

0.642 

0.405 

0.182 

LOG(N) 

0.820 

0.699 

0.591 

0.477 

0.362 

0.255 

0.176 

0.079 

LOG(N) 

0.279 

0.176 

0.079 

1 04 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

6.6 

5.0 

3.9 

3.0 

2.3 

1.8 

1.5 

1.2 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.9 

1.5 

1.2 

ACS-36 

ACS-37 
SYSTEM 

AL203(5.92l ,CA0(53.86), 

SI02 (40. 21 (X) 

AL203(10.0 ,CA0(50.0) I 

SI02(40.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 

1850.00 

1900.00 

1950.00 

2000.00 

SYSTEM 

4.824 

4.710 

4.602 

4.498 

4.399 

LN(N) 

1.668 

1.361 

1.030 

0.742 

0.470 

0.262 

0.095 

0.000 

-0.105 

-0.223 

-0.357 

-0.511 

AL203(12.46) ICA0(45.28) I 

SI02 (42. 26) (X) 

AL203(20.0) ICA0(40.0) I 

SI02(40.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

2.688 

2.219 

1.825 

1.459 

1.099 

0.788 

0.693 

0.588 

0.470 

0.336 

0.262 

0.182 

LOG (N) 

0.724 

0.591 

0.447 

0.322 

0.204 

0.114 

0.041 

0.000 

-0.046 

-0.097 

-0.155 

-0.222 

LOG(N) 

1.167 

0.964 

0.792 

0.633 

0.477 

0.342 

0.301 

0.255 

0.204 

0.146 

0.114 

0.079 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.3 

3.9 

2.8 

2.1 

1.6 

1.3 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

14.7 

9.2 

6.2 

4.3 

3.0 

2.2 

2.0 

1.8 

1.6 

1.4 

1.3 

1.2 

ACS-38 

ACS-39 

Three-Component Systems 1 05 
SYSTEM AL203(19.68) CA0(35.79)~ 

SI02 (44.53) (X) 

AL203(30.0) ICA0(30.0) I 

SI02(40.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

3.669 

3.246 

2.821 

2.398 

2.028 

1.668 

1.335 

1.030 

0.833 

0.693 

0.588 

0.470 

SYSTEM 

AL203(27.73) 1 CA0(25.21) 1 

SI02(47.06) (X) 

AL203(40.0) 1 CA0(20.0) 1 

SI02(40.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

2.991 

2.632 

2.262 

1.960 

1.668 

1.411 

1.131 

SYSTEM AL203(46.92)~CA0(0.0) 1 SI02 (53. 08) (X) 

AL203(60.0) ICAO(O.O) I 

SI02(40.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

2050.00 4.305 

2100.00 4.214 

LN(N) 

1.194 

0.875 

0.588 

0.405 

0.262 

0.182 

LOG(N) 

1.593 

1.410 

1.225 

1.041 

0.881 

0.724 

0.580 

0.447 

0.362 

0.301 

0.255 

0.204 

LOG(N) 

1.299 

1.143 

0.982 

0.851 

0.724 

0.613 

0.491 

LOG (N) 

0.519 

0.380 

0.255 

0.176 

0.114 

0.079 

106 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

39.2 

25.7 

16.8 

11.0 

7.6 

5.3 

3.8 

2.8 

2.3 

2.0 

1.8 

1.6 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.9 

13.9 

9.6 

7.1 

5.3 

4.1 

3.1 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.3 

2.4 

1.8 

1.5 

1.3 

1.2 

ACS-40 

A C S-4 1 

ACS-42 
SYSTEM 

AL203(24.96) ,CA0(25.05), 

SI02 ( 49. 99) (X) 

AL203(36.6) ,CA0(20.2), 

SI02 ( 43. 2) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

SYSTEM 

LN(N) 

3.235 

2.809 

2.370 

1.988 

1.723 

AL203(0.0) ,CA0(51.72), 

SI02 ( 48. 28) (X) 

AL203(0.0),CA0(50.0), 

SI02 (50. 0) (%) MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1900.00 4.602 

2000.00 4.399 

LN(N) 

0.875 

0.588 

0.336 

0.095 

-0.105 

-0.223 

-0.223 

-0.357 

LOG(N) 

1.405 

1.220 

1.029 

0.863 

0.748 

LOG(N) 

0.380 

0.255 

0.146 

0.041 

-0.046 

-0.097 

-0.097 

-0.155 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

25.4 

16.6 

10.7 

7.3 

5.6 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) 

N 

2.4 

1.8 

1.4 

1.1 

0.9 

0.8 

0.8 

0.7 

(1/K) 

ACS-43 

ACS-4 4 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.97l ,CA0(43.40), SI02 (50. 63 (X) 

AL203(10.0 ,CA0(40.0), 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

2.510 

2.152 

1.825 

1.504 

1.224 

0.956 

0.693 

0.588 

0.470 

0.336 

0.182 

0.000 

LOG(N) 

1.090 

0.934 

0.792 

0.653 

0.531 

0.415 

0.301 

0.255 

0.204 

0.146 

0.079 

0.000 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

12.3 

8.6 

6.2 

4.5 

3.4 

2.6 

2.0 

1.8 

1.6 

1.4 

1.2 

1.0 

A C S-45 

Three-Component Systems 1 07 
SYSTEM 

AL203(12.55) ,CA0(34.22) I 

SI02 (53. 23) (X) 

AL203(20.0),CA0(30.0), 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1600.00 5.339 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

3.747 

3.472 

3.096 

2.760 

2.451 

2.128 

1.775 

1.482 

1.253 

1.099 

0.993 

0.916 

SYSTEM 

AL203(19.84),CA0(24.05), 

SI02 (56 .12) (X) 

AL203(30.0) ,CA0(20.0), 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1650.00 5.200 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

SYSTEM 

LN(N) 

3.509 

3.105 

2.688 

2.370 

2.079 

1.792 

1.526 

1.335 

AL203(27.97) ,CA0(12.71), 

SI02 (59. 32) (X) 

AL203(40.0) ,CA0(10.0), 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

LN(N) 

2.862 

2.518 

2.152 

1.808 

1.482 

1.308 

LOG(N) 

1.627 

1.508 

1.344 

1.199 

1.064 

0.924 

0.771 

0.643 

0.544 

0.477 

0.431 

0.398 

LOG(N) 

1.524 

1.348 

1.167 

1.029 

0.903 

0.778 

0.663 

0.580 

LOG(N) 

1.243 

1.093 

0.934 

0.785 

0.643 

0.568 

1 08 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

42.4 

32.2 

22.1 

15.8 

11.6 

8.4 

5.9 

4.4 

3.5 

3.0 

2.7 

2.5 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

33.4 

22.3 

14.7 

10.7 

8.0 

6.0 

4.6 

3.8 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17.5 

12.4 

8.6 

6.1 

4.4 

3.7 

ACS-46 

A C S-4 7 

ACS-48 
SYSTEM 

AL203(37.08) ICAO(O.O) I 

SI02 (62. 92) (X) 

AL203(50.0) ICAO(O.O) I 

SI02(50.0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

2050.00 4.305 

2100.00 4.214 

SYSTEM 

LN(N) 

1.758 

1.411 

1.131 

0.916 

0.788 

0.642 

AL203(0o0) 1 CA0(41o67), 

SI02 (58 o 33) (X) 

AL203(0o0) ICA0(40o0) I 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1500o00 5o640 

1550o00 5o485 

1600o00 5o339 

1650o00 5o200 

1700o00 5o068 

1750o00 4.943 

1800o00 4o824 

1850o00 4o710 

1900o00 4o602 

1950o00 4.498 

2000.00 4.399 

LN(N) 

2.230 

1.872 

1.548 

10281 

0.993 

0.788 

0.588 

0.405 

0.262 

0.095 

0.000 

SYSTEM 

AL203(6.01l 1 CA0(32.79) 1 

SI02 (61. 20 (X) 

AL203(10o0 ICA0(30o0) I 

SI02 (60 o 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 

1650.00 5.200 

1700.00 5.608 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

2.885 

2.518 

2.186 

1o887 

1.609 

1.361 

1o099 

LOG(N) 

0.763 

0.613 

0.491 

0.398 

Oo342 

Oo279 

LOG(N) 

0.968 

0.813 

Oo672 

Oo556 

0.431 

0.342 

0.255 

0.176 

0.114 

0.041 

0.000 

LOG(N) 

1.253 

1.093 

Oo949 

0.820 

0.699 

0.591 

Oo477 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1o0 ATM. 

Z = 10000 o 0/T (K) (1/K) 

N 

SoB 

401 

301 

2.5 

2.2 

1o9 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000o0/T(K) (1/K) 

N 

9.3 

6o5 

4o7 

3o6 

2.7 

2.2 

1.8 

1o5 

1.3 

1.1 

1.0 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17.9 

12.4 

8.9 

6.6 

5o0 

3.9 

3o0 

ACS-49 

ACS-50 

A c s- 51 

Three-Component Systems 1 09 
SYSTEM 

AL203(12.65) ,CA0(22.99), 

SI02 (64. 37) (X) 

AL203(20.0) ,CA0(20.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

2000.00 4.399 

SYSTEM 

LN(N) 

3.638 

3.300 

2.929 

2.580 

2.313 

2.128 

1.988 

AL203(20.00) ,CA0(12.12), 

SI02 (67. 88) (X) 

AL203(30.0),CA0(10.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

1950.00 4.498 

SYSTEM 

LN(N) 

3.239 

2.821 

2.518 

2.282 

AL203(0.0) ,CA0(31.47), 

SI02 (68. 53) (X) 

AL203(0.0),CA0(30.0), 

SI02 (70. 0) (%) 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1700.00 5.068 

1750.00 4.943 

1800.00 4.824 

1850.00 4.710 

1900.00 4.602 

LN(N) 

2.510 

2.230 

2.001 

1.825 

1.686 

LOG(N) 

1.580 

1.433 

1.272 

1.121 

1.004 

0.924 

0.863 

LOG(N) 

1.407 

1.225 

1.093 

0.991 

LOG(N) 

1.090 

0.968 

0.869 

0.792 

0.732 

11 0 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

38.0 

27.1 

18.7 

13.2 

10.1 

8.4 

7.3 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

25.5 

16.8 

12.4 

9.8 

AUTHOR 

KOZAKEVITCH (1960) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.3 

9.3 

7.4 

6.2 

5.4 

ACS-52 

ACS-53 

ACS-54 
3 

I I I I I I I I I I I I I 

Al 20 3 - CoO- Si02 

KOZAKEVITCH (1960) 

I .....-.. 

LU 

V') 2 -

0 

a... 

-........ 

>-

..... 

- 1L V') ACS-17 

0 

u 

V') 

-

> 

0 

0 0 

....J - • 

-1~~--~--~~~~--~--~~~~--~--~~~~--~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
......... 

UJ 

V') 

-

0 

a.. 

.......... 

>- 1-

V') -

0 

u 

V') 

-

> 

0 

0 

__, 

3 ~----~------~------~------~------~----~ 

2 

1 

0 

~ ACS-22 

Al20 3 - CoO- Si02 

KOZAKEVITCH (1960) 

ACS-17 

-1 ~----~------~------~------~------~------~ 

4 5 6 7 

10 000/T (KELVINS-1

) 

112 Viscosity of Synthetic and Natural Melts and Glasses 
3 

I I I I I I I I I I I I I 

Al20 3 - CaO -Si02 

KOZAKEVITCH (1960} I ..,......__ 

LU 2 ll) 

-

0 

0... 

-

>-

1--

-

U') 1 0 

u 

ll) 

-

> 

l? 

0 

__. 

0 

-1 ~~--~--~~--~--~--~~--~--~~--~--~~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
............ 

lU 

(./) 

-

0 

CL 

-

>-

~ 

-(./) 

0 

u 

(./) 

-

> 

0 

0 

__. 

3~----~--------------~------~------r------. 

2 

1 

0 

Al 20 3- CoO -Si0 2 

KOZAKEVITCH (1960) 

ACS-24 

-1 ~----~~----~------~------~------~------~ 

4 5 6 7 

10 000/T (KELVINS- 1

) 

114 Viscosity of Synthetic and Natural Melts and Glasses 
3 

I I I I I I . I . . I I 

AI20 3 -Ca0-Si02 

KOZAKEVITCH (1960) 

~ 

I 

UJ 2 (./") 

-

0 

Q.. 

...__.. 

>- 1-

- 1 I ACS-30 (./") 

0 

u 

(./") 

-

> 

0~ -\..-.1- LU 

<-' 

0 :: ~ 

.. 

-1 ~~--~--~--~~--~--~~~~--~--~~~~--~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
.......... 

UJ 

c.l) 

0 

a.. 

....__ 

>-

..,_ 

-

c.l) 

0 

u 

c.l) 

-

> 

0 

0 

__. 

3~------~------~------~------~------~----~ 

2 

1 

0 

Al 20 3 - Ca0-Si02 

KOZAKEVITCH (1960) 

ACS-32 

ACS-30 

-1 ~------~------~------~------~------~----~ 

4 5 6 7 

10 000/T (KELVINS- 1

) 

116 Viscosity of Synthetic and Natural Melts and Glasses 
3 

I I I I I I I I I I I 

Al20 3- CaO- Si02 

KOZAKEVITCH (1960) 

I ....--.. 

UJ 2 (./') 

-

0 

a_ I ACS-35 

-

>-

~ 

-

(./') 1 0 

u 

(./') 

-

> I ACS-33 

0 

0 0 ___J 

-1~~--~--~~~~--~--~--~~--~--~--~~--~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
.......... 

UJ 

V') 

-

0 

a.. 

-......... 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

0 

0 

__, 

3 ~------~----~~----~------~------~------~ 

2 

1 

0 

-1 

4 

A120 3 - Ca0-Si02 

KOZAKEVITCH {1960) 

ACS-35 

5 6 

10 000/T (KELVINS-1

) 

7 

118 Viscosity of Synthetic and Natural Melts and Glasses 
0 

.q 

I 

V') 

u 

<( 

N 

.q 

I 

V') 

u 

<( 

0 

(3SIOd) AliSOJSIA 901 

0 

0 

~ 

N 

0 

0 

0 

N 

0 

0 

~ ~ 

0 

0 

00 

~ 

0 

0 

r-.... 

~ 

0 

0 

~ ~ 

0 

0 

V") 

~ 

0 

0 

~ .-- r-- 1 

.......... 

u 

___.. 

0 

UJ 

~ 

:J 

~ 0::: 

UJ 

a... 

~ UJ 

1-
---- UJ 

V) 

-

0 

a.. 

....._... 

>- 1-

-

V) 

0 

u 

V) 

-

> 

0 

0 

-I 

3 ~----~------~------~----~~-----.------~ 

2 

1 

0 

Al 20 3- CoO- Si02 

KOZAKEVITCH (1960} 

ACS-41 

ACS-40 

ACS-39 

ACS-38 

·-1 L----..--L----J...---...J-----'-----.&....------' 

4 5 6 7 

10 000/T (KELVINS- 1

) 

120 Viscosity of Synthetic and Natural Melts and Glasses 
0 

~--~--~------~------------~---- 0 ~ 

N~ 0 ~ ·- Qi;. c.f) ..... 

I ...._ 

0 ~ 0 ...... u ~ I ~ 

M~ 0 ~ 

~~ <( ~ 

M 

~ 

I 

c./) 

u 

<( 

(3SIOd) AliSOJSIA 901 

N 

0 

0 

0 

C"' 

0 

0 

o-. 

~ 

0 

0 

00 

~ 

0 

0 

"' ~ 

0 

0 

tJ") 

..-

............ 

u 

0 

-.....,.... 

UJ 

~ 

:::::> 

~ ~ 

UJ 

a.. 

~ UJ 

1-
~ 

UJ 

(./) 

0 

Q.. 

---

>- 1-

-(./) 

0 

u 

(./) 

-

> 

l? 

0 

__. 

3 ~----~------~------~------~------~----~ 

2 

1 

0 

Al 20 3- Ca0-Si02 

KOZAKEVITCH ( 1960) 

ACS-43 

-1 ~----~------~------~------~------L-----~ 

4 5 6 7 

10 000/T (KELVINS- 1

) 

122 Viscosity of Synthetic and Natural Melts and Glasses 
3--~------~--~--~~--~--~--~--~--~~--~--~ 

__.... 

~ 2 

0 

a_ 

....__ 

>-. 

~ 

(./') 1 

0 

u 

(./') 

> 

~ 

0 0 

__J 

ACS-46 

ACS-45 

ACS-44 

Al20 3 - CaO- Si02 

KOZAKEVITCH (1960) 

-1 ~~--~--~--~~--~--~~~~--~--~~~~--~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
..---

UJ 

l/') 

0 

a.. 

----

>- 1---

-l/') 

0 

u 

l/') 

-

> 

~ 

0 

--1 

3 ~------~------~------~------~------~----~ 

2 

1 

0 

-1 

4 

AI203-CaO-Si02 

KOZAKEVITCH (1960) 

ACS-46 

ACS-45 

5 6 

10 000/T (KELVINS- 1

) 

7 

124 Viscosity of Synthetic and Natural Melts and Glasses 
3~~--~--~--~~--~--~--~~--~--~--~~--~ 

.......... 

~ 2 

0 

a.. 

-

>- 1-

(./) 1 

0 

u 

(./) 

> 

0 

0 0 

_J 

ACS-51 

ACS-50 

ACS-52 

Al20 3- CaO- Si02 

KOZAKEVITCH {1960) 

-1~~--~--~--~~--~--~--~~--~--~--~~--~ 

1400 1500 1600 1700 1800 1900 2000 2100 

TEMPERATURE (°C) 
~ 

LU 

V') 

-

0 

a... 

>- 1--

-

3 ~----~~----~------~------~------~------~ 

2 

ACS-52 

ACS- 51 

AI20 3-Ca0-Si02 

KOZAKEVITCH /1960) 

V') 1 

0 ACS-50 

u 

V') 

-

> 

l? 

0 

~ 

0 

-1 ~----~~----~------~------~------~------~ 

4 5 6 7 

10 000/T (KELVINS- 1) 

126 Viscosity of Synthetic and Natural Melts and Glasses 
N~ 0 '0 ·- ~ V') "" •'-

0 ~ 0 "' u ~ 

IM ~ 

0 ~ N~ 

- C) <( ~ 

~ 

V") 

I 

V") 

u 

<( 

N 0 

(3SIOd) A!ISOJSI/\ 901 

0 

0 

~ 

N 

0 

0 

0 

N 

0 

0 

~ ~ 

0 

0 

00 

~ 

0 

0 

1'. 

~ 

0 

0 

-o 

~ 

0 

0 

1.() 

~ 

.........._ 

u 

~ 

0 

UJ 

0:: 

:J 

~ 0:: 

UJ 

a.. 

~ UJ 

.,...._ 
..---.. 

lU 

(./) 

-

0 

a.. 

............ 

>-

...... 

-

(./) 

0 

u 

(./) 

-

> 

~ 

0 

__, 

3 ~----~------~------~----~~----~-------

2 

1 

0 

ACS-54 

AI203- CaO- Si02 

KOZAKEVITCH (1960} 

-1 ~----~------~------~----~~----~------~ 

4 5 6 7 

10 000/T (KELVINS- 1

) 

128 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUTHOR 

AL203(5.92) ,CA0(53.86),SI02. (40.22) (X)MACHIN AND HANNA (1945) 

AL203 (10. 0) , CAO (50. 0) I SI02 (40. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1400.00 5.977 2.120 0.921 8.33 

1450.00 5.804 1.654 0.719 5.23 

1500.00 5.640 1.389 0.603 4.01 

SYSTEM AUTHOR 

AL203(9.10) ,CA0(49.66),SI02(41.24) (X)MACHIN AND HANNA (1945) 

AL203 (15. 0), CAO (45. 0) I SI02 (40. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1250.00 6.566 4.452 1.933 85.8 

1300.00 6.357 3.696 1.605 40.27 

1350.00 6.161 3.099 1.346 22.18 

1400.00 5.977 2.582 1.122 13.23 

1450.00 5.804 2.107 0.915 8.22 

1500.00 5.640 1.641 0.713 5.16 

A C S -55 

ACS-56 

---------------------------------------------------------------------------- SYSTEM 

AL203(12.44) 1 CA0(45.27), 

SI02 ( 42. 29) (X) 

AL203(20.0),CA0{40.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N JPOISES) T DEGREES c

2

) 

LN(N) LOG(N) 1250.00 6.566 4.997 2.170 

1300.00 6.357 4.213 1.830 

1350.00 6.161 3.557 1.545 

1400.00 

1450.00 

1500.00 

5.977 

5.804 

5.640 

3.067 

2.617 

2.119 

SYSTEM 

AL203(15.96),CA0(40.65), 

1.332 

1.136 

0.920 

SI02 ( 43. 39) (X) 

AL203(25.0),CA0(35.0), 

SI02 ( 40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N {POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.645 

4.854 

4.157 

3.554 

3.077 

2.663 

LOG(N) 

2.452 

2.108 

1.806 

1.543 

1.337 

1.157 

AUTHOR 

MACHIN AND HANNA {1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) {1/K} 

N 

147.9 

67.56 

35.07 

21.48 

13.69 

8.32 

AUTHOR 

MACHIN AND HANNA {1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

283. 

128.3 

63.90 

34.94 

21.70 

14.34 

ACS-57 

A c s- 5 a 

Three-Component Systems 129 
SYSTEM 

AL203(19.67) ,CA0(35.78), 

SI02 (44.55) (X) 

AL203(30.0) ,CA0(30.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.864 

4.240 

3.676 

3.301 

LOG(N) 

2.112 

1.841 

1.597 

1.434 

130 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

129.5 

69.39 

39.50 

27.14 

(1/K) ACS-59 
......... 

w 

V') 

-

0 

a.. 

......_.. 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

~ 

0 

_,J 

4~----~------~------~----~~----~------~ 

3 

2 

1 

ACS-55 

ACS-56 

ACS-58 

Al20 3- CoO -Si02 

MACHIN and HANNA (194.5) 

0 ~----~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 131 
>- 1-

-

4 ~------~------~----------------------~----~ 

3 

AI20 3 -Ca0-Si02 

MACHIN and HANNA (1945) 

V) 2 

0 

u 

V) 

> 

~ 

0 

--1 

1 

ACS- 57 

ACS-55 

ACS-56~ 

ACS-58 

ACS -59 

0 ~------~------~------~------~------~----~ 

5 6 7 

10 000/T (KELVINS- 1

) 

132 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(23.41),CA0(42.55), 

SI02 (34. 04) (X) 

AL203(35.0),CA0(35.0), 

SI02 ( 30. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

T Z LN(N) 

2.322 

Z = 10000. 0/T (K) (1/K) 

LOG(N) N 

1500.00 5.640 1.009 10.2 

SYSTEM 

AL203(12.41) ,CA0(50.75), 

SI02 (36. 84) (X) 

AL203(20.0) ,CA0(45.0), 

SI02(35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.610 1.134 

1450.00 5.804 2.028 0.881 

1500.00 5.640 1.601 0.695 

SYSTEM 

AL203(15.91),CA0(46.29), 

SI02(37.80) (X) 

AL203(25.0) ,CA0(40.0), 

SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T 

1400.00 

1450.00 

1500.00 

z 

5.977 

5.804 

5.640 

LN(N) 

2.991 

2.477 

2.019 

SYSTEM 

AL203(19.60),CA0(41.58), 

SI02 (38. 81) (X) 

AL203(30.0),CA0(35.0), 

SI02(35.0) (%) 

LOG(N) 

1.299 

1.076 

0.877 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 3.456 1.501 

1450.00 5.804 2.939 1.276 

1500.00 5.640 2.451 1.064 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

13.6 

7.60 

4.96 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

19.9 

11.9 

7.53 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

31.7 

18.9 

11.6 

ACS-60 

ACS-61 

ACS-62 

ACS-63 

Three-Component Systems 133 
SYSTEM 

AL203(23.50),CA0(36.62), 

SI02 ( 39. 88) (X) 

AL203(35.0) ,CA0(30.0), 

SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

5.513 

4.691 

4.002 

3.447 

2.944 

AL203(27.62) ,CA0(31.38), 

SI02(41.00) (X) 

AL203(40.0) ,CA0(25.0), 

SI02 (35.0) (%) 

LOG(N) 

2.394 

2.037 

1.738 

1.497 

1.279 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1450.00 5.804 3.711 1.612 

1500.00 5.640 3.215 1.396 

SYSTEM 

AL203(5.92),CA0(53.86), 

SI02 ( 40. 2) (X) 

AL203(10.0),CA0(50.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1400.00 5.977 2.120 0.921 

1450.00 5.804 1.654 0.719 

1500.00 5.640 1.389 0.603 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

248. 

109. 

54.7 

31.4 

19.0 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

40.9 

24.9 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8.33 

5.23 

4.01 

ACS-64 

A CS-6 5 

ACS-66 

---------------------------------------------------------------------------- SYSTEM 

AL203(9.11~,CA0(49.68), 

SI02(41.21 (X) 

AL203(15.0 ,CA0(45.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.452 

3.696 

3.100 

2.580 

2.107 

1.641 

LOG(N) 

1.933 

1.605 

1.346 

1.121 

0.915 

0.713 

134 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE {1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

85.8 

40.3 

22.2 

13.2 

8.22 

5.16 

ACS-67 
SYSTEM 

AL203(12.46),CA0(45.28), 

SI02(42.26) (X) 

AL203(20.0) ,CA0(40.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.977 

4.214 

3.558 

3.068 

2.617 

2.119 

SYSTEM 

AL203(15.97),CA0(40.66), 

SI02 ( 43. 37) (X) 

AL203(25.0) ,CA0(35.0), 

SI02(40.0) (%) 

LOG(N) 

2.170 

1.830 

1.545 

1.332 

1.137 

0.920 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

5.645 

4.852 

4.157 

3.552 

1450.00 5.804 3.077 

1500.00 5.640 2.660 

LOG(N) 

2.452 

2.107 

1.806 

1.542 

1.336 

1.155 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

148. 

67.6 

35.1 

21.5 

13.7 

8.32 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

283. 

128. 

63.9 

34.9 

21.7 

14.3 

ACS-68 

ACS-69 

------------------------------------------------------------------------------ SYSTEM 

AL203(19.68) ,CA0(35.79), 

SI02 ( 44. 53) (X) 

AL203(30.0) ,CA0(30.0), 

SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.860 

4.240 

3.676 

3.300 

LOG(N) 

2.111 

1.841 

1.597 

1.433 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

129. 

69.4 

39.5 

27.1 

ACS-70 

------------------------------------------------------------------------------ SYSTEM 

AL203(0.0),CA0(56.70), 

SI02(43.30) (X) 

AL203(0.0) ,CAO(SS.O), 

SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 0.846 0.367 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.33 

ACS-71 

Three-Component Systems 135 
SYSTEM 

AL203(2.90) ,CA0(52.77), 

SI02 (44. 33) (X) 

AL203(5.0) ,CA0(50.0), 

SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1450.00 5.804 1.569 0.681 

1500.00 5.640 1.227 0.533 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

·4.80 

3.41 

ACS-72 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.95l ,CA0(48.65), SI02 ( 45.40 (X) 

AL203(10.0 ,CA0(45.0), 

SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1400.00 5.977 2.451 1.064 

1450.00 5.804 2.024 0.879 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.6 

7.57 

1500.00 5.640 1.585 0.688 4.88 

SYSTEM 

AL203(9.14l,CA0(44.32), 

SI02(46.54 (X) 

AL203(15.0 ,CA0(40.0), 

SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.500 

2.965 

2.526 

2.145 

LOG(N) 

1.520 

1.288 

1.097 

0.931 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

33.1 

19.4 

12.5 

8.54 

ACS-73 

ACS-74 

·-----------------------------------------------------------------------------

SYSTEM 

AL203(12.50),CA0(39.77), 

SI02(47.72) (X) 

AL203(20.0) ,CA0(35.0), 

SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.513 

5.606 

4.828 

4.148 

3.614 

3.118 

2.708 

LOG(N) 

2.829 

2.435 

2.097 

1.801 

1.569 

1.354 

1.176 

136 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

674. 

272. 

125. 

63.3 

37.1 

22.6 

15.0 

ACS-75 
SYSTEM 

AL203(16.04) 1 CA0(34.99) 1 

SI02 (24. 98) (X) 

AL203(25.0) ICA0(30.0) I 

SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.883 

4. 250 

3.714 

3.270 

SYSTEM 

AL203(19.76) 1 CA0(29.94) 1 

SI02 (50. 30) (X) 

AL203(30.0) ICA0(25.0) I 

SI02 ( 45. 0) (%) 

LOG(N) 

2.121 

1.846 

1.613 

1.420 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

132. 

70.1 

41.0 

26.3 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

T (DEGREES C) 

T Z LN(N) 

Z = 10000.0/T(K) (1/K) 

LOG(N) N 

1500.00 5.640 4.256 1.848 70.5 

SYSTEM 

AL203(2.91) ICA0(47.66) I 

SI02(49.43) (X) 

AL203(5.0) ICA0(45.0) I 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 1.564 0.679 

SYSTEM 

AL203(5.90l ICA0(43.40) I 

SI02 (50. 63 (X) 

AL203(10.0 ICA0(40.0) I 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.955 1.283 

1450.00 5.804 2.493 1.083 

1500.00 5.640 2.108 0.915 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4.78 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED fROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

19.2 

12.1 

8.23 

ACS-76 

ACS-77 

A C S-7 8 

ACS-79 

Three-Component Systems 137 
SYSTEM 

AL203(9.17l ,CA0(38.92), 

SI02 (51. 90 (X) 

AL203(15.0 ,CA0(35.0), 

SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

7.131 

6.151 

5.342 

4.654 

4.045 

3.547 

3.086 

2.660 

AL203(12.55) ,CA0(34.22), 

SI02 (53. 23) (X) 

AL203(20.0) ,CA0(30.0), 

SI02 (50. 0) (%) 

LOG (N) 

3.097 

2.671 

2.320 

2.021 

1.757 

1.540 

1.340 

1.155 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.271 

5.509 

4.828 

4.261 

3.745 

3.408 

SYSTEM 

AL203(16.10),CA0(29.27), 

SI02 (54. 63) (X) 

AL203(25.0) ,CA0(25.0), 

SI02 (50. 0) (%) 

LOG(N) 

2.723 

2.393 

2.097 

1.851 

1.626 

1.480 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.603 1.999 

1500.00 5.640 4.055 1.761 

SYSTEM 

AL203(2.92) ,CA0(42.52), 

SI02 (54. 56) (X) 

AL203(5.0),CA0(40.0), 

SI02 (55. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 2.549 1.107 

1500.00 5.640 2.128 0.924 

138 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1250. 

469. 

209. 

105. 

57.1 

34.7 

21.9 

14.3 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

529. 

247. 

125. 

70.9 

42.3 

30.2 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

99.8 

57.7 

AUTHOR 

MACHIN AND YEE ( 1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.8 

8.40 

ACS-80 

ACS-81 

ACS-82 

ACS-83 
SYSTEM 

AL203(5.99l,CA0(38.11), 

SI02 (55. 90 (X) 

AL203(10.0 ,CA0(35.0), 

SI02 (55. 0) (%) 

MEASUREMENT METIIOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.762 

4.108 

3.575 

3.105 

2.715 

AL203(9.2) ,CA0(33.49), 

SI02 (57. 30) (X) 

AL203(15.0),CA0(30.0), 

SI02 (55. 0) (%) 

LOG(N) 

2.068 

1.784 

1.553 

1.348 

1.179 

MEASUREMENT METIIOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

7.930 

6.985 

6.122 

5.146 

4.796 

4. 293 

3.802 

3.353 

AL203(12.60) ,CA0(28.62), 

SI02 (58. 78) (X) 

AL203(20.0) ,CA0(25.0) I 

SI02 (55 0 0) (%) 

LOG(N) 

3.444 

3.033 

2.659 

2.352 

2.083 

1.865 

1.651 

1.456 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

8.981 

7.962 

7.090 

6.363 

5.733 

5.142 

4.592 

4.119 

LOG(N) 

3.900 

3.458 

3.079 

2.763 

2.490 

2.233 

1.994 

1.789 

AUTIIOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

117. 

60.8 

35.7 

22.3 

15.1 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2780. 

1080. 

456. 

225. 

121. 

73.2 

44.8 

28.6 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

7950. 

2870. 

1200. 

580. 

309. 

171. 

98.7 

61.5 

ACS-84 

ACS-85 

ACS~86 

Three-Component Systems 139 
SYSTEM 

AL203(16.16),CA0(23.50), 

SI02 (60. 33) (X) 

AL203(25.0) ,CA0(20.0), 

SI02 (55. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1400.00 5.977 6.492 

1450.00 5.804 5.759 

1500.00 5.640 5.153 

SYSTEM 

AL203(0.0) ,CA0(41.67), 

SI02 (58. 33) (X) 

AL203(0.0),CA0(40.0), 

SI02 (60. 0) (%) 

LOG(N) 

2.820 

2.501 

2.238 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1500.00 5.640 2.222 0.965 

SYSTEM 

AL203(2.93) ,CA0(37.33), 

SI02 (59. 74) (X) 

AL203(5.0),CA0(35.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1400.00 5.977 3.674 1.595 

1450.00 5.804 3.219 1.398 

1500.00 5.640 2.839 1.233 

SYSTEM 

AL203(6.01l ,CA0(32.79), SI02 (61. 20 (X) 

AL203(10.0 ,CA0(30.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.832 

6.898 

6.043 

5.394 

4.836 

4.402 

3.945 

3.484 

LOG(N) 

3.401 

2.996 

2.624 

2.342 

2.100 

1.912 

1.713 

1.513 

140 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

660. 

317. 

173. 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

9.23 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

39.4 

25.0 

17.1 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2520. 

990. 

421. 

220. 

126. 

81.6 

51.7 

32.6 

ACS-87 

ACS-88 

ACS-89 

ACS-90 
SYSTEM 

AL203(9.24l,CA0(28.01), 

SI02 (62. 75 (X) 

AL203(15.0 ,CA0(25.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1150.00 7.027 9.269 

1200.00 6.789 8.224 

1250.00 6.566 7.352 

1300.00 6.357 6.593 

1350.00 6.161 5.969 

1400.00 5.977 5.366 

1450.00 5.804 4.852 

1500.00 5.640 4.353 

SYSTEM 

AL203(12.65) ,CA0(22.99), 

SI02 (64. 37) (X) 

AL203(20.0),CA0(20.0), 

SI02 (60. 0) (%) 

4.025 

3.572 

3.193 

2.863 

2.592 

2.330 

2.107 

1.890 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

9.596 

8.657 

7.836 

7.139 

6.497 

5.866 

5.318 

AL203(16.22) ,CA0(17.70), 

SI02 (66. 08) (X) 

AL203(25.0),CA0(15.0), 

SI02 (60. 0) (%) 

LOG(N) 

4.167 

3.760 

3.403 

3.100 

2.822 

2.548 

2.310 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 7.824 3.398 

1450.00 5.804 7.107 3.086 

1500.00 5.640 6.431 2.793 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10600. 

3730. 

1560. 

730. 

391. 

214. 

128. 

77.7 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

14700. 

5750. 

2530. 

1260. 

663. 

353. 

204. 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2500. 

1220. 

621. 

ACS-91 

A c s- 9 2 

ACS-93 

Three-Component Systems 141 
SYSTEM 

AL203(0.0) ,CA0(36.58), 

SI02 (63. 42) (X) 

AL203(0.0) ,CA0(35.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 3.122 1.356 

SYSTEM 

AL203(2.94) ,CA0(32~12), 

SI02 (64. 94) (X) 

AL203(5.0),CA0(30.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1450.00 5.804 4.247 1.844 

1500.00 5.640 3.742 1.625 

SYSTEM 

AL203(6.03l,CA0(27.42), 

SI02(66.54 (X) 

AL203(10.0 ,CA0(25.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.315 

8.333 

7.484 

6.750 

6.131 

5.545 

5.024 

4.550 

SYSTEM 

AL203(9.28l,CA0(22.49), 

SI02 (68. 23 (X) 

AL203(15.0 ,CA0(20.0), 

SI02 (65. 0) (%) 

LOG(N) 

4.045 

3.619 

3.250 

2.931 

2.663 

2.408 

2.182 

1.976 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

8.412 

7.581 

6.947 

6.353 

5.740 

LOG(N) 

3.653 

3.292 

3.017 

2.759 

2.493 

142 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

22.7 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

69.9 

42.2 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11100. 

4160. 

1780. 

854. 

460. 

256. 

152. 

94.6 

AU'IHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4500. 

1960. 

1040. 

574. 

311. 

ACS-94 

ACS-95 

ACS-96 

ACS-97 
SYSTEM 

AL203(12.69) ,CA0(17.31), 

SI02 (70. 0) (X) 

AL203(20.0),CA0(15.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) 

1250.00 6.566 10.35 

1300.00 6.357 9.596 

1350.00 6.161 8.770 

1400.00 5.977 8.074 

1450.00 5.804 7.371 

1500.00 5.640 6.846 

SYSTEM 

AL203(16.29) ,CA0(11.84), 

SI02 (71. 87) (X) 

AL203(25.0) ,CA0(10.0), 

SI02 (65. 0) (%) 

LOG(N) 

4.494 

4.167 

3.809 

3.507 

3.201 

2.973 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 8.284 3.598 

1500.00 5.640 7.550 3.279 

SYSTEM 

AL203(6.06l,CA0(22.02), 

SI02 (71. 93 (X) 

AL203(10.0 ,CA0(20.0), 

SI02 (70. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1400.00 5.977 6.975 3.029 

1450.00 5.804 6.397 2.778 

1500.00 5.640 5.889 2.558 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

31200. 

14700. 

6440. 

3210. 

1590. 

940. 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3960. 

1900. 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1070. 

600. 

361. 

ACS-98 

ACS-99 

ACS-100 

Three-Component Systems 143 
SYSTEM 

AL203(9.31l,CA0(16.93), 

SI02 (73. 75 (X) 

AL203(15.0 ,CA0(15.0), 

SI02 (70. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

12.002 

10.946 

10.008 

9.197 

8.453 

7.779 

7.185 

LOG(N) 

5.212 

4.754 

4.346 

3.994 

3.671 

3.378 

3.121 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVl;:D FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.63*10E5 

56700. 

22200. 

9870. 

4690. 

2390. 

1320. 

ACS-101 

------·------------------------------------------------------------------------

SYSTEM 

AL203(12.74) ,CA0(11.58) I 

SI02 {75. 67) (X) 

AL203(20.0),CA0(10.0), 

SI02 (10. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

11.760 

10.741 

9.809 

9.020 

8.281 

LOG(N) 

5.107 

4.665 

4.260 

3.918 

3.597 

144 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1948) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.28*10E5 

46200. 

18200. 

8270. 

3950. 

ACS-102 
............ 

lU 

V) 

0 

~ 

......... 

>- .,_ 

V) -

0 

u 

V) 

-

> 

l? 

0 

--' 

4 ~----~------~------~----~------~----~ 

3 

2 

1 

AI203- CoO- Si02 

MACHIN and YEE /1948) 

ACS-64 

ACS-61 

0 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 145 
...--.. 

LU 

V") 

0 

Cl.. 

-....... 

>- 1-

-

V") 

0 

u 

V") 

-

> 

l? 

0 

....J 

4 ~----~~----~------~------~------~-------, 

3 

2 

1 

AI203-CaO-Si02 

MACHIN and YEE (1948) 

ACS-64 

ACS-63 

ACS-62 

ACS-61 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

146 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

LU 

V') 

-

0 

~ 

........... 

>- r-

-

V') 

0 

u 

c./) 

-

> 

~ 

0 

~ 

4~----~------~------~----~------~----~ 

3 

2 

1 

AI 203-Co0- Si02 

MACHIN and YEE (1948) 

ACS-75 

0 ------~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 147 
4 ~----~--------------~------~------~----~ 

~ 

LU 

(./') 

0 

CL 

>-

~ 

3 

(./') 2 

0 

u 

(./') 

> 

<-' 

0 

__. 

l 

Al20 3- CaO- Si02 

MACHIN and YEE (1948) 

ACS-76 

ACS-75 

ACS-74 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

148 Viscosity of Synthetic and Natural Melts and Glasses 
.,......._, 

u.J 

(/) 

-

0 

a.. 

........... 

>- I-

-(/) 

0 

u 

(/) 

-

> 

0 

0 

__. 

4 ~----~----~----~----~----------~-----

3 

2 

1 

ACS-81 

ACS-80 

Al 20 3- CaO- Si02 

MACHIN and YEE /1948) 

0 ~----~----~--~~--~~----~--~~--~ 

1150 1250 1350 1450 

TEMPERATURE (°C) 

Three-Component Systems 149 
...,....._ 

UJ 

V') 

-

0 

a.. 

........... 

>- 1--

-

4~----~------~------~-----.------,-------, 

3 

A1 20 3- CaO- Si02 

MACHIN and YEE (1948) 

V') 2 

0 

ACS-82 I u 

V') 

> 

0 ACS- 81 

0 

__J 

1 

0 ~----~------~------._----~~----~-------

4.5 5.5 6.5 7.5 

10 000/T {KELVINS- 1

) 

150 Viscosity of Synthetic and Natural Melts and Glasses 
4 r-----~----~----~----~-----------------

3 

.......... 

lU 

(/) 

0 

a_ 

___... 

>-

I-

-

(/) 2 0 

u 

(/) 

-

> 

l? 

0 

__. 

1 

Al 20 3- CoO- Si02 

MACHIN and YEE (1948) 

0 ~----~----~----~----~----~----~----~ 

1150 1250 1350 1450 

TEMPERATURE (°C} 

Three-Component Systems 151 
....-.. 

LU 

V') 

-

0 

a... 

.......... 

>-

~ 

V') -

0 

u 

V') 

-

> 

~ 

0 

....J 

4~----~~----~------~------~------~------~ 

3 

2 

1 

Al20 3- CaO- Si02 

MACHIN and YEE (1948/ 

ACS-87 

ACS-86 

ACS-85 

ACS-84 

ACS-83 / 

0 ------~~----~------~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

152 Viscosity of Synthetic and Natural Melts and Glasses 
~ 

UJ 

lf) 

0 

Cl.. 

-

>-

1-

-lf) 

0 

u 

lf) 

-

> 

~ 

0 

....J 

5 

4 

3 

2 

1 

1150 

ACS-92 

Al20 3- CoO- Si02 

MACHIN and YEE (1948) 

1250 1350 1450 

TEMPERATURE (°C) 

Three-Component Systems 153 
...--.. 

LU 

V) 

0 

a.. 

__... 

.,_ >-

-

V) 

0 

u 

V) 

-

> 

0 

0 

__. 

5~----~~----------------------------~------~ 

4 

3 

2 

1 

4.5 

Al 20 3- CaO- Si02 

MACHIN and YEE (1948) 

ACS-93 

ACS-92 

ACS- 91 

ACS-90/ / 

ACS-89 / 

5.5 6.5 

10 000/T (KELVINS- 1

) 

Z5 

154 Viscosity of Synthetic and Natural Melts and Glasses 
5 ~----~----~----~----~----~----~----~ 

ACS-98 

4 

.......... 

UJ 

(./) ACS-97 

0 

a... 

-

>-

1-

-(./) 3 0 

u 

(./) 

-

> 

0 

0 

.....J 

2 

AI203- CoO- Si02 

MACHIN and YEE (1948} 

1 ------~----~----~----~-----------------

1150 1250 1350 1450 

TEMPERATURE {°C) 

Three-Component Systems 155 
..--

lU 

V') 

-

0 

Q.. 

-...... 

>-

1-

-

V') 

0 

u 

V') 

-

> 

l? 

0 

~ 

5------~--------------~------~------~----~ 

4 

3 

2 

AI203- CoO- Si02 

MACHIN and YEE {1948) 

ACS-99 I 

ACS-98 

ACS-97 

ACS-96 

ACS-95/ 

1 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

156 Viscosity of Synthetic and Natural Melts and Glasses 
............. 

w 

(./) 

-

0 

a.. 

......__. 

>- 1-

-

(./) 

0 

u 

(./) 

-

> 

0 

0 

_..J 

6 ~----~------~----~------~------~-----, 

5 

4 

3 

ACS-102 

ACS-101 

AI203- CaO- Si02 

MACHIN and YEE {1948) 

ACS-100 

2 ~----~------~----~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 157 
.,........_, 

LU 

V) 

-

0 

a.. 

...__... 

>- 1-

V) -

0 

u 

V) 

-

> 

0 

0 

--I 

6 ~----~------~------~------~------~----~ 

5 

4 

3 

2 

4.5 

Al20 3- CaO- Si02 

MACHIN anr/ YEE (1948) 

ACS-102 

ACS -101 

ACS-100 

5.5 6.5 

10 000/T (KELVINS- 1

) 

Z5 

158 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(3.0),CA0(37.0),SI02(60.0) (X) 

AL203(5.0),CA0(35.0),SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

AUTHOR 

MACHIN AND YEE (1954:) 

DERIVED FROM 

TABLE I 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

14:00.00 5.977 3.674: 1.595 

14:50.00 5.804: 3.219 1.398 

1500.00 5.64:0 5.839 1.233 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

39.4: 

25.0 

17.1 

SYSTEM 

AL203(6.0),CA0(33.0),SI02(61.0) (X) 

AL203(10.0),CA0(30.0),SI02(60.0) (%) 

MEASUREMENT METHOD 

AUTHOR 

MACHIN AND YEE (1954:) 

DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE I 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

14:00.00 5.977 

14:50.00 5.804: 

1500.00 5.64:0 

SYSTEM 

LN(N) 

6.04:3 

5.394: 

4:.836 

4:.4:02 

3.94:5 

3.4:84: 

LOG(N) 

2.624: 

2.34:2 

2.100 

1.912 

1.713 

1.513 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4:21. 

220. 

126. 

81.6 

51.7 

32.6 

AUTHOR 

AL203(9.0) ,CA0(28.0),SI02(63.0) (X) 

AL203(15.0) ,CA0(25.0),SI02(60.0) (%) 

MEASUREMENT METHOD 

MACHIN AND YEE (1954:) 

DERIVED FROM 

OSCILLATING-CYC. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

14:00.00 5.977 

14:50.00 5.804: 

1500.00 5.64:0 

SYSTEM 

LN(N) 

7.352 

6.593 

5.966 

5.366 

4:.852 

4:.353 

AL203(12.65) ,CA0(22.98), 

SI02 (64:.37) (X) 

AL203(20.0),CA0(20.0), 

SI02 (60. 0) (%) 

LOG(N) 

3.193 

2.863 

2.591 

2.330 

2.107 

1.890 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

14:00.00 5.977 

14:50.00 5.804: 

1500.00 5.64:0 

LN(N) 

8.657 

7.836 

7.139 

6.4:97 

5.866 

5.318 

LOG(N) 

3.760 

3.4:03 

3.100 

2.822 

2.54:8 

2.310 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

1560. 

730. 

390. 

214:. 

128. 

77.7 

AUTHOR 

(1/K) 

MACHIN AND YEE (1954:) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5750. 

2530. 

1260. 

663. 

353. 

204:. 

ACS-103 

ACS-104 

ACS-105 

ACS-106 

Three-Component Systems 159 
SYSTEM 

AL203(16.22) CA0(17.70)~ 

SI02 (66. 08) (X) 

AL203(25.0) ICA0(15.0) I 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 7.863 3.415 

1450.00 5.804 7.107 3.086 

1500.00 5.640 6.431 2.793 

SYSTEM 

AL203(2.94) ICA0(32.11) I 

SI02 (64. 94) (X) 

AL203(5.0) ICA0(30.0) I 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 4.247 

1500.00 5.640 3.742 

LOG (N) 

1.844 

1.625 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2600. 

1220. 

621. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

69.9 

42.2 

ACS-107 

ACS-108 

------------------------------------------------------------------------------

SYSTEM 

AL203(6.03l 1 CA0(27.42) 1 

SI02 (66. 55 (X) 

AL203(10.0 ICA0(25.0) I 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.484 

6.750 

6.131 

5.545 

5.024 

4.550 

LOG(N) 

3.250 

2.931 

2.663 

2.408 

2.182 

1.976 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1780. 

854. 

460. 

256. 

152. 

94.6 

ACS-109 

------------------------------------------------------------------------------

SYSTEM 

AL203(9.28l ICA0(22.49) I 

SI02 (68. 23 (X) 

AL203(15.0 ICA0(20.0) I 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) LOG(N) 

1300.00 6.357 8.412 3.653 

1350.00 6.161 7.581 3.292 

1400.00 5.977 6.947 3.017 

1450.00 5.804 6.353 2.759 

1500.00 5.640 5.740 2.493 

160 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4500. 

1960. 

1040. 

574. 

311. 

ACS-110 
SYSTEM 

AL203(12.69) ,CA0(17.31), 

SI02 (70. 00) (X) 

AL203(20.0) ,CA0{15.0), 

SI02 {65. 0) (%9) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N {POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

10.348 

9.596 

8.770 

8.074 

7.371 

6.846 

LOG(N) 

4.494 

4.167 

3.809 

3.507 

3.201 

2.973 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

31200. 

14700. 

6440. 

3210. 

1590. 

940. 

ACS-111 

------------------------------------------------------------------------------

SYSTEM 

AL203(16.29) ,CA0(11.84), 

SI02 (71. 87) (X) 

AL203(25.0) ,CA0(10.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 8.284 3.598 

1500.00 5.640 7.550 3.279 

SYSTEM 

AL203(15.91),CA0(46.29), 

SI02{37.80) (X) 

AL203(25.0) ,CA0(40.0), 

SI02(35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.991 1.299 

1450.00 5.804 2.468 1.072 

1500.00 5.640 2.015 0.875 

SYSTEM 

AL203(23.50) ,CA0(36.62), 

SI02 ( 39. 88) (X) 

AL203(35.0) ,CA0{30.0), 

SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.513 

4.691 

4.004 

3.447 

2.944 

LOG(N) 

2.394 

2.037 

1.739 

1.497 

1.279 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3960. 

1900. 

AUTHOR 

ACS-112 

MACHIN, YEE AND HANNA {1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.9 

11.8 

7.5 

AUTHOR 

ACS-113 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

248. 

109. 

54.8 

31.4 

19.0 

ACS-114 

Three-Component Systems 161 
SYSTEM 

AL203(2.90),CA0(52.77), 

SI02 ( 44. 33) (X) 

AL203(5.0) ,CA0(50.0), 

SI02 ( 45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1450.00 5.804 

1500.00 5.640 

LN(N) 

1.560 

1.227 

LOG(N) 

0.681 

0.533 

162 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4.80 

3.41 

ACS-115 
....-.-.. 

w 

c./) 

0 

a.. 

>-

~ 

-

4 ~--------------------------~----~----~ 

3 

ACS-114 

c./) 2 

0 

u 

c./) 

-

> 

~ 

g 

1 

AI203- CaO- Si02 

MACHIN, YEE and HANNA /1952} 

0 ~----~------~----~----~~----~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 163 
.......... 

UJ 

V') 

0 

0... 

........... 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

~ 

0 

~ 

4 ~----~------~------~----~~----~------~ 

3 

2 

1 

Al20 3- CoO- Si02 

MACHIN, YEE and HANNA (1952/ 

ACS-114 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

1 64 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(5.95l,CA0(48.65), 

SI02 ( 45.41 (X) 

AL203(10.0 ,CA0(45.0), 

SI02 ( 45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.451 1.064 

1450.00 5.804 2.023 0.879 

1500.00 5.640 1.625 0.706 

SYSTEM 

AL203(9.14l,CA0(44.32), 

SI02(46.54 (X) 

AL203(15.0 ,CA0(40.0), 

SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.500 

2.965 

2.534 

2.145 

AL203(12.50) ,CA0(39.78), 

SI02 (47. 73) (X) 

AL203(20.0),CA0(35.0), 

SI02 ( 45. 0) (%) 

LOG(N) 

1.520 

1.288 

1.100 

0.931 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.606 

4.828 

4.148 

3.616 

3.118 

2.708 

SYSTEM 

AL203(16.03),CA0(34.99), 

SI02 ( 48. 98) (X) 

AL203(25.0) ,CA0(30.0) I 

SI02 ( 45. 0) (%) 

LOG(N) 

2.435 

2.097 

1.801 

1.571 

1.354 

1.176 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.883 

4.248 

3.714 

3.270 

LOG(N) 

2.121 

1.843 

1.613 

1.420 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.6 

7.56 

5.08 

AUTHOR 

ACS-116 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

33.1 

19.4 

12.6 

8.54 

AUTHOR 

ACS-117 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

272. 

125. 

63.3 

37.2 

22.6 

15.0 

AUTHOR 

ACS-118 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

132. 

70.0 

41.0 

26.3 

ACS-119 

Three-Component Systems 165 
SYSTEM 

AL203(19.76),CA0(29.94), 

SI02 (50. 30) (X) 

AL203(30.0),CA0(25.0), 

SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 4.256 1.848 

SYSTEM 

AL203(18.8),CA0(51.2), 

SI02 {30. 0) (X) 

AL203(29.08),CA0(43.57), 

SI02(27.35) 

MEASUREMENT METHOD 

ROTATIONAL-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1555.2 5.470 

1561.9 5.450 

1570.3 5.425 

1617.4 5.290 

1622.7 5.275 

1691.6 5.090 

1699.4 5.070 

1711.1 5.040 

1747.2 4.950 

1772.0 4.890 

1801.7 4.820 

1872.9 4.660 

1924.8 4.550 

1979.3 4.440 

1986.9 4.425 

LN(N) 

1.957 

1.911 

1.911 

1.554 

1.497 

1.094 

1.094 

1.036 

.829 

.783 

.599 

.345 

.161 

-.046 

-.092 

LOG(N) 

.850 

.830 

.830 

.675 

.650 

.475 

.475 

.450 

.360 

.340 

.260 

.150 

.070 

-.020 

-.040 

166 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

70.5 

AUTHOR 

ACS-120 

ROSSIN, BERSAN, AND URBAIN 

(1964) 

DERIVED FROM 

FIG. 9 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7.079 

6.761 

6.761 

4.732 

4.467 

2.985 

2.985 

2.818 

2.291 

2.188 

1.820 

1.413 

1.175 

.955 

.912 

ACS-121 
:; """ 

ttl 

ttl 

h 

Q 

3 

'8 

:I 

ttl 

a 

tl'l 

-< fll 

;' 

3 

fll 

.... 

a--

..... 

--UJ 

(./) 

-

0 

a... 

-

>-

I-

-(./) 

0 

u 

(./) 

-

> 

() 

0 

__. 

3 ~--~--~--~----~--~--~--~~--~--~ 

Al20 3 - CaO- Si02 

ROSSIN, BERSAN and URBAIN (1964} 

2 

1t- ACS -121 

0 

-1 ~------~----~--~--~~--~--~---------

1550 1650 1750 1850 1950 

TEMPERATURE {°C) 
3 ~----~------~------~------~------r------. 

AI203- CaO- Si02 

ROSSIN, BERSAN and URBAIN (1964) 

2 

........... 

lLJ 

V') 

0 

a.. 

.......... 

>-

~ 

-

V') 1 0 

u 

V') 

-

> 

~ 

0 

__J 

0 ACS-121 

-1 ~----~------~------~------~------~----~ 

3 4 5 6 

10 000/T (KELVINS- 1

) 

168 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

Al203(.25)K20(.25)Si02(.50) (X) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T 

1711. 

1751. 

1796. 

1826. 

z 

5.040 

4.940 

4.833 

4.764 

LN(N) 

7.48 

7.13 

6.52 

6.17 

LOG(N) 

3.24 

3.09 

2.83 

2.67 

AUTHOR 

N'DALA et al. (1984) 

DERIVED FROM 

TABLE 1 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N 

1772. 

1248. 

678. 

478. 

AKS-1 

Three-Component Systems 169 
SYSTEM 

AL203(5.0) ,MG0(41.0) ,SI02(54.0) (X) 

AL203(10.0) ,MG0(30.0) ,SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) 

T Z LN(N) LOG(N) 1500.00 5.640 3.016 1.310 

Z = 10000. 0/T (K) (1/K) 

N 

20.4 

SYSTEM 

AL203(8.0),MG0(35.0),SI02(57.0) (X) 

AL203(15.0),MG0(25.0),SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1400.00 5.977 4.771 2.072 

1450.00 5.804 4.228 1.836 

1500.00 5.640 3.706 1.610 

SYSTEM 

AL203(11.60) ,MG0(29.34), 

SI02(59.06) (X) 

AL203(20.0),MG0(20.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.288 

5.595 

4.997 

4.464 

LOG(N) 

2.731 

2.430 

2.170 

1.939 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

118. 

68.6 

40.7 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

538. 

269. 

148. 

86.8 

(1/K) 

A MgS-1 

AMgS-2 

AMgS-3 

------------------------------------------------------------------------------

SYSTEM 

AL203(15.17) ,MG0(23.03), 

SI02 (61. 80) (X) 

AL203(25.0) ,MG0(15.0), 

SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.019 

8.020 

7.178 

6.417 

5.762 

5.165 

LOG(N) 

3.917 

3.483 

3.117 

2.787 

2.502 

2.243 

170 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8260. 

3040. 

1310. 

612. 

318. 

175. 

AMgS-4 
SYSTEM 

AL203(8.53l,MG0(28.76), 

SI02 (62. 71 (X) 

AL203(15.0 ,MG0(20.0), 

SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.479 

6.657 

5.971 

5.375 

4.836 

SYSTEM 

AL203(11.89),MG0(22.55), 

SI02 (65.56) (X) 

AL203(20.0) ,MG0(15.0), 

SI02 (65. 0) (%) 

LOG(N) 

3.248 

2.891 

2.593 

2.334 

2.100 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.425 

8.311 

7.591 

6.863 

6.190 

5.572 

SYSTEM 

AL203(15.57},MG0(15.75), 

SI02 (68. 68) (X) 

AL203(25.0) ,MG0(10.0), 

SI02 (65. 0) (%) 

LOG(N) 

4. 093 

3.610 

3.297 

2.980 

2.688 

2.420 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 1400.00 5.977 7.758 3.369 

1450.00 5.804 7.003 3.041 

1500.00 5.640 6.342 2.754 

AUTHOR 

MACHIN AND YEE 8 (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1770. 

778. 

392. 

216. 

126. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

12400. 

4070. 

1980. 

956. 

488. 

263. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K} (1/K) 

N 

2340. 

1100. 

568. 

SYSTEM AUTHOR 

AL203(26.25) ,MG0(26.25),SI02(47.5) (X)RIEBLING (1964) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1700.00 5.068 1.792 0.778 6. 

A MgS-5 

AMgS-6 

AMgS-7 

AMg S-8 

Three-Component Systems 171 
SYSTEM AL203(6.125) MG0(43.875)~ 

SI02 (50. 0) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1700.00 5.068 1.082 

SYSTEM 

LOG(N) 

0.470 

AL203(6.25) 1 MG0(43.75) 1 SI02(50.0) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1600.00 5.339 1.664 0.723 

SYSTEM 

AUTHOR 

RIEBLING (1964) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/f(K) (1/K) 

N 

2.95 

AUTHOR 

(X) RIEBLING (1964) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

5.28 

AL203 (12. 9) I MGO (37 .1) I SI02 (50. 0) (X) 

MEASUREMENT METHOD 

AUTHOR 

RIEBLING (1964) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z 

1600.00 5.339 LN(N) 

2.268 LOG(N) 

0.985 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.66 

AMgS-9 

AMgS-10 

AMgS-11 

------------------------------------------------------------------------------ SYSTEM AL203(12.9)~MG0(37.1)~SI02(50.0) (X) MEASUREMENT METHOD 

AUTHOR 

RIEBLING (1964) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 1700.00 5.068 1.649 0.716 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.2 

SYSTEM AUTHOR 

AL203(19.76) 1 MG0(30.24) 1 SI02(50.0) (X)RIEBLING (1964) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN (N) LOG (N) N 

1600.00 5.339 2.565 1.114 13.0 

AMgS-12 

AMgS-13 

------------------------------------------------------------------------------

SYSTEM 

AL203(19.8) MG0(30.2)~SI02(50.0) (X) MEASUREMENT METHOD 

AUTHOR 

RIEBLING {1964) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N {POISES) 

T (DEGREES C) 

T Z LN{N) LOG{N) 1700.00 5.068 1.946 0.845 

172 Viscosity of Synthetic and Natural Melts and Glasses 

P = 1.0 ATM. 

Z = 10000. 0/T {K) (1/K) 

N 

7. 

AMgS-14 
SYSTEM 

AL203(25.0),MG0(25.0),SI02(50.0) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 1600.00 5.339 2.833 1.230 

AUTHOR 

(X) RIEBLING (1964) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17.0 

AMgS-15 

--------------------------------------------------------------------------- SYSTEM 

AL203(25.0),MG0(25.0),SI02(50.0) (X) 

MEASUREMENT METHOD 

AUTHOR 

RIEBLING (1964) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z 

1700.00 5.068 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

LN(N) LOG(N) N 

2.079 0.903 8. 

AMgS-16 

--------------------------------------------------------------------------- SYSTEM 

AL203(24.0) ,MG0(24.0),SI02(52.0) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1700.00 5.068 2.3:2 1.000 

AUTHOR 

(X) RIEBLING (1964) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

10. 

AMgS-17 

----------------------------------------------------------------------------- SYSTEM 

AL203(22.5) ,MG0(22.5),SI02(55.0) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1700.00 5.068 2.639 1.146 

SYSTEM 

AUTHOR 

(X) RIEBLING (1964) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

14. 

AL203(18.5),MG0(18.5),SI02(63.0) (X) 

MEASUREMENT METHOD 

AUTHOR 

RIEBLING (1964) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1700.00 5.068 3.738 1.623 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

42. 

SYSTEM AUTHOR 

AL203(20.25) ,MG0(20.25) ,SI02(63.0) (X)RIEBLING (1964) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1700.00 5.068 3.135 1.362 23. 

AMgS-18 

AMgS-19 

AMgS -20 

Three-Component Systems 1 73 
SYSTEM 

AL203(15.75) ,MG0(15.75),SI02(68.5) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

AUTHOR 

(X)RIEBLING (1964) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) T Z LN(N) LOG(N) N 

1700.00 5.068 4.317 1.875 75. 

SYSTEM AUTHOR 

AL203(14.75),MG0(14.75),SI02(70.5) (X)RIEBLING (1964) MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N JPOISES) P = 1.0 ATM. 

T DEGREES C) Z = 10000. 0/T (K) (1/K) 

Z LN (N) LOG (N) N 

1700.00 5.068 4.787 2.079 120. 

SYSTEM AUTHOR 

AL203(12.25),MG0(12.25) ,SI02(75.0) (X)RIEBLING (1964) MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN (N) LOG (N) N 

1700.00 5.068 5.704 2.477 300. 

174 Viscosity of Synthetic and Natural Melts and Glasses 

AMgS-21 

AMgS-22 

AMgS-23 
SYSTEM 

Al203(.25)Na20{.25)Si02{.50) (X) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN{N) 

1594. 5.356 7.55 

1624. 5.271 6.98 

1678. 5.125 6.45 

1728. 4.997 6.03 

AUTHOR 

N'DALA et al. {1984) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) ANS-1 

LOG(N) N 

3.27 1900. 

3.03 1074. 

2.80 632. 

2.61 415. 

Three-Component Systems 175 
SYSTEM CA0(9.0) MG0(39.0)~SI02(52.0) (X) 

CA0(10.0) 1 MG0(30.0) 1 SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1500.00 5.640 2.031 0.882 

SYSTEM 

CA0(14.0) 1 MG0(33.0) 1 SI02(53.0) (X) CA0(15.0)~MG0(25.0) SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.885 1.253 

1450.00 5.804 2.361 1.025 

1500.00 5.640 1.981 0.860 

SYSTEM 

CA0(19.0) 1 MG0(27.0) 1 SI02(54.0) (X) CA0(20.0) MG0(20.0)~SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.288 

2.827 

2.398 

2.054 

LOG(N) 

1.428 

1.228 

1.041 

0.892 

SYSTEM 

CA0(25.0) 1 MG0(20.0) 1 SI02(55.0) (X) 

CA0(25.0) 1 MG0(15.0) 1 SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.321 

2.901 

2.501 

2.166 

LOG (N) 

1.442 

1.260 

1.086 

0.941 

CA0(34.0) 1 MG0(2.0) 1 SI02(64.0) (X) 

CAO (30. 0) I MGO (10. 0) I SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.405 

2.960 

2.534 

2.180 

LOG(N) 

1.479 

1.286 

1.100 

0.947 

176 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM .. Z = 10000.0/T(K) (1/K) 

N 

7.62 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17.9 

10.6 

7.25 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

26.8 

16.9 

11.0 

7.8 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

27.7 

18.2 

12.2 

8.72 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

30.1 

19.1 

12.6 

8.85 

M gCS- 1 

MgCS-2 

MgCS-3 

MgCS-4 

Mg C S-5 
SYSTEM 

CA0(36.0),MG0(7.0),SI02(57.0) (X) 

CA0(35.0) ,MG0(5.0),SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.411 

2.950 

2.549 

2.178 

LOG(N) 

1.481 

1.281 

1.107 

0.946 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

30.3 

19.1 

12.8 

8.83 

MgCS-6 

Three-Component Systems 177 
........... 

UJ 

(/') 

0 

a.. 

..........-

...,_ 

>-

-

(/') 

0 

u 

(/') 

-

> 

l? 

0 

_,J 

4 ~------------~----------------------~----~ 

3 

2 

1 

Ca0-Mg0-Si02 

MACHIN and YEE (1954) 

CMS-5 

CMS-4 

0 ~----~~----~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

178 Viscosity of Synthetic and Natural Melts and Glasses 
..--

LU 

V') 

-

0 

a.. 

........... 

.,_ >-

-

V') 

0 

u 

V') 

-

> 

l? 

0 

__, 

4 ~----~------~------~----~------~----~ 

3 

2 

1 

Co0-Mg0-Si02 

MACHIN and YEE (1954) 

CMS-2 

CMS-6 

0 ~----~------~------~----~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Three-Component Systems 179 
SYSTEM AUTHOR 

MGO (7. 03) , CAO (50. 53) , SI02 ( 42. 44) (X) 

MG0(5.0),CA0(50.0),SI02(45.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

MACHIN, YEE AND HANNA (1952) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1400.00 5.977 1.495 0.649 

1450.00 5.804 1.125 0.489 

1500.00 5.640 0.811 0.352 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4.46 

3.08 

2.25 

SYSTEM AUTHOR 

MG0(13.79) ,CA0(44.59) ,SI02(41.62) (X) MACHIN, YEE AND HANNA 

MGO (10. 0), CAO (45. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE II 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1400.00 5.977 1.493 0.648 4.45 

1450.00 5.804 1.122 0.487 3.07 

1500.00 5.640 0.806 0.350 2.24 

SYSTEM AUTHOR 

MgCS-7 

(1952) 

MgCS-8 

MG0(20.28) ,CA0(38.88) ,SI02(40.83) (X) MACHIN, YEE AND HANNA (1952) 

MGO (15. 0) , CAO (40. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE II 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) z = 10000. 0/T (K) (1/K) M g c s- 9 

T Z LN(N) LOG(N) N 

1400.00 5.977 1.413 0.614 4.11 

1450.00 5.804 1.061 0.461 2.89 

1500.00 5.640 0.742 0.322 2.10 

SYSTEM AUTHOR 

MG0(26.54) ,CA0(33.39) ,SI02(40.07) (X) MACHIN, YEE AND HANNA (1952) 

MG0(20.0),CA0(35.0),SI02(45.0) (%) MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE II 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) z = 10000. 0/T (K) (1/K) M g c s - 1 0 

T Z LN(N) LOG(N) N 

1400.00 5.977 1.376 0.598 3.96 

1450.00 5.804 1.044 0.453 2.84 

1500.00 5.640 0.747 0.324 2.11 ---------------------------------------------------------------------------- SYSTEM AUTHOR 

MG0(32.57) ,CA0(28.10) ,SI02(39.33) (X) MACHIN, YEE AND HANNA (1952) 

MG0(25.0),CA0(30.0),SI02(45.0) (%) MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE II 

N (POISES) P = 1.0 ATM . . T (DEGREES C) z = 10000. 0/T (K) (1/K) M g c s- 1 1 

T Z LN(N) LOG(N) N 

1500.00 5.640 0.663 0.288 1.94 

180 Viscosity of Synthetic and Natural Melts and Glasses 
...--.. 

lU 

V) 

0 

a.. 

...__. 

>- r-

-tl') 

0 

u 

V) 

-

> 

~ 

g 

4~----~------~--------------~----~------~ 

3 

2 

1 

CoO -MgO- Si02 

MACHIN, YEE and HANNA (1952) 

CMS-7 

0 ------~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Three-Component Systems 181 
~ 

UJ 

V') 

-

0 

a.. 

...........-

>-

~ 

-

V') 

0 

u 

V') 

-

> 

0 

0 

....J 

4~--------------------~------~------~----~ 

3 

2 

1 

CaO-MgO-Si02 

MACHIN, YEE and HANNA (1952/ 

CMS-7 

CMS- 8 

CMS-9 

CMS-10 

0~----~------~------~------~------~----~ 

5 6 7 

10 000/T (KELVINS- 1) 

182 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

NA20(23.4),CA0(5.6),SI02(71.0) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1000.00 7.855 

1050.00 7.559 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

8.003 

7.371 

6.797 

6.263 

5.775 

5.303 

4.828 

4.387 

4.055 

LOG(N) 

3.476 

3.201 

2.952 

2.720 

2.508 

2.303 

2.097 

1.905 

1.761 

AUTHOR 

MACKENZIE (1957) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2990. 

1590. 

895. 

525. 

322. 

201. 

125. 

80.4 

57.7 

NCS-1 

Three-Component Systems 183 
-I 

V') 

u 

z 

0 

0 

M 

~ 

.......... 0 u 

0 0 N __.. ~ 

0 

0 

0 

~ 

0 ------~------~----~------~----~------~----~----~ 0 

M 0~ 

{3SIOd) AliSOJSI/\ 901 

184 Viscosity of Synthetic and Natural Melts and Glasses 
I 

V') 

u 

z 

(3SIOd) A!IS.O)SIA 901 

-

N 

0 ~ V) ~ I ~ 

0 l.l, 

0 ..... 

1\.1 u ~ 00 

I l.l, 

0 

N t5 

0 'q: ...--

z ~ -I 

U") 

z 

> _,J 

w ........ ~ -: 

1-

........... 

0 

0 

0 

0 

,--

Three-Component Systems 185 
SYSTEM 

NA20(7.2) ,K20{18.5) ,SI02{74.3) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

{X) 

N {POISES) 

T {DEGREES C) T Z 

1050.00 7.559 

1100.00 7.283 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN{N) 

7.901 

7.320 

6.777 

6.303 

5.817 

5.336 

4.934 

4.566 

LOG{N) 

3.431 

3.179 

2.943 

2.737 

2.526 

2.318 

2.143 

1.983 

186 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACKENZIE {1957) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) {1/K) 

N 

2700. 

1510. 

877. 

546. 

336. 

208. 

139. 

96.2 

NKS-1 
-I 

\1) 

~ 

z 

M 

(3SIOd) AliSOJSI/\ 901 

N 

0 ~ 

V) ~ I ~ 

ON 

l.t., 

~ ~ <:: I l.t., 

0 

N ~ 0 ~ 

z ~ 

0 

0 

M 

,... 

0 

0 

N 

,... 

0 

0 

,... 

,... 

0 

0 

0 

,... 

0 

0 

oo-. 

.........-.. 

u 

0 

-._...... 

UJ 

0::: 

:::::> 

~ a::: 

UJ 

a.. 

~ UJ 

~ 

Three-Component Systems 187 
NKS-1 

3 

-w 

V) 

0 

a_ 

-

>- f-

-

V) 2 0 

u 

V) 

-

> 

~ 

0 

......J 

1 

Na20- K20- Si02 

MACKENZIE (1957) 

0 ----~~--~----~----~----~----~----~----~ 

5 6 7 8 9 

10 000/T (KELVINS-1

) 

188 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

NA20(21.8) ,LI20(11.4) ,8102(66.8) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

900.00 8.525 

950.00 8.177 

1000.00 7.855 

1050.00 7.559 

1100.00 7.027 

LN(N) 

7.979 

7.340 

6.719 

6.192 

5.204 

LOG(N) 

3.465 

3.188 

2.918 

2.689 

2.260 

AUTHOR 

(X) MACKENZIE (1957) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2920. 

1540. 

828. 

489. 

182. 

NLS-1 

Three-Component Systems 189 
-I 

c./') 

...... 

z 

• 

(3SIOd) A!ISOJSIA 901 

190 Viscosity of Synthetic and Natural Melts and Glasses 

0 

0 

0 

M 

r--

0 .,......._ 

0 u N~ 

0 

0 

0 

r--

0 

0 

~ 
3 

..--

w 

V') 

0 

a... 

-

>- NLS-1 

...._ 

V') 2 0 

u 

V') 

-

> 

~ 

0 

_J 

1 

Na20- Li20-Si02 

MACKENZIE (19,57) 

0 ----~----~----~----~----~----~----~-----

5 6 7 8 9 

10 000/T (KELVINS-1

) 

Three-Component Systems 191 

Four-Component Systems 

Four-Component Systems 193 
SYSTEM 

AL203(8.8) ,CA0(37.3), 

CAF2 (4. 0) , SI02 (49. 9) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.812 

4.191 

3.730 

3.247 

2.947 

2.579 

AL203(12.2) ,CA0(45.5), 

CAF2 (1. 6), SI02 (41. 6) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.605 

3.868 

3.247 

2.809 

2.372 

2.049 

LOG(N) 

2.09 

1.82 

1.62 

1.41 

1.28 

1.12 

LOG(N) 

2.00 

1.68 

1.41 

1.22 

1.03 

0.89 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

TABLE 

P = 1. 0 ATM. 

Z = 10000.0/t(K) (1/K) 

N 

123.0 

66.07 

41.69 

25.70 

19.05 

13.18 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

100.0 

47.86 

25.70 

16.60 

10.72 

7.762 

A C C S-1 

ACCS- 2 

----------------------------------------------------------------------------

SYSTEM 

AL203(11.4),CA0(41.6), 

CAF2 (8. 2) , SI02 (38. 9) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.753 

3.178 

2.602 

2.257 

2.164 

1.911 

SYSTEM 

AL203(8.0),CA0(34.0), 

CAF2 (12. 4) , SI02 (45. 5) (X) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.500 

3.062 

2.901 

2.556 

2.533 

2.441 

LOG(N) 

1.63 

1.38 

1.13 

0.98 

0.94 

0.83 

LOG(N) 

1.52 

1.33 

1.26 

1.11 

1.10 

1.06 

194 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

TABLE 

P = 1 . 0 ATIJJ . 

Z = 10000.0/T(K) (1/K) 

N 

42.66 

23.99 

13.49 

9.550 

8.710 

6.761 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

33.11 

21.38 

18.20 

12.88 

12.59 

11.48 

AC cs- 3 

A C C S -4 
.,......._ 

LU 

V') 

-

0 

a... 

......... 

>-

...... 

-

V') 

0 

u 

V') 

-

> 

l? 

g 

4 ~----~------~------------~----~----~ 

3 

2 

1 

AI203-CaO- CaF2-Si02 

BILLS (1963) 

ACCS-1 

ACCS-2 

ACCS-3 

0 ~----~------~----~----~~----~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 195 
.---... 

UJ 

c./) 

0 

a.. 

..__.. 

>- 1--

-

c./) 

0 

u 

c./) 

-

> 

<-? 

0 

__, 

4 ~----~----------------------~------------~ 

3 

2 

1 

AI203- CoO- CaF2- Si02 

BILLS {196.1) 

ACCS-1 

ACCS-2 

ACCS-3 

0 ~----~------~------~------~------~------~ 

4.5 5.5 6.5 7. 5 

10 000/T (KELVINS- 1

} 

196 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(8.83),CA0(17.41), 

E'EO (0. 0), SI02 (73. 76) (X) 

AL203(14.2),CA0(15.4), 

FEO (0. 0) , SI02 (69. 9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1350.00 6.161 9.413 

1400.00 5.977 8.678 

1450.00 5.804 8.033 

SYSTEM 

AL203(8.29),CA0(13.82), 

FEO (3. 92) , SI02 (73. 97) (X) 

AL203(13.2),CA0(12.1), 

FE0(4.4),SI02{69.4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1350.00 6.161 9.319 

1400.00 5.977 8.648 

1450.00 5.804 8.006 

SYSTEM 

AL203(9.93),CA0(10.35), 

FEO (7. 09) , SI02 (7 2. 63) (X) 

AL203(15.7),CA0{9.0), 

E'EO (7. 9) , SI02 (67. 7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1350.00 6.161 9.200 

1400.00 5.977 8.585 

1450.00 5.804 7.962 

LOG(N) 

4.088 

3.769 

3.489 

LOG(N) 

4.047 

3.756 

3.477 

LOG(N) 

3.996 

3.728 

3.458 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

z = 1 o o 0 0 . 0 /T (K) ( 1/K) A C F S - 1 

N 

12300. 

5870. 

3080. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A c F s - 2 

N 

11200. 

5700. 

3000. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

9900. 

5350. 

2870. 

ACFS-3 

---------------------------------------------------------------------------- SYSTEM 

AL203(11.08),CA0(24.439, 

FEO (0. 0) , SI02 (64. 49) (X) 

AL203(17.4),CA0(21.1), 

FEO (0. 0) , SI02 (59. 7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.997 

1450.00 5.804 

LN(N) 

9.292 

8.240 

7.444 

6.780 

6.273 

LOG(N) 

4. 035 

3.579 

3.233 

2.944 

2.724 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10900. 

3790. 

1710. 

880. 

530. 

ACFS-4 

Four-Component Systems 197 
SYSTEM 

AL203(12o12) ICA0(19o91) I 

FEO (3 0 86) I SI02 (64 o11) (X) 

AL203(18o7) 1 CA0(16o9) 1 

FEO (4 0 2) I SI02 (58 0 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

T (DEGREES C) 

T Z LN(N) 

8o916 

8o055 

7o293 

6o593 

5o966 

LOG(N) 

3o872 

3.498 

3o167 

2.863 

2.591 

Z = 10000.0/T(K) (1/K) 

N 

7450. 

3150. 

1470. 

ACFS-5 

1250o00 6o566 

1300o00 6o357 

1350o00 6o161 

1400o00 5o977 

1450o00 5o804 

SYSTEM 

AL203(11o24) ICA0(16o87) I 

FEO (7 0 24) I SI02 (64 0 65) (X) 

AL203(17o2) ICA0(14o2) I 

FEO (7 0 8) I SI02 (58 0 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

730. 

390o 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

N (POISES) P = 1o0 ATM. 

T (DEGREES C) 

T Z LN(N) 

8.674 

7.804 

7.090 

6.446 

5.799 

LOG(N) 

3.767 

3.389 

3.079 

2.799 

2.519 

z = 10000oO/T(K) (1/K) ACFS-6 

N 

5850. 

2450. 

1200. 

1250o00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450o00 5.804 

SYSTEM 

AL203(11.89) 1 CA0(16o92), 

FEO (6. 60) , SI02 (64. 59) (X) 

AL203(18.4) ,CA0(14.4), 

FEO (7. 2) , SI02 (58. 9) (%) 

630. 

330. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 6 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1250.00 6.566 8.669 3.765 5820. 

1300o00 6.357 7.824 3.398 2500. 

1350.00 6.161 7.155 3.107 1280. 

1400.00 5.977 6.492 2o820 660. 

1450.00 5.804 5.858 2.544 350. 

ACFS-7 

------------------------------------------------------------------------------ SYSTEM AUTHOR 

AL203(5o58) ICA0(33.47), JOHANNSEN AND BRUNION (1959) FEO (0. 0) , SI02 (60. 95) (X) 

AL203(9.3) ,CA0(30.7), 

FEO (0. 0) , SI02 (59. 9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350o00 6.161 

1400.00 5.977 

1450.00 5o804 

LN(N) 

7.467 

6o579 

5.784 

4.942 

4.094 

3.689 

LOG(N) 

3.243 

2.857 

2.512 

2.146 

1.778 

1.602 

198 Viscosity of Synthetic and Natural Melts and Glasses 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1750. 

7200 

325. 

140o 

60. 

40. 

ACFS-8 
SYSTEM 

AL203(5.55),CA0(29.l4), 

FEO (3. 98) , SI02 (61. 33) (X) 

AL203(9.1),CA0(26.3), 

FEO (4.6), SI02 (59. 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.346 

6.454 

5.652 

4.828 

3.912 

3.555 

SYSTEM 

AL203(5.91),CA0(27.36), 

FEO (6. 89) , SI02 (59. 84) (X) 

AL203(9.5),CA0(24.2), 

FEO (7. 8) , SI02 (56. 7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.170 

6.328 

5.561 

4.745 

3.807 

3.401 

SYSTEM 

AL203(12.50),CA0(12.35), 

. FEO (0. 0) , SI02 (75 .15) (X) 

AL203(19.5) ,CA0(10.6), 

FEO (0. 0) , SI02 (69 .1) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 9.036 

SYSTEM 

AL203(12.18),CA0(9.14), 

FEO ( 3. 75) , SI02 (74. 92) (X) 

AL203(18.9) ,CA0(7.8), 

FEO (4 .1), SI02 (68. 5) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 8.902 

LOG(N) 

3.190 

2.803 

2.455 

2.097 

1.699 

1.544 

LOG(N) 

3.114 

2.748 

2.415 

2.061 

1.653 

1.477 

LOG(N) 

3.924 

LOG(N) 

3.866 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1. 0 ATM. 

z = 10000.0/T(K) (1/K) ACFS-9 

N 

1550. 

635. 

285. 

125. 

50.0 

35.0 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) N 

1300. 

560. 

260. 

115. 

45. 

30. 

AUTHOR 

ACFS -10 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8400. 

AUTHOR 

ACFS-11 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7350. 

ACFS-12 

Four-Component Systems 199 
SYSTEM 

AL203(12.20),CA0(5.52), 

FEO (7. 49) , SI02 (74. 79) (X) AL203(18.5),CA0(4.6), 

FEO (8. 0) , SI02 (66. 5) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) T (DEGREES C) 

T Z LN(N) 1450.00 5.804 8.666 LOG(N) 

3.763 

200 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5800. 

ACFS-13 
.......-.. 

lU 

V) 

0 

a.. 

--..... 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

~ 

0 

_,J 

5 ~----~------~------~------~------~----~ 

4 

3 

2 

Al20 3- CaO- FeO- Si02 

JOHANNSEN and BRUNtON (1959) 

ACFS-4 

ACFS-5 

ACFS-6 

ACFS-8 

1 ~----~------~------~--------------------~ 

1150 1250 1350 1450 

TEMPERATURE (°C) 

Four-Component Systems 201 
~ 

lU 

(./') 

-

0 

a_ 

___. 

>- 1-

-(./') 

0 

u 

(./') 

-

> 

~ 

0 

......J 

5 ~------~------~------~------~------~------~ 

4 

3 

2 

1 

5 

AI203-CaO- FeO- Si02 

JOHANNSEN and BRUNtON (1959) 

ACFS-2 ACFS-4 ACFS-3 

ACFS-5 

ACFS-6 

ACFS-7 

ACFS-8 

ACFS-9 

6 7 

10 000/T (KELVINS- 1

) 

8 

202 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUTHOR 

A1203(.19)Ca0(.11)K20(.08)Si02(.62) (X) N1

DALA et al. (1984) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN(N) LOG(N) N ACKS-1 

1285. 6.418 10.63 4.61 41357. 

1289. 6.402 10.48 4.55 35596. 

1345. 6.180 9.58 4.16 14472. 

1350. 6.161 9.44 4.09 12581. 

1423. 5.896 R.46 3.67 4722. 

1425. 5.889 8.42 3.65 4536. 

1431. 5.868 8.35 3.62 4230. 

1454. 5.790 8.12 3.52 3361. 

1463. 5.760 7.91 3.43 2724. 

1494. 5.659 7.47 3.24 1754. 

1499. 5.643 7.40 3.21 1635. 

1566. 5.437 6.66 2.89 780. 

1571. 5.422 6.61 2.87 742. 

1617. 5.291 6.10 2.64 445. 

1625. 5.268 5.91 2.56 368. -------------------------------------------------------------------------------- SYSTEM AUTHOR 

A1203(.19)Ca0(.14)K20(.06)Si02(.62) (X) N1

DALA et al. (1984) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN( N) LOG(N) N AC KS-2 

1323. 6.265 10.50 4.56 36315. 

1414. 5.927 8.64 3.75 5653. 

1403. 5.966 7.71 3.34 2230. 

1466. 5.750 7.73 3.35 2275. 

1467. 5.747 7.72 3.35 2252. 

1556. 5.467 6.91 3.00 1002. 

1630. 5.254 6.00 2.60 403. 

1671. 5.144 5.36 2.32 212. 

1672. 5.141 5.35 2.32 210. 

1699. 5.070 5.15 2.23 172. 

1703. 5.060 4.92 2.13 137. 

1710. 5.042 4.92 2.13 137. 

1719. 5.020 4.91 2.13 135. 

1765. 4.906 4.38 1.90 79. 

1771. 4.892 4.36 1.89 78. 

Four-Component Systems 203 
SYSTEM 

AL203(14.91),CA0(18.19), 

MNO (0. 0) , SI02 (66. 91) (X) 

AL203(22.8),CA0(15.39), 

MNO (0. 0) , SI02 (60. 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1400.00 5.977 8.039 

1450.00 5.804 7.162 

SYSTEM 

AL203(14.70),CA0(14.98), 

MNO (4. 08) , SI02 (66. 24) (X) 

AL203(22.3),CA0(12.5), 

MNO (4. 3), SI02 (59. 2) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

"'9.105 

8.256 

7.534 

6.898 

AL203(15.20) ,CA0(11.27), 

MNO (7. 57) , SI02 (6.5. 96) (X) AL203(22.8) ,CA0(9.3), 

MNO (7. 9) , SI02 (58. 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

"'8.613 

7.808 

7.131 

6.579 

LOG(N) 

3.491 

3.111 

LOG(N) 

"'3.954 

3.585 

3.272 

2.996 

LOG(N) 

"'3.740 

3.391 

3.097 

2.857 

204 Viscosity of Synthetic and Natural Melts and Glasses 

I AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3100. 

1290. 

AUTHOR 

ACMS-1 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

"'9000. 

3850. 

1870. 

990. 

AUTHOR 

ACMS-2 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 6 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

"'5500. 

2460. 

1250. 

720. 

ACMS-3 
.,__ 

>-

5.5 ,....--------------------------. 

4.5 

Al 20 3- Ca0-Mn0-Si02 

JOHANNSEN and BRUNION (1959) 

Q3.5 

u 

V') 

> 

0 

g 

2.5 

ACMS-1 

ACMS-2 

ACMS-3 

1.5 "----__ __...... ___ _.__ __ ___. ___ --'-----""------' 

1250 1350 1450 1550 

TEMPERATURE (°C) 

Four-Component Systems 205 
.,........_ 

w 

(./) 

-

0 

a.. 

>- 1--

-

5.5 r------.-----,....-----.--------,r-------r-------, 

4.5 

A1 20 3- Ca0-Mn0-Si02 

JOHANNSEN and BRUNION /1959) 

()3.5 

u 

(./) 

-

> 

l? 

g 

2.5 

ACMS-2 

ACMS-3 

1.5 L.-..----~----....1..-.-----L----------....._ __ ___. 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1) 

206 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUTHOR 

A1203(.19)Ca0(.12)Na20(.08)Si02(.61) (X) N • DALA et al. (1984) 

MEASURE ~NT ~THOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN( N) LOG(N) N ACNS-1 

1253. 6.553 10.34 4.49 30946. 

1310. 6.317 9.34 4.05 11384. 

1316. 6.293 9.30 4.03 10938. 

1370. 6.086 8.49 3.68 4865. 

1372. 6.079 8.30 3.60 4023. 

1453. 5.793 7.39 3.20 1619. 

1460. 5.770 7.34 3.18 1540. 

1550. 5.485 6.32 2.74 555. 

1554. 5.473 6.29 2.73 539. 

1556. 5.467 6.23 2.70 507. 

1614. 5.299 5.74 2.49 311. 

1619. 5.285 5.59 ~.42 267. 

lfi17. 5.291 5.64 2.44 281. 

1643. 5.219 5.42 2.35 225. 

1648. 5.205 5.31 2.30 202. 

SYSTEM AUTHOR 

A1203(.19)Ca0(.13)Na20(.06)Si02(.62) (X) N'DALA et a 1 • ( 1984) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN(N) LOG(N) N ACNS-2 

1435. 5.854 8.10 3.51 3294. 

1438. 5.844 7.20 3.12 1339. 

1495. 5.656 6.84 2.97 934. 

1574. 5.414 5.87 2.54 354. 

1576. 5.408 6.00 2.60 403. 

1634. 5.243 5.28 2.29 196. 

1696. 5.078 4.81 2.08 122. 

1721. 5.015 4.73 2.05 113. 

1748. 4.948 4.29 1.86 72. 

Four-Component Systems 207 
SYSTEM 

AL203(11.08) ,CA0(24.43), 

TI02(0.0),SI02(64.49) (X) 

AL203(17.4) ,CA0(21.1), 

TI02(0.0),SI02(59.7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

9.292 

8.240 

7.444 

6.780 

6.273 

SYSTEM 

AL203(12.22),CA0(19.97), 

TI02 (3.40) ,SI02 (64.41) (X) 

AL203(18.8),CA0(16.9), 

TI02(4.1) ,SI02(58.4) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

9.220 

8.189 

7.409 

6.768 

6.109 

AL203(12.29) ,CA0(15.89), 

TI02 (7. 04) , SI02 (64. 78) (X) 

AL203(18.7),CA0(13.3), 

TI02 (8. 4) , SI02 (58 .1) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1250.00 6.566 9.042 

1300.00 6.357 8.175 

1350.00 6.161 7.396 

1400.00 5.977 6.721 

1450.00 5.804 6.040 

LOG(N) 

4.035 

3.579 

3.233 

2.944 

2.724 

LOG(N) 

4.004 

3.556 

3.217 

2.940 

2.653 

LOG(N) 

3.927 

3.550 

3.212 

2.919 

2.623 

208 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

10900. 

3790. 

1710. 

880. 

530. 

AUTHOR 

ACTS-1 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

10100. 

3600. 

1650. 

870. 

450. 

AUTHOR 

ACTS-2 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8450. 

3550. 

1630. 

830. 

420. 

ACTS-3 
SYSTEM 

AL203(10.57)1CA0(29.05) I 

TI02(0.0)~SI02(60.38) (X) 

AL203(17.2) ICA0(26.0) I 

TI02 (0. 0) I SI02 (57. 9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

7.450 

6.579 

5.829 

5.193 

4.787 

AL203(11.02) ICA0(23.81) I 

TI02 (5. 54) I SI02 (59. 63) (X) 

AL203(17.0) ICA0(20.2) I 

TI02(6.7) 1SI02(54.2) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

7.139 

6.337 

5.720 

5.136 

4.654 

AL203(12.05) 1CA0(24.42) 1 

TI02(11.26) 1SI02(52.28) (X) 

AL203(18.3) 1CA0(20.4) 1 

TI02(13.4) 1SI02(46.8) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

5.193 

4.605 

3.912 

3.401 

LOG(N) 

3.236 

2.857 

2.531 

2.255 

2.079 

LOG(N) 

3.100 

2.752 

2.484 

2.230 

2.021 

LOG(N) 

2.255 

2.000 

1.699 

1.477 

~AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

z = 10000.0/T(K) (1/K) ACTS-4 

N 

1720. 

720. 

340. 

180. 

120. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1260. 

565. 

305. 

170. 

105. 

AUTHOR 

ACTS-5 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

180. 

100. 

50. 

30. 

ACTS-6 

------------------------------------------------------------------------------ SYSTEM 

AL203(12.90) CA0(24.18)~ 

TI02(16.20) 1SI02(46.72) (X) 

AL203(19.3)1CA0(19.9) I 

TI02 (19. 0) I SI02 (41. 2) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

4.942 

3.807 

3.401 

2.996 

LOG(N) 

2.146 

1.653 

1.477 

1.301 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A c T s- 7 

N 

140. 

45. 

30. 

20. 

Four-Component Systems 209 
........... 

lU 

V') 

0 

a... 

-.-. 

>- 1-

-

V') 

0 

u 

V') 

-

> 

l? 

0 

_..J 

5 ~------~----------------------~------------~ 

Al 20 3- CoO- Ti02-Si02 

JOHANNSEN and BRUNION (1959) 

4 ACTS-2 

ACTS-3 

ACTS-4 

ACTS-5 

3 

ACTS-6 

ACTS -7 

2 

ACTS-1 

1 --------~------~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

210 Viscosity of Synthetic and Natural Melts and Glasses 
.......-.-

LU 

(./) 

-

0 

a.. 

.......... 

>-

~ 

-(./) 

0 

u 

(./) 

-

> 

0 

0 

~ 

5 ~----~------~------~------~------~----~ 

4 

3 

2 

AI203- CaO- Ti02- Si02 

JOHANNSEN and BRUNtON (1959) 

ACTS-1 

I 

ACTS-2 

ACTS-3 

ACTS-4 

ACTS-5 

ACTS-6 

ACTS-7 

1 ~----~------~------~------~------~----~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

Four-Component Systems 211 
SYSTEM 

AL203(5.84) ,CA0(37.18), 

MGO (7. 39), SI02 (49. 58) (X) 

AL203(10.0) ,CA0(35.0), 

MGO (5. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1400.00 5.977 3.077 

1450.00 5.804 2.701 

1500.00 5.640 2.186 

LOG(N) 

1.336 

1.173 

0.949 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

21.7 

14.9 

8.9 

1550.00 5.485 1.775 0.771 5.9 

SYSTEM 

AL203(5.72) ,CA0!31.22), 

MG0(14.48),SI02 48.57) {X) 

AL203(10.0) ,CAO 30.0), 

MGO (10. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T 

1400.00 

1500.00 

1550.00 

z 

5.977 

5.640 

5.485 

LN(N) 

2.950 

1.825 

1.459 

SYSTEM 

AL203(5.82),CA0(42.35), 

MGO (7. 36), SI02 (44.46) (X) 

AL203{10.9) ,CA0(40.0), 

MGO (5. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T {DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.303 

2.001 

1.686 

1.386 

AL203(5.70) ,CA0!36.30), 

MG0(14.43) ,SI02 43.56) {X) 

AL203{10.0),CAO 35.0), 

MGO {10. 0) , SI02 {45. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N {POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN{N) 

2.175 

1.841 

1.435 

1. o-3o 

LOG(N) 

1.281 

0.792 

0.633 

LOG(N) 

1.000 

0.869 

0.732 

0.602 

LOG{N) 

0.944 

0.799 

0.623 

0.447 

212 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.1 

6.2 

4.3 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.0 

7.4 

5.4 

4.0 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

8.8 

6.3 

4.2 

2.8 

AMgC$-1 

AMgCS-2 

AMgCS-3 

AMgCS-4 
SYSTEM 

AL203(5.59),CA0!30.50), 

MG0(21.21),SI02 42.69) (X) 

AL203(10.0),CAO 30.0), 

MGO (15. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.740 

1.435 

1.131 

0.875 

SYSTEM 

AL203(5.80),CA0(47.47), 

MGO (7. 34) , SI02 (39. 39) (X) 

AL203(10.0),CA0(45.0), 

MGO (5. 0) , SI02 (40. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.758 

1.131 

1.065 

0.788 

LOG(N) 

0.756 

0.623 

0.491 

0.380 

LOG(N) 

0.763 

0.491 

0.462 

0.342 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.7 

4.2 

3.1 

2.4 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.8 

3.1 

2.9 

2.2 

AMgCS-5 

AMgCS-6 

------------------------------------------------------------------------------ SYSTEM 

AL203(5.69),CA0!41.35), 

MG0(14.38),SI02 38.59) (X) 

AL203(10.0),CAO 40.0), 

MGO (10. 0) , SI02 (40. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.723 

1.335 

0.956 

0.642 

LOG(N) 

0.748 

0.580 

0.415 

0.279 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.6 

3.8 

2.6 

1.9 

AMgCS-7 

---------------------------------------------------------------------------~-

SYSTEM 

AL203(5.57) ,CA0!35.46), MGO (21.14) , SI02 37. 82) (X) 

AL203(10.0),CAO 35.0), 

MGO (15. 0) , SI02 ( 40. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.504 

1.131 

0.693 

0.336 

LOG(N) 

0.653 

0.491 

0.301 

0.146 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4.5 

3.1 

2.0 

1.4 

AMgCS-8 

Four-Component Systems 213 
SYSTEM 

AL203(11.64),CA0(31.74), 

MGO (22. 07) , SI02 (34. 55) (X) 

AL203(20.0),CA0(30.0), 

MGO (15. 0) , SI02 (35. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.104 

1.589 

1.163 

0.993 

SYSTEM 

AL203(5.78),CA0(52.56), 

MGO (7. 31) , SI02 (34. 34) (X) 

AL203(10.0) ,CA0(50.0), 

MGO (5. 0), SI02 (35. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 1.902 

1500.00 5.640 1.099 

1550.00 5.485 0.788 

LOG(N) 

0.914 

0.690 

0.505 

0.431 

LOG(N) 

0.826 

0.477 

0.342 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.2 

4.9 

3.2 

2.7 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.7 

3.0 

2.2 

AMgCS-9 

AMgCS-1 0 

------------------------------------------------------------------------------ SYSTEM 

AL203(5.67),CA0~46.35), 

MG0(14.33) ,SI02 33.65) (X) 

AL203(10.0),CAO 45.0), 

MG0(10.0),SI02(35.0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

1.589 

1.030 

0.588 

0.336 

AL203(5.55) ,CA0~40.39), 

MG0(21.07) ,SI02 32.98) (X) 

AL203(10.0),CAO 40.0), 

MG0815. 0) , SI02 (35. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.253 

0.742 

0.336 

0.095 

LOG(N) 

0.690 

0.447 

0.255 

0.146 

LOG(N) 

0.544 

0.322 

0.146 

0.041 

214 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.9 

2.8 

1.8 

1.4 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3.5 

2.1 

1.4 

1.1 

AMgCS-11 

AMgCS-12 
SYSTEM 

AL203(5.65),CA0~51.33), 

MG0(14.28) ,SI02 28.74) (X) 

AL203(10.0) ,CAO 50.0), 

MGO (10. 0), SI02 (30. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 3.332 

1500.00 5.640 2.674 

1550.00 5.485 2.116 

SYSTEM 

AL203(5.54),CA0(45.28), 

MGO (21. 0) , SI02 (28 .18) (X) 

AL203(10.0),CA0(45.0), 

MGO (15. 0) , SI02 (30. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 2.460 

1500.00 5.640 1.099 

1550.00 5.485 0.742 

SYSTEM 

AL203(11.56) ,CA0(42.02), 

MG0(21.92),SI02(24.51) (X) 

AL203(20.0) ,CA0(40.0), 

MGO (15. 0) , SI02 (25. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.740 

1.163 

0.916 

0.742 

LOG(N) 

1.447 

1.161 

0.919 

LOG(N) 

1.068 

0.477 

0.322 

LOG(N) 

0.756 

0.505 

0.398 

0.322 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

28.0 

14.5 

8.3 

AUTHOR 

HOFMANN ( 1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.7 

3.0 

2.1 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.7 

3.2 

2.5 

2.1 

AMgCS-13 

AMgCS-14 

AMgCS-15 

---------------------------------------------------------------------------- SYSTEM 

AL203(11.76) ,CA0(53.43), 

MG0(14.87) ,SI02(19.95) (X) 

AL203(20.0) ,CA0(50.0), 

MG0(10.0) ,SI02(20.0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 3.059 

1500.00 5.640 1.668 

1550.00 5.485 1.482 

LOG(N) 

1.328 

0.724 

0.643 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

21.3 

5.3 

4.4 

AMgCS-16 

Four-Component Systems 215 
4 ~----~------~------~----~~----~~----~ 

.......... 

UJ 

V) 

0 

a.. 

........... 

>-

...... 

3 

V) 2 

0 

u 

V) 

> 

~ 

g 

1 

0 

1300 

AI203-Ca0-Mg0-Si02 

HOFMANN (1959) 

ACMgS-1 

ACMgS-2 

1400 1500 

TEMPERATURE (°C) 

216 Viscosity of Synthetic and Natural Melts and Glasses 

1600 
...--.. 

lU 

V') 

-

0 

Q.. 

........... 

>- 1-

-

V') 

0 

u 

V') 

-

> 

() 

0 

~ 

4 ~----~----~~----------~------~----~ 

3 

2 

1 

Al20 3 - CaO- MgO-Si02 

HOFMANN (1959) 

ACMgS-1 

ACMgS-2 

0 ~----~----~~----~----~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 217 
..--.. 

UJ 

ll) 

0 

a.. 

........... 

>-

....... 

-

ll) 

0 

u 

ll) 

-

> 

~ 

0 

__, 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

HOFMANN (1959) 

ACMgS-3 

ACMgS-4 

ACMgS-5 

0 ~----~------~------~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C} 

218 Viscosity of Synthetic and Natural Melts and Glasses 
..---

lU 

c./) 

0 

a.. 

----

>- 1-

c./) -

0 

u 

c./) 

-

> 

0 

0 

--J 

4 ~----~------~------------~------~----~ 

3 

2 

1 

AI203- CaO- MgO-Si02 

HOFMANN (1959) 

ACMgS-3 

ACMgS-4 

ACMgS-5 

0 ------~------~----~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 219 
.......--... 

LU 

V') 

0 

...__... 

~ 

>- 1--

-

V') 

0 

u 

V') 

-

> 

0 

0 

....J 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203 -CoO- Mg0-Si02 

HOFMANN (1959) 

ACMgS-8 

ACMgS-6 

ACMgS-7 

0 ~----~------~------~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

220 Viscosity of Synthetic and Natural Melts and Glasses 
......--

UJ 

V') 

0 

a.. 

___. 

>- r-

-

V') 

0 

u 

V') 

-

> 

0 

0 

~ 

4 ~------------~--------------------~----~ 

3 

2 

1 

AI203- CoO- MgO-Si02 

HOFMANN (1959) 

ACMgS- 6 

ACMgS-7 

ACMgS- 8 

0 ~----~------~----~------~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 221 
........... 

lU 

(./) 

0 

Q.. 

....__ 

>- r-

-(./) 

0 

u 

(./) 

-

> 

0 

0 

_,J 

4 ------~------~--------------~------~------~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

HOFMANN (19.59) 

ACMgS-9 

ACMgS -11 

ACMgS-12 

0 ~------~----~~----~~----~----------------

1300 1400 1500 1600 

TEMPERATURE {°C) 

222 Viscosity of Synthetic and Natural Melts and Glasses 
...---

lU 

(./') 

-

0 

a.. 

...__ 

>- 1--

-(./') 

0 

u 

(./') 

-

> 

~ 

0 

___. 

4 ~----~------~------~----~~----~------~ 

3 

2 

1 

AI203-CaO- Mg0-Si02 

HOFMANN (1959) 

ACMgS-9 

ACMgS-11 

ACMgS-12 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS-1) 

Four-Component Systems 223 
............ 

UJ 

V') 

0 

a.. 

~ 

>- r-

-l/') 

0 

u 

(./") 

-

> 

l? 

0 

.....J 

4 ~----~------~------~------~----~------~ 

3 

2 

1 

AI203- CoO- MgO- Si02 

HOFMANN (1959) 

ACMgS-13 

ACMgS-14 

0 ~----~------~------~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

224 Viscosity of Synthetic and Natural Melts and Glasses 
........... 

lU 

(./') 

0 

a.. 

>-

...... 

-

4 ~----~------~--------------------~----~ 

3 

AI203- CaO- MgO- Si02 

HOFMANN (1959) 

(./') 2 

0 

u 

(./') 

> 

0 

0 ACMgS-13 

~ 

1 ACMgS-14 

0 ~----~------~----~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 225 
_..... 

UJ 

V') 

0 

CL 

-

>- 1-

-

V') 

0 

u 

(./') 

-

> 

l? 

0 

_J 

4 ~----~--------------~----~~----~------~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

HOFMANN /1959) 

ACMgS-15 

0 ~----~------~------~------~-------------

1300 1400 1500 1600 

TEMPERATURE (°C) 

226 Viscosity of Synthetic and Natural Melts and Glasses 
.....--.. 

lU 

(./') 

0 

a.. 

----

>-

~ 

-(./') 

0 

u 

(./') 

-

> 

~ 

0 

__. 

4 ~----~--~~~----~----~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

HOFMANN (1959) 

ACMgS-15 

0 ~----~----~~----~----~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 227 
..--.... 

lLJ 

V') 

0 

0... 

___. 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

0 

0 

__,J 

4 ~----~----------------------~----~------~ 

3 

2 

1 

A120 3- CaO- Mg0-Si02 

HOFMANN (1959) 

ACMgS-16 

0 ~----~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE {°C) 

228 Viscosity of Synthetic and Natural Melts and Glasses 
...--.. 

l.U 

(./') 

0 

a... 

>- 1-

4 ~----~----~~----~----~------~----~ 

3 

AI20 3 -Ca0-Mg0-Si02 

HOFMANN (1959) 

(./') 2 

0 

u 

(./') 

> 

() 

g ACMgS-16 

1 

0 ~----~------~----~----~~----~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 229 
SYSTEM 

AL203(10.94),CA0(10.0), 

MGO (9. 89) , SI02 (69 .17) (X) 

AL203(17.9),CA0(9.0), 

MG0(6.4),SI02(66.7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

9.132 

8.355 

7.682 

6.985 

SYSTEM 

AL203(10.96),CAO(O.O), 

MG0(20.03),SI02(69.01) (X) 

AL203(18.4),CAO(O.O), 

MG0(13.3),SI02(68.3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

9.148 

8.331 

7.565 

6.877 

AL203(10.96) ,CA0(19.94), 

MGO (0. 0) , SI02 (69 .10) (X) 

AL203(17.5) ,CA0(17.5), 

MGO(O.O),SI02(65.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

9.629 

8.825 

8.036 

7.320 

6.659 

SYSTEM 

AL203(9.22),CAO~O.O), 

MG0(28.10),SI02 62.68) (X) 

AL203(16.1),CAO 0.0), 

MG0(19.4) ,SI02(64.5) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.534 

6.768 

6.040 

5.298 

LOG(N) 

3.966 

3.628 

3.336 

3.033 

LOG(N) 

3.973 

3.618 

3.286 

2.987 

LOG(N) 

4.182 

3.833 

3.490 

3.179 

2.892 

LOG(N) 

3.272 

2.940 

2.623 

2.301 

230 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9250. 

4250. 

2170. 

1080. 

AUTHOR 

AMgCS-17 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9400. 

4150. 

1930. 

970. 

AUTHOR 

AMgCS-18 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

15200. 

6800. 

3090. 

1510. 

780. 

AUTHOR 

AMgCS-1 9 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1870. 

870. 

420. 

200. 

A MgC S- 2 0 
SYSTEM 

AL203(14.33) ,CA0(13.02), 

MGO (13 .12) , SI02 (59. 53) (X) 

AL203(23.2) ,CA0(11.6), 

MGO (8. 4) , SI02 (56. 8) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.300 

6.507 

5.737 

5.011 

SYSTEM 

AL203(9.21),CAOl13.94), 

MGO (13. 99) , SI02 62.86) (X) 

AL203(15.5),CAO 12.9), 

MGO (9. 3) , SI02 (62. 3) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1250.00 

1300.00 

1350.00 

1400.00 

1450.00 

6.566 

6.357 

6.161 

5.977 

5.804 

7.990 

7.139 

6.430 

5.737 

5.011 

LOG(N) 

3.170 

2.826 

2.491 

2.176 

LOG(N) 

3.470 

3.100 

2.792 

2.491 

2.176 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1480. 

670. 

310. 

150. 

AUTHOR 

AMgCS-21 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2950. 

1260. 

620. 

310. 

150. 

AMgCS- 22 

------------------------------------------------------------------------------

SYSTEM 

AL203(14.34) ,CAO(O.O), 

MGO (26 .15) , SI02 (59. 52) (X) 

AL203(24.0) ,CAO(O.O), 

MGO (17. 3) , SI02 (58. 7) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.462 

6.380 

5.598 

5.011 

LOG(N) 

3.241 

2.771 

2.431 

2.176 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1740. 

590. 

270. 

150. 

AMgCS-2 3 

Four-Component Systems 231 
SYSTEM 

AL203(14.36),CA0(26.10), 

MGO (0. 0) , SI02 (59. 55) (X) 

AL203(22.5),CA0(22.5), 

MGO (0. 0) , SI02 (55. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

7.056 

6.254 

5.598 

4.977 

AL203(9.24) ,CA0(28.0), 

MGO (0. 0) , SI02 (62. 75) (X) 

AL203(15.0),CA0(25.0), 

MGO (0. 0) , SI02 (60. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

7.450 

6.579 

5.829 

5.193 

4.787 

LOG(N) 

3.064 

2.716 

2.431 

2.161 

LOG(N) 

3.236 

2.857 

2.531 

2.255 

2.079 

232 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1160. 

520. 

270. 

145. 

AUTHOR 

AMgCS-2 4 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 7 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

1720. 

720. 

340. 

180. 

120. 

AMgCS-25 
5 ~----~~----~~--------------------~------~ 

>-

...... 

4 

V) 3 

0 

u 

V) 

> 

l? 

g 

2 

Al 20 3- Ca0-Mg0-Si02 

JOHANNSEN and BRUNION ( 1959) 

ACMgS-19 

ACMgS-22 

ACMgS-25 

1 

1200 1300 1400 

TEMPERATURE (°C) 

ACMgS-17 

ACMgS-20 

1500 

Four-Component Systems 233 
5 ~------~------~------~------~------~------~ 

~ 

LU 

(./') 

0 

a... 

>-

~ 

-

4 

(./') 3 

0 

u 

(./') 

> 

~ 

0 

__, 

2 

1 

5 

Al 20 3- CaO- Mg0-Si02 

JOHANNSEN and BRUNtON (1959) 

ACMgS-17 

ACMgS-18 

ACMgS-20 

ACMgS-19 

ACMgS-22 

6 7 

10 000/T (KELVI NS- 1

) 

234 Viscosity of Synthetic and Natural Melts and Glasses 

8 
SYSTEM 

AL203(19.22) ,MG0(8.10), 

CA0(29.15),SI02(43.53) (X) 

AL203(30.0),MG0(5.0), 

CAO (25. 0) , SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.564 

3.939 

3.414 

2.941 

AL203(18.70) ,MG0(15.85), 

CAO (22. 81) , SI02 (42. 55) (X) 

AL203(30.0),MG0(10.0), 

CAO (20. 0) , SI02 (40. 0) (%) 

LOG(N) 

1.982 

1.711 

1.483 

1.277 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.251 

3.662 

3.140 

2.687 

SYSTEM 

AL203(15.60),MG0(7.90), 

CAO (35. 08) , SI02 (42 o 42) (X) 

AL203(25.0),MG0(5.0), 

CAO (30. 0), SI02 (40 o 0) (%) 

LOG(N) 

1.846 

1.590 

1.364 

1.167 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5o977 

1450.00 5.804 

1500o00 5.640 

SYSTEM 

LN(N) 

5.366 

4.590 

3.898 

3.359 

2.906 

2.497 

AL203(15.26) ,MG0(15.45), 

CA0(27.79),SI02(41.50) (X) 

AL203(25.0) ,MG0(10.0), 

CAO (25. 0), SI02 (40. 0) (%) 

LOG(N) 

2o330 

1.993 

1.693 

1.459 

1o262 

1.085 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250o00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5o640 

LN(N) 

5.065 

4.321 

3o684 

3.141 

2o731 

2o416 

LOG(N) 

2.200 

1.877 

1.600 

1.364 

1.186 

1.049 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

96.0 

51.37 

30.40 

18.94 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

AMgCS-26 

z = 10 0 0 0 0 0 /T (K) ( 1/K) A M g c s - 2 7 

N 

70.18 

38.94 

23.10 

14.69 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A M g c s - 2 8 

N 

214.0 

98.46 

49.32 

28.75 

18.29 

12.15 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

158.4 

75.26 

39.81 

23.12 

15.35 

11.20 

AMgCS-29 

Four-Component Systems 235 
SYSTEM 

AL203(12.17) IMG0(7.70) I 

CAO (38. 76) I SI02l41. 37) (X) AL203(20.0)~MGO 5.0)~ 

COAO (30. 0) I SI02 40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1250.00 6.566 4.751 2.063 

1300.00 6.357 4.016 1.744 

1350.00 6.161 3.382 1.469 

1400.00 5.977 2.886 1.253 

1450.00 5.804 2.421 1.052 

1500.00 5.640 2.040 0.886 

SYSTEM 

AL203(11.91),MG0(15.08), 

CAO ( 32. 52) , SI02 ( 40. 49) (X) 

AL203(20.0), MG0(10.0), 

CAO (30. 0) , SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.587 

3.791 

3.209 

2.718 

2.307 

1.937 

AL203(11.67) IMG0(22.14), 

CAO (26. 55) , SI02 ( 39. 64) (X) 

AL203(20.0),MG0(15.0), 

CAO (25. 0), SI02 (40. 0) (%) 

LOG(N) 

1.992 

1.646 

1.394 

1.134 

1.002 

0.841 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.313 

3.564 

3.032 

2.552 

2.125 

1.725 

AL203(11.43) IMG0(28.92) I 

CAO (20. 82), SI02 (38. 83) (X) 

AL203(20.0) 1 MG0(20.0), 

CAO (20. 0) I SI02 (40. 0) (%) 

LOG(N) 

1.873 

1.548 

1.317 

1.108 

0.923 

0.749 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1400.00 5.977 2.526 

1450.00 5.804 2.041 

1500.00 5.640 1.688 

LOG(N) 

1.097 

0.887 

0.733 

236 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

p = 1 . 0 ATM. A M C S 3 0 

Z = 10000. 0/T (K) (1/K) 9 - N 

115.7 

55.50 

29.43 

17.92 

11.26 

7.69 

AUTHOR 

MACHINA AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

98.2 

44.30 

24.76 

15.15 

10.04 

6.94 

AUTHOR 

MACHIN AND HANNA(1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

74.63 

35.29 

20.74 

12.83 

8.37 

5.61 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

AMgCS-31 

AMgCS-32 

Z = 10000.0/T(K) (1/K) 

N 

AMgCS-33 

12.50 

7.70 

5.41 
SYSTEM 

AL203(8.91),MG0~7.52), 

CAO (43. 21), SI02 40. 36) (X) 

AL203(15.0),MGO 5.0), 

CA0(40.0),SI02(40.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.447 

2.975 

2.476 

2.091 

1.613 

SYSTEM 

AL203(8.72),MG0~14.72), 

CA0(37.02) ,SI02 39.53) (X) 

AL203(15.0),MGO 10.0), 

CAO (35. 0) , SI02 (40. 0) (%) 

LOG(N) 

1.497 

1.292 

1.075 

0.908 

0.701 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.310 

2.792 

2.300 

1.872 

1.454 

AL203(8.38) ,MG0~28.26), 

CA0(25.41) ,SI02 37.95) (X) 

AL203(15.0),MGO 20.0), 

CAO (25. 0), SI02 (40. 0) (%) 

LOG(N) 

1.438 

1.213 

0.999 

0.813 

0.631 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.121 0.921 

1450.00 5.804 1.714 0.744 

1500.00 5.640 1.194 0.584 

SYSTEM 

AL203(8.55) ,MG0~21.63), 

CA0(31.10) ,SI02 38.72) (X) 

AL203(15.0) ,MGO 15.0), 

CAO (30. 0), SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.082 

3.094 

2.544 

2.082 

1.673 

1.314 

LOG(N) 

1.773 

1.344 

1.105 

0.904 

0.737 

0.571 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

31.42 

19.58 

11.89 

8.09 

5.02 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

27.39 

16.32 

9.97 

6.5 

4.28 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

AMgCS-34 

AM gCS-35 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A M g c s - 3 6 

N 

8.34 

5.55 

3.84 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

59.28 

22.07 

12.73 

8.02 

5.33 

3.72 

AMgCS-3 7 

Four-Component Systems 237 
SYSTEM 

AL203(8.21),MGOl34.64), 

CA0(19.94),SI02 37.95) (X) 

AL203(15.0),MGO 25.0), 

CA0(20.0),SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 1.194 0.519 

SYSTEM 

AL203(5.80),MGOl7.34), 

CAO (47 .45), SI02 39 .41) (X) 

AL203(10.0),MGO 5.0), 

CA0(45.0),SI02(40.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.329 

1.913 

1.526 

1.191 

SYSTEM 

AL203(5.68),MGOl14.38), 

CA0(41.33),SI02 38.61) (X) 

AL203(10.0),MGO 10.0), 

CAO (40. 0) , SI02 (40. 0) (%) 

LOG(N) 

1.012 

0.831 

0.663 

0.517 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.276 

1.856 

1.452 

1.092 

SYSTEM 

AL203(5.46),MGOl27.63), 

CAO (29. 81) , SI02 37 .10) (X) 

AL203(10.0),MGO 20.0), 

CAO (30. 0) , SI02 (40. 0) (%) 

LOG(N) 

0.989 

0.806 

0.630 

0.474 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.169 

1.705 

1.330 

1.033 

LOG(N) 

0.942 

0.740 

0.577 

0.449 

238 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3.30 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

AMgCS-38 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A M g c s - 3 9 

N 

10.27 

6.77 

4.60 

3.29 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A M g c s - 4 0 

N 

9.74 

6.40 

4.27 

2.98 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.75 

5.50 

3.78 

2.81 

AMgCS-41 
SYSTEM 

AL203(5.57) ,MG0~21.14), 

CA0(35.45) ,SI02 37.84) (X) 

AL203(10.0) ,MGO 15.0), 

CAO (35. 0), SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.117 

1.660 

1.292 

0.963 

LOG(N) 

0.920 

0.721 

0.561 

0.418 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

z = 10 0 0 0 . 0 /T (K) ( 1/K) A M g c s - 4 2 

N 

8.31 

5.26 

3.64 

2.62 

----------------------------------------------------------------------------- SYSTEM 

AL203(5.36) ,MG0~33.88), CA0(24.37) ,SI02 36.39) (X) 

AL203(10.0),MGO 25.0), 

CA0(25.0),SI02(40.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 0.900 0.391 

SYSTEM 

AL203(2.78),MG0(14.05), 

CA0(45.44) ,SI02(37.73) (X) 

AL203(5.0) ,MG0(15.0), 

CAO (40. 0), SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 0.806 0.350 

SYSTEM 

AL203(2.72),MG0(20.67), 

CAO (39. 61) , SI02 (37. 0) (X) 

AL203(5.0) ,MG0(15.0), 

CAO (40. 0), SI02 (40. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 0.959 0.417 

1500.00 5.640 0.688 0.299 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.46 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.24 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.61 

1.99 

AMgCS-43 

AM gCS-44 

AMgCS-45 

Four-Component Systems 239 
SYSTEM 

AL203(2.67),MG0(20.67), 

CA0(34.01),SI02(36.29) (X) AL203(5.0) ,MG0(20.0), 

CAO (35. 0) , SI02 (40. 0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1450.00 5.804 0.917 0.422 

1500.00 5.640 0.647 0.281 

SYSTEM 

AL203(2.62) ,MG0(33.16), 

CA0(28.61) ,SI02(35.61) (X) AL203(5.0) ,MG0(25.0), CAO (30. 0) , SI02 ( 40. 0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1500.00 5.640 0.642 0.279 

240 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10 0 0 o . o /T (K) ( 1/K) A M g C S - 4 6 

N 

2.64 

1.91 

AUTHOR 

MACHIN AND HANNA (1945) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.90 

AMgCS-47 
4 ~----~------~------------~------~-----, 

.--... 

UJ 

c./') 

0 

~ 

>- 1-

3 

c./') 2 

0 

u 

c./') 

> 

0 

g 

1 

Al20 3- CoO- MgO-Si02 

MACHIN and HANNA /1945) 

ACMgS-26 

ACMgS -27 

0 ~----~------~----~------~------~------

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 241 
---- UJ 

(./') 

0 

a.. 

>-

~ 

4 ~----~--------------~------~------~----~ 

3 

AI 20 3 -Ca0-Mg0-Si02 

MACHIN and HANNA /1945) 

(./') 2 

0 ACMgS-26 

u ACMgS-27 

(./') 

> 

{.? 

0 

.....J 

1 

0 ~----~~----~------~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

242 Viscosity of Synthetic and Natural Melts and Glasses 
4 ~----~------~------~----~------~----~ 

.--.... 

UJ 

V') 

0 

3 

AI203- Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

0.. ACMgS-28 

>- ACMgS-29 

IV') 2 

0 

u 

V') 

> 

0 

g 

1 

0 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 243 
---- UJ 

V') 

0 

a_ 

>-

~ 

4 ~----~~----~------~------~------~------~ 

3 

AI 20 3-Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

ACMgS-28 

ACMgS-29 

V') 2 

0 

u 

V') 

> 

~ 

0 

___, 

l 

0 ~----~------~------~------~------~------

4.5 5.5 6.5 7. 5 

10 000/T (KELVINS- 1

) 

244 Viscosity of Synthetic and Natural Melts and Glasses 
.---... 

UJ 

V') 

0 

a... 

>-

t4 ~--------------------------~~----~------~ 

3 

AI20 3-Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

V') 2 

0 

ACMgS-30 

ACMgS-31 

u 

V') 

> 

l? 

g 

1 ACMgS-32----'--~ 

ACMgS-33 ------....._ 

0 ~----~------~------~----~~-------------

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 245 
4 ~------~----~~----~------~------~-------, 

>-

~ 

3 

ll) 2 

0 

u 

ll) 

> 

l? 

0 

__,J 

1 

Al 20 3- Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

ACMgS-30 

ACMgS-31 

0 ~----~~----~------~------~------~--------

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

246 Viscosity of Synthetic and Natural Melts and Glasses 
...--... 

UJ 

(./') 

0 

Cl.. 

-

>-

~ 

4 ~----~----------------------~----~------~ 

3 

A120 3 -Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

(./') 2 8 ACMgS-34 

<.I) ACMgS-35 

> 

l') 

0 

_..J 

1 

ACMgS-36--~~ 

ACMgS-37----~~ 

0 ~----~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 247 
4 ~----~~----~------~------~------~------~ 

,......... 

lU 

V") 

0 

a... 

>- 1-

-

3 

V") 2 

0 

u 

V") 

> 

~ 

0 

....J 

1 

0 

4.5 

AI203- CoO -Mg0-Si02 

MACHIN and HANNA (1945) 

5.5 6.5 

ACMgS-34 

ACMgS-35 

10 000/T (KELVINS- 1

) 

248 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
4 ~----~------~------~----~~----~------~ 

---.. 

lU 

V) 

0 

a.. 

>- 1-

3 

V) 2 

0 

u 

V) 

> 

0 

0 

_J 

1 

0 

1200 

AI203- Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

ACMgS-39 

ACMgS-42 

1300 1400 

TEMPERATURE (°C} 

1500 

Four-Component Systems 249 
...--.. 

UJ 

lf') 

0 

a... 

-

>- I-

-

lf') 

0 

u 

lf') 

-

> 

{) 

0 

__. 

4 ~------~------~------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN and HANNA (1945) 

0 ~------~------~------~------~--~--~-------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

250 Viscosity of Synthetic and Natural Melts and Glasses 
.......--. 

UJ 

V') 

0 

0.. 

.......... 

>-

t-

-

V') 

0 

u 

V') 

-

> 

0 

0 

_J 

4 ~----~--------------------~------~----~ 

3 

2 

1 

AI203-CaO-MgO-Si02 

MACHIN and HANNA (1945) 

ACMgS-46 

0 --------~------~------~----------~----------------------

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 251 
.........--. 

UJ 

(./) 

0 

a.. 

-....... 

>-

~ 

-lf) 

0 

u 

(./) 

-

> 

() 

0 

__, 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

A4ACHIN and HANNA (1945) 

ACMgS-45~ ACMgS-46 

0 ~----~------~------~------~------~------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

252 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(15.92),CA0(5.79), 

MGO (8. 05) , SI02 (70. 24) (X) 

AL203(25.0),CA0(5.0), 

MGO (8. 05) , SI02 (70. 24) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 6.937 3.013 

SYSTEM 

AL203(12.41) ,CA0(11.28), 

MGO (7. 85) , SI02 (68. 46) (X) 

AL203(20.0) ,CA0(10.0), 

MGO (5. 0) , SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

10.319 

9.384 

8.547 

7.787 

7.090 

6.509 

AL203(12.15) ,CA0(5.52), 

MG0(15.36),SI02(66.97) (X) 

AL203(20.0),CA0(5.0), 

MG0(10.0),SI02(65.0) (%) 

LOG (N) 

4.481 

4. 076 

3.712 

3.382 

3.079 

2.827 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.770 

8.841 

8.010 

7.265 

6.603 

6.038 

LOG(N) 

4.243 

3.839 

3.479 

3.155 

2.867 

2.622 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1030. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

30300. 

11900. 

5150. 

2410. 

1200. 

671. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

17500. 

6910. 

3010. 

1430. 

737. 

419. 

AMgCS-48 

AMgCS-49 

AMgCS-50 

Four-Component Systems 253 
SYSTEM 

AL203(15.86),CA0(11.53), 

MGO (8. 02) , SI02 (64. 59) (X) 

AL203(25.0) ,CA0(10.0), 

MG0(5.0),SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.798 

8.883 

7.983 

7.208 

6.503 

5.855 

SYSTEM 

AL203(9.08),CA0(16.5l, 

MG0(7.65) ,SI02(66.76 (X) 

AL203(15.0) ,CA0(15.0 , MGO (5. 0) , SI02 (65. 0) (%) 

LOG (N) 

4.255 

3.858 

3.467 

3.130 

2.824 

2.543 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

9.051 

8.126 

7.371 

6.711 

6.096 

5.549 

AL203(15.51) ,CA0(5.64), 

MG0(15.69) ,SI02(63.16) (X) 

AL203(25.0) ,CAO(S.O), 

MG0(10.0) ,SI02(60.0) (%) 

LOG(N) 

3.931 

3.529 

3.201 

2.914 

2.647 

2.410 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

9.393 

8.309 

7.450 

6.703 

6.023 

5.429 

LOG(N) 

4.079 

3.609 

3.236 

2.911 

2.616 

2.358 

254 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

18000. 

7210. 

2930. 

1350. 

667. 

349. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8530. 

3380. 

1590. 

821. 

444. 

257. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12000. 

4060. 

1720. 

815. 

413. 

228. 

AMgCS-51 

AMgCS-52 

AMgCS-53 
SYSTEM 

AL203(8.89) ,CA0~10.77), 

MG0(14.99),SI02 65.35) (X) 

AL203(15.0) ,CAO 10.0), 

MGO (10. 0) , SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

8.828 

7.979 

7.258 

6.579 

5.969 

5.412 

AL203(12.37) ,CA0(16.86), 

MG0(7.82) ,SI02(62.95) (X) 

AL203(20.0) ,CA0(15.0), 

LOG(N) 

3.834 

3.465 

3.152 

2.857 

2.592 

2.350 

MGO (5. 0) , SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

8.747 

7.890 

7.082 

6.392 

5.778 

5.209 

AL203(8.70) ,CA0~5.28), 

MGO (22. 01) , SI02 64. 01) (X) 

AL203(15.0) ,CAO 5.0), 

MG0(15.0) ,SI02(65.0) (%) 

LOG(N) 

3.799 

3.427 

3.076 

2.776 

2.509 

2.262 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.804 

7.021 

6.323 

5.727 

5.198 

LOG(N) 

3.389 

3.049 

2.746 

2.487 

2.258 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6820. 

2920. 

142). 

72l'. 

391. 

224. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6290. 

2670. 

1190. 

597. 

323. 

183. 

AUTHOR 

MA:HIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2450. 

1120. 

557. 

307. 

181. 

AMgCS-54 

AMgCS-55 

AMgCS-56 

Four-Component Systems 255 
SYSTEM 

AL203(12.10) ,CA0(11.00), 

MGO (15. 30) , SI02 (61. 60) (X) 

AL203(20.0) ,CA0(10.0), 

MG0(10.0) ,SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

8.394 

7.539 

6.752 

6.087 

5.472 

4.920 

AL203(5.91) ,CA0(21.47), 

MG0(7.47) ,SI02(65.15) (X) 

AL203(10.0) ,CA0(20.0), 

MGO (5. 0) , SI02 (65. 0) (%) 

LOG(N) 

3.645 

3.274 

2.932 

2.643 

2.377 

2.137 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

7.816 

7.021 

6.360 

5.762 

1450.00 5.804 5.263 

1500.00 5.640 4.736 

LOG(N) 

3.394 

3.049 

2.762 

2.502 

2.286 

2.057 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4420. 

1880. 

856. 

440. 

238. 

137. 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2480. 

1120. 

578. 

318. 

193. 

114. 

AMgCS-57 

AMgCS-58 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.78) ,CA0~15.78), 

MGO (14. 63) , SI02 63. 81) (X) 

AL203(10.0) ,CAO 15.0), 

MGO (10. 0) , SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.918 

6.225 

5.595 

5.056 

4.577 

LOG (N) 

3.004 

2.703 

2.430 

2.196 

1.988 

256 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1010. 

505. 

269. 

157. 

97.2 

AMgCS-59 
SYSTEM 

AL203(5.67) ,CA0~10.30), 

MG0(21.50) ,SI02 62.52) (X) 

AL203(10.0) ,CAO 10.0), 

MGO (15. 0) , SI02 (65. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 5.464 2.373 

1450.00 5.804 4.913 2.134 

1500.00 5.640 4.459 1.937 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

236. 

136. 

86.4 

AMgCS-60 

------------------------------------------------------------------------------

SYSTEM 

AL203(11.85) ,CA0(5.38), 

MG0(22.47),SI02(60.30) (X) 

AL203(20.0) ,CA0(5.0), 

MG0(15.0) ,SI02(60.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.754 

6.937 

6.196 

5.553 

4.942 

4.432 

SYSTEM 

AL203(9.0),CA0(22.0), 

MGO (8. 0) , SI02 (61. 0) (X) 

AL203(15.0),CA0(20.0), 

MG0(5.0),SI02(60.0) (%) 

LOG(N) 

3.367 

3.013 

2.691 

2.412 

2.146 

1.925 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

7.507 

6.723 

6.033 

5.416 

4.883 

4.417 

LOG(N) 

3.260 

2.920 

2.620 

2.352 

2.121 

1.919 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2330. 

1030. 

491. 

258. 

140. 

84.1 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1820. 

831. 

417. 

225. 

132. 

82.9 

AMgCS-61 

AMgCS-62 

Four-Component Systems 25 7 
SYSTEM 

AL203(9.0) CA0(16.0)~ 

MG0(15.0)~SI02(60.0) (X) 

AL203(15.0) ICA0(15.0) I 

MGO (10. 0) I SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

7.346 

6.541 

5.864 

5. 268 

4.718 

4. 236 

AL203(9.0) ICA0(10.0) I 

MG0(22.0) 1SI02(59.0) (X) 

AL203(15.0) CA0(10.0)~ 

MG0(15.0) ISI02(60.0) (%) 

LOG (N) 

3.190 

2.841 

2.547 

2.288 

2.049 

1.839 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1250.00 6.566 7.073 

1300.00 6.357 6.273 

1350.00 6.161 5.609 

1400.00 5.977 5.004 

1450.00 5.804 4.468 

1500.00 5.640 3.985 

SYSTEM 

AL203(2.88)1CA0(26.21) I 

MG0(7.29) ISI02(63.62) (X) 

AL203(5.0) ICA0(25.0) I 

MG0(5.0) 1SI02(65.0) (%) 

3.072 

2.724 

2.436 

2.173 

1.941 

1.731 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.191 1.820 

1500.00 5.640 3.833 1.665 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z. = 10000. 0 /T (K) (1/K) 

N 

1550. 

693. 

352. 

194. 

112. 

69.1 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1180. 

530. 

273. 

149. 

87.2 

53.8 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

66.1 

46.2 

AMgCS-63 

AMgCS-64 

AMgCS-65 

------------------------------------------------------------------------------

SYSTEM 

AL203(8.0) 1CA0(5.0) 1 

MGO (29. 9) I SI02 (58. ol (X) AL203(15.0) ICA0(5.0 I 

MG0(20.0) 1SI02(60.0 (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN (N) 

5.464 

4.796 

4.319 

3.809 

LOG (N) 

2.373 

2.083 

1.876 

1.654 

258 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

236. 

121. 

75.1 

45.1 

AMgCS-66 
SYSTEM 

AL203(2.82) 1CA0(20.55) 1 

MGO (14. 29) I SI02 (62. 34) (X) 

AL203(5.0) ICA0(20.0) I 

MG0(10.0) 1SI02(65.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.191 1.820 

1500.00 5.640 3.684 1.600 

SYSTEM 

AL203(2.77)1CA0(15.11) I 

MG0(21.01) 1SI02(61.11) (X) 

AL203(5.0) ICA0(15.0) I 

MG0(15.0) 1SI02(65.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.159 1.806 

1500.00 5.640 3.603 1.565 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

66.1 

39.8 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

64.0 

36.7 

AMgCS-67 

AMgCS-68 

------------------------------------------------------------------------------ SYSTEM AL203(6.0) CA0(27.0)~ 

MGO (7. 0) I SI02 (60. 0) (X) 

AL203(10.0) 1CA0(25.0) 1 

MGO (5. 0) I SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.428 

5.694 

5.063 

4.526 

4.057 

3.600 

LOG(N) 

2.792 

2.473 

2.199 

1.966 

1.762 

1.563 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

619. 

297. 

158. 

92.4 

57.8 

36.6 

AMgCS-69 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.56) ICA0~5.05) I 

MGO (28 .11) , SI02 61. 28) (X) 

AL203(10.0) ,CAO 5.0), 

MG0(20.0) 1SI02(65.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1450.00 5.804 4.828 2.097 

1500.00 5.640 4.312 1.873 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

125. 

34.6 

AMgCS-70 

Four-Component Systems 259 
SYSTEM 

AL203(6.0),CA0(21.0), 

MG0(14.0),SI02(59.0) (X) 

AL203(10.0),CA0(20.0), 

MG0(10.0),SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.286 

5.557 

4.934 

4.378 

3.920 

3.481 

SYSTEM 

AL203(6.0),CA0(15.0), 

MG0(21.0) ,SI02(58.0) (X) 

AL203(10.0),CA0(15.0), 

LOG (N) 

2.730 

2.413 

2.143 

1.901 

1.702 

1.512 

MG0(15.0),SI02(60.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.170 

5.424 

4.804 

4.263 

3.754 

3.350 

SYSTEM 

AL203(6.0),CA0(10.0), 

MG0(28.0),SI02(56.0) (X) 

AL203(10.0),CA0(10.0), 

MG0(20.0),SI02(60.0) (%) 

LOG(N) 

2.679 

2.356 

2.086 

1.851 

1.630 

1.455 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.710 

4.132 

3.645 

3.215 

SYSTEM 

AL203(5.0),CA0(5.0), 

MGO (34. 0) , SI02 (55. Ol (X) AL203(10.0) ,CA0(5.0 , MG0(25.0) ,SI02(60.0 (%) 

LOG (N) 

2.045 

1.794 

1.583 

1.396 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 3.558 1.545 

1500.00 5.640 3.118 1.354 

260 Viscosity of Synthetic and Natural Melts and Glasses 

' 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z. = 10000. 0/T (K) (1/K) 

N 

537. 

259. 

139. 

79.7 

50.4 

32.5 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

478. 

227. 

122. 

71.0 

42.7 

28.5 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

111. 

62.3 

38.3 

24.9 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

35.1 

22.6 

AMgCS-71 

AMgCS-72 

AMgCS-73 

AMgCS-74 
SYSTEM 

AL203(3.0),CA0(31.0), 

MGO (7. 0) , SI02 (59. 0) (X) 

AL203(5.0) ,CA0(30.0), 

MGO (5. 0) , SI02 (60. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.481 

4.787 

4.206 

3.689 

3.246 

2.868 

SYSTEM 

AL203(3.0),CA0!26.0l, MG0(14.0),SI02 57.0 (X) 

LOG(N) 

2.380 

2.079 

1.827 

1.602 

1.410 

1.246 

AL203(5.0) ,CAO 25.0 , MG0(10.0),SI02 60.0 (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.193 

4.553 

3.991 

3.575 

3.266 

2.851 

LOG(N) 

2.255 

1.977 

1.733 

1.553 

1.418 

1.238 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 A1M. 

Z = 10000. 0/T (K) (1/K) 

N 

240. 

120. 

67.1 

40.0 

25.7 

17.6 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

180. 

94.9 

54.1 

35.7 

26.2 

17.3 

AMgCS-75 

AMgCS-76 

------------------------------------------------------------------------------ SYSTEM 

AL203(3.0),CA0!20.0l, MG0(21.0) ,SI02 56.0 (X) 

AL203(5.0) ,CAO 20.0 , MG0(15.0) ,SI02 60.0 (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.654 

4.059 

3.589 

3.148 

2.754 

LOG(N) 

2.021 

1.763 

1.559 

1.367 

1.196 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 A1M. 

Z = 10000. 0/T (K) (1/K) 

N 

105. 

57.9 

36.2 

23.3 

15.7 

AMgCS-77 

Four-Component Systems 261 
SYSTEM 

AL203(3.0)~CA0115.0l 1 MG0(27.0) 1 SI02 55.0 (X) 

AL203(5.0) ICAO 15.0 I 

MG0(20.0) 1 SI02 60.0 (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.951 

3.456 

3.025 

2.632 

SYSTEM 

AL203(3.0) 1 CA0!9.0) 1 

MGO (34. o) I SI02 54. ol (X) 

AL203(5.0) ICAO 10.0 I 

MG0(25.0) 1 SI02 60.0 (%) 

LOG(N) 

1.716 

1.501 

1.314 

1.143 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450.00 5.804 2.976 

1500.00 5.640 2.610 

SYSTEM 

AL203(3.0) ICA0!5.0) I 

MGO (39. 0) I SI02 52. 0) (X) 

AL203(5.0) ,CAO 5.0), 

MG0(30.0) ,SI02 60.0) (%) 

LOG(N) 

1.292 

1.134 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 2.451 1.064 

262 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

52.0 

31.7 

20.6 

13.9 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.6 

13.6 

AUTHOR 

MACHIN AND YEE (1954) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.6 

AMgCS-78 

AMgCS-79 

AMgCS-80 
.......... 

UJ 

ll) 

0 

a.. 

............ 

>-

~ 

-ll) 

0 

u 

ll) 

-

> 

{) 

0 

__, 

5~----~--------------~------------------~ 

4 

3 

2 

ACMgS-49 

ACMgS-50 

AI 20 3-Ca0-Mg0-Si02 

MACHIN and YEE (1954) 

1 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C} 

Four-Component Systems 263 
...--.. 

UJ 

(./') 

0 

a.. 

--

>- I-

-(./') 

0 

u 

(./') 

-

> 

{) 

0 

___. 

5 ~----~~------------~------~------~------~ 

4 

3 

2 

Al 20 3- Ca0-Mg0-Si02 

MACHIN and YEE (1954) 

ACMgS-49 

ACMgS-50 

1 ~----~~----~------~------~------~------~ 

4.5 5.5 6.5 75 

lO 000/T (KELVINS- 1

) 

264 Viscosity of Synthetic and Natural Melts and Glasses 
__.... 

lU 

V') 

0 

a.. 

...__ 

>- 1-

-

V') 

0 

u 

V') 

-

> 

0 

0 

__. 

5 ~----~------~------~----~------~----~ 

4 

3 

2 

Al 2 0 3- CoO- MgO-Si02 

MACHIN and YEE (1954) 

ACMgS-51 

ACMgS-53 

1 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C} 

Four-Component Systems 265 
........... 

lU 

ll) 

0 

a_ 

-...... 

...,_ 

>-

-ll) 

0 

u 

ll) 

-

> 

0 

0 

__. 

5 ~----~~----~------~------~--~--~------~ 

4 

3 

2 

AI2 03- Ca0-Mg0-Si02 

MACHIN and YEE /1954) 

ACMgS-51 

ACMgS-53 

1 ~----~------~------~------~------~----~~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

266 Viscosity of Synthetic and Natural Melts and Glasses 
...--.. 

UJ 

V') 

0 

a_ 

.__.... 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

l? 

0 

__. 

4 ~----~--------------------~------------~ 

3 

2 

1 

ACMgS-54 

AI 20 3-Ca0-Mg0-Si02 

MACHIN and YEE ( 1954) 

0 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 267 
...--.. 

lU 

V) 

0 

a_ 

.,_ >-

4 ~----~~----~------~------~------~------~ 

3 

ACMgS-52 

ACMgS-56 

ACMgS-54 

V) 2 

0 

u 

V) 

> 

~ 

g 

1 

Al2 0 3 - CaO- MgO- Si02 

MACHIN and YEE (1954) 

0 ~----~~----~~----~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

268 Viscosity of Synthetic and Natural Melts and Glasses 
--... 

lU 

V') 

0 

a_ 

.._._ 

>- r-

-

V') 

0 

u 

V') 

-

> 

l? 

0 

__. 

4 ~----~------~------~----~------~----~ 

3 

2 

1 

ACMgS-55 

ACMgS-57 

ACMgS-61 

Al20 3- CaO- Mg0-Si02 

MACHIN and YEE (1954) 

0 ~------~----------~------------~------~--------~--------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 269 
...--

LU 

V') 

-

0 

a... 

........-

...,_ 

>-

V') -

0 

u 

V') 

-

> 

l? 

0 

__. 

4 ~------~------------~------~------~------~ 

3 

2 

1 

Al 20 3- CoO- Mg0-Si02 

MACHIN and YEE (1954) 

ACMgS-55 

ACMgS-57 

ACMgS-61 

0 ~----~~----~------~------~------~------~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

270 Viscosity of Synthetic and Natural Melts and Glasses 
........... 

u.J 

V') 

0 

a.. 

...__ 

>- 1-

-

V') 

0 

u 

V') 

-

> 

0 

0 

_J 

4 ~----------------------------~------------~ 

3 

2 

l 

ACMgS-62 

ACMgS-63 

ACMgS-64 

Al 20 3- CoO -MgO- Si02 

MACHIN and YEE (1954) 

0 ~----~------~------~------~--------------

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 271 
..--.. 

UJ 

V') 

-

0 

Q.. 

........... 

>- 1--

-

4 ~----~------~------~------~------r------. 

ACMgS-62 

3 ACMgS-64 

V') 2 

0 

u 

V') 

-

> 

~ 

g 

1 

ACMgS-63 

ACMgS-66 

Al 20 3- CoO- Mg0-Si02 

MACHIN and YEE (1954) 

0 ~~~~------~------~----~~-------------

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

272 Viscosity of Synthetic arid Natural Melts and Glasses 
4 ~----~------~----~------~------~----~ 

........... 

lU 

tl) 

0 

a... 

>-

~ 

3 

tl) 2 

0 

u 

tl) 

> 

l? 

g 

1 

Al203- CoO- MgO -Si02 

MACHIN and YEE (1954} 

ACMgS-68~ 

ACMgS-.67--~ 

AC::MgS-65/ 

0 ~----~------~----~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four~(;omponent Systems 273 
4~----~~------~~----~~~----~~------~~----~ 

_......... 

UJ 

(./) 

0 

a_ 

-

>-

~ 

-

3 ~ 

(./) 2~ 

0 

u 

(./) 

> 

0 

0 

__J 

1~ 

0 

4.5 

Al20 3- CoO- Mg0-Si02 

MACHIN and YEE /1954) 

I 

ACMgS-65 .4 ACMgS-67 

~ACMgS-68 

I I I 

5.5 6.5 

10 000/T (KELVINS- 1

) 

274 Viscosity of Synthetic and Natural Melts and Glasses 

-

-

-

-

-

-

-

I 

75 
.--.. 

lU 

V) 

0 

~ 

-

>- r-

-

V) 

0 

u 

V) 

-

> 

l? 

0 

_,J 

4 ~----~------~------~------~----~------~ 

3 

2 

1 

ACMgS-58 

Al20 3- Ca0-Mg0-Si02 

MACHIN and YEE (1954} 

0 ~----~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 275 
4 ~------~------~------~------~------~----~ 

............ 

lU 

V') 

0 

a... 

>- I3 

V') 2 

0 

u 

V') 

> 

<..? 

0 

__. 

1 

Al 20 3- Ca0-Mg0-Si02 

MACHIN and YEE (1954/ 

ACMgS-58 

0 ~------~------~------~------~------~-------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

276 Viscosity of Synthetic and Natural Melts and Glasses 
__..... 

lU 

V) 

0 

a.. 

....__ 

>- I-

-

V) 

0 

u 

V) 

-

> 

0 

0 

--l 

4 .-----~~----~------~------~------~----~ 

3 

2 

1 

AI203- Ca0-Mg0-Si02 

MACHIN and YEE (1954) 

ACMgS-69 

ACMgS-72 

ACMgS-71 

0 ~----~------~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

Four-Component Systems 277 
~ 

UJ 

ll') 

0 

a.. 

....._,._ 

>-

1-

-

ll') 

0 

u 

ll') 

-

> 

0 

0 

_J 

4 ~------~------~------~--------------~----~ 

3 

2 

1 

AI203- CoO- Mg0-Si02 

MACHIN and YEE (1954) 

'~-ACMgS-72 

ACMgS-718 

ACMgS-74v 

ACMgS-69 

0 ~------~------~------~------~------~----~ 4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

278 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

lU 

V') 

0 

~ 

>-

~ 

4 ~----------------------------~--,----------~ 

3 

Al 20 3- CoO- Mg0-Si02 

MACHIN and YEE (1954) 

ACMgS-75 

ACMgS-76 

V') 2 

0 

u 

V') 

> 

0 

g 

1 

0 ~----~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATUR,E (°C) 

Four-Component Systems 279 
....--

LU 

(./') 

0 

a.. 

--

>- I4 ~------~------~------~------~------~----~ 

3 

AI203- Ca0-Mg0-Si02 

MACHIN and YEE (1954) 

ACMgS-75 

~ACMgS-76 

(./') 2 

0 

ACMgS-77 

u 

(./') 

> 

l? 

0 

__. 

1 

0 ~------~------~------~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

280 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(5.67) ,MG0~14.33), 

CA0(46.35),SI02 33.65) (X) 

AL203(10.0},MGO 10.0), 

CAO (45. 0) , SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1500.00 5.640 0.833 0.362 

SYSTEM 

AL203(5.55),MG0!21.07), 

CA0(40.39) ,SI02 32.99) (X) 

AL203(10.0),MGO 15.0), 

CAO (40. 0), SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 0.742 0.322 

SYSTEM 

AL203(8.10) ,MG0!20.50), CA0(39.30) ,SI02 32.10) (X) 

AL203(15.0) ,MGO 15.0), 

CA0(40.0) ,SI02(35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 1.946 0.845 

1450.00 5.804 1.526 0.663 

1500.00 5.640 1.099 0.477 

SYSTEM 

AL203(8.70) ,MG0114.67), CA0(42.18) ,SI02 34.45) (X) 

AL203(15.0) ,MGO 10.0) I 

CA0(40.0) ,SI02(35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 1.792 0.778 

1450.00 5.804 1.361 0.591 

1500.00 5.640 0.993 0.431 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.3 

AUTHOR 

A MgCS-81 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.1 

AUTHOR 

AM gCS-82 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

7.0 

4.6 

3.0 

AUTHOR 

AMgCS-83 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.0 

3.9 

2.7 

AMgCS-84 

Four-Component Systems 281 
SYSTEM 

AL203(8.52) ,MG0!21.56), CAO (36 .16), SI02 33. 76) (X) 

AL203(15.0) ,MGO 15.0), 

CA0(35.0), SI02 35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

2.116 

1.668 

1.281 

0.956 

AL203(12.14) ,MG0(7.67), 

CA0(44.14) ,SI02(36.05) (X) 

AL203(20.0),MG0(5.0), 

CA0(40.0),SI02(35.0) (%) 

LOG(N) 

0.919 

0.724 

0.556 

0.415 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.434 1.057 

1450.00 5.804 1.974 0.857 

1500.00 5.640 1.569 0.681 

SYSTEM 

AL203(11.88) ,MG0(15.03), 

CA0(37.80) ,SI02(35.29) (X) 

AL203(20.0),MG0(10.0), 

CAO (35. 0), SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

2.617 

2.104 

1.686 

1.411 

AL203(11.64) ,MG0(22.07), 

CAO (31. 73), SI02 (34. 56) (X) 

AL203(20.0),MG0(15.0), 

CA0(30.0),SI02(35.0) (%) 

LOG(N) 

1.137 

0.914 

0.732 

0.613 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 

1450.00 

1500.00 

5.977 

5.804 

5.640 

2.186 

1.740 

1.361 

0.949 

0.756 

0.591 

282 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.3 

5.3 

3.6 

2.6 

AUTHOR 

AMgCS-85 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.4 

7.2 

4.8 

AUTHOR 

A MgCS-86 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

13.7 

8.2 

5.4 

4.1 

AUTHOR 

A MgC S-8 7 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.9 

5.7 

3.9 

AMgCS-88 
SYSTEM 

AL203(15.56) ,MG0(7.87), 

CA0(39.60) ,SI02(36.97) (X) 

AL203(25.0) ,MG0(5.0), 

CAO (35. 0) , SI02 (35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.239 

2.728 

2.241 

1.872 

SYSTEM 

AL203(15.22),MG0(15.40), 

CAO (33. 21) , SI02 (36 .17) (X) 

AL203(25.0),MG0(10.0), 

CAO (30. 0) , SI02 (35. 0) (%) 

LOG(N) 

1.407 

1.185 

0.973 

0.813 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.684 

3.068 

2.565 

2.092 

1.723 

LOG(N) 

1.600 

1.332 

1.114 

0.908 

0.748 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

25.5 

15.3 

9.4 

6.5 

AUTHOR 

AMgCS-89 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

39.8 

21.5 

13.0 

8.1 

5.6 

AMgCS-90 

------------------------------------------------------------------------------ SYSTEM 

AL203(14.75),CA0(5.36), 

MG0(29.84) ,SI02(50.05) (X) 

AL203(25.0),CA0(5.0), 

MG0(20.0),SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.308 

4.625 

4.006 

3.506 

3.045 

LOG (N) 

2.305 

2.009 

1.740 

1.522 

1.322 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

202. 

102. 

54.9 

33.3 

21.0 

AMgCS-91 

------------------------------------------------------------------------------

SYSTEM 

AL203(19.16) ,MG0(8.07), 

CA0(34.84) ,SI02(37.93) (X) 

AL203(30.0),MG0(5.0), 

CA0(30.0),SI02(35.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.526 

3.875 

3.258 

2.809 

2.416 

LOG(N) 

1.966 

1.683 

1.415 

1.220 

1.049 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

92.4 

48.2 

26.0 

16.6 

11 . .2 

AMgCS-92 

Four-Component Systems 283 
SYSTEM 

AL203(18.73) ,MG0(15.80), 

CAO (28. 38) , SI02 (37. 09) (X) 

AL203(30.0),MG0(10.0), 

CAO (25. 0) , SI02 ( 35. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 3.447 1.497 

1450.00 5.804 2.815 1.223 

1500.00 5.640 2.219 0.964 

SYSTEM 

AL203(2.84),MG0(7.19), 

CAO (46 .53), SI02 (43 .44) (X) 

AL203(5.0) ,MGO(S.O), 

CAO (45. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.011 0.873 

1450.00 5.804 1.591 0.691 

1500.00 5.640 1.338 0.581 

SYSTEM 

AL203(2.79) ,MG0(14.19), 

CA0(40.54),SI02(42.57) (X) 

AL203(5.0),MG0(10.0), 

CA0(40.0),SI02(45.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.332 

1.881 

1.433 

1.095 

SYSTEM 

AL203(2.73),MG0(20.74), 

CA0(34.78),SI02(41.75) (X) 

AL203(5.0),MG0(15.0), 

CA0(35.0) ,SI02(45.0) (%) 

LOG(N) 

1.013 

0.817 

0.622 

0.476 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.201 

1.737 

1.381 

1.043 

LOG(N) 

0.956 

0.754 

0.600 

0.453 

284 Viscosity'of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE I 

P = 1.0 A1M. 

Z = 10000.0/T(K) (1/K) 

N 

31.4 

16.7 

9.2 

AUTHOR 

AMgCS-93 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 A1M. 

Z = 10000. 0/T (K) (1/K) 

N 

7.47 

4.91 

3.81 

AUTHOR 

AMgCS-94 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.3 

6.56 

4.19 

2.99 

AUTHOR 

AMgCS-95 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 A1M. 

Z = 10000.0/T(K) (1/K) 

N 

9.03 

5.68 

3.98 

2.84 

AMgCS-96 
SYSTEM 

AL203(2.68) ,CA0(29.25), 

MG0(27.13) ,SI02(40.95) (X) 

AL203(5.0),CA0(30.0), 

MGO (20. 0), SI02 ( (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 1.778 0.772 

1450.00 5.804 1.335 0.580 

1500.00 5.640 1.026 0.446 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

5.92 

3.80 

2.79 

AMgCS-97 

------------------------------------------------------------------------------ SYSTEM 

AL203(2.63) ,MG0(33.27), 

CA0(23.92) ,SI02(40.18) (X) 

AL203(5.0) ,MG0(25.0), 

CA0(25.0) ,SI02(45.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 0.900 0.391 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.46 

AMgCS-98 

------------------------ ---------------------------------------------------- SYSTEM 

AL203(5.82),MG017.36), 

CA0(42.35) ,SI02 44.47) (X) 

AL203(10.0),MGO 5.0), 

CAO ( 40. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 ·6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.059 

3.388 

2.827 

2.361 

1.942 

1.567 

AL203(5.71) ,MG0114.43), CA0(36.30) ,SI02 43.56) (X) 

AL203(10.0),MGO 10.0), 

CAO (35. 0) I SI02 (45. 0) (%) 

LOG(N) 

1.763 

1.471 

1.228 

1.025 

0.843 

0.680 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.314 

2.773 

2.322 

1.932 

1.522 

LOG(N) 

1.439 

1.204 

1.009 

0.839 

0.661 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

57.9 

29.6 

16.9 

10.6 

6.97 

4.79 

AUTHOR 

AMgCS-99 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

27.5 

16.0 

10.2 

6.90 

4.58 

AMgCS-100 

Four-Component Systems 285 
SYSTEM 

AL203(5.59),MG0~21.21), 

CA0(30.50),SI02 42.70) (X) 

AL203(10.0),MGO 15.0), 

CAO (30. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.822 

3.135 

2.595 

2.174 

1.778 

1.404 

LOG(N) 

1.660 

1.362 

1.127 

0.944 

0.772 

0.610 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

45.7 

23.0 

13.4 

8.79 

5.92 

4.07 

AMgCS-101 

---------------------------------------------------------------------------- SYSTEM 

AL203(5.48),MG0~27.73), 

CA0(24.92),SI02 41.86) (X) 

AL203(10.0) ,MGO 20.0), 

CAO (25. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.128 

1.686 

1.361 

SYSTEM 

AL203(5.38),MG0~34.00), 

CA0(19.55),SI02 41.07) (X) 

AL203(10.0),MGO 25.0), 

CAO (20. 0) , SI02 (45. 0) (%) 

LOG(N) 

0.924 

0.732 

0.591 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

8.40 

5.40 

3.90 

AUTHOR 

(1/K) AMgCS-102 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) AMgCS-103 T Z LN(N) LOG(N) N 

1500.00 5.640 1.300 0.565 3.67 

---------------------------------------------------------------------------- SYSTEM 

AL203(8.95) ,MG0~7.54), CAO (37. 96), SI02 45. 55) (X) 

AL203(15.0),MGO 5.0), 

CAO (35. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.625 

3.928 

3.360 

2.851 

2.407 

2.028 

LOG(N) 

2.009 

1.706 

1.459 

1.238 

1.045 

0.881 

286 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

102. 

50.8 

28.8 

17.3 

11.1 

7 .. 60 

AMgCS-104 
SYSTEM 

AL203(8.76) ,MG0(14.77) I 

CA0(31.86),SI02(44.60) (X) 

AL203(15.0) ,MG0(10.0) I 

CAO ( 3 0 . 0) I s I 0 2 ( 45 . 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.408 

3.747 

3.190 

2.715 

2.282 

1.911 

AL203(8.58) ,MG0~21.71), CAO (26. 01) I SI02 43. 70) (X) 

AL203(15.0),MGO 15.0), 

CAO (25. 0) I SI02 (45. 0) (%) 

LOG(N) 

1.914 

1.627 

1.386 

1.179 

0.991 

0.830 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.716 

3.148 

2.667 

2.246 

1.899 

AL203(8.41) ,MG0~28.37) I 

CA0(20.39) ,SI02 42.83) (X) 

AL203(15.0) ,MGO 20.0), 

CAO (20. 0) I SI02 ( 45. 0) (%) 

LOG (N) 

1.614 

1.367 

1.158 

0.975 

0.825 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.501 1.086 

1450.00 5.804 2.103 0.913 

1500.00 5.640 1.787 0.776 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

82.1 

42.4 

24.3 

15.1 

9.80 

6.76 

AUTHOR 

AMgCS-105 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

41.1 

23.3 

14.4 

9.45 

6.68 

AUTHOR 

AMgCS-106 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.2 

8.19 

5.97 

AMgCS-107 

----------------------------------------------------------------------------- SYSTEM 

AL203(12.23) ,MG0(7.73), 

CA0(33.35),SI02(46.69) (X) 

AL203(20.0),MG0(5.0), 

CA0(30.0),SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.357 

4.605 

3.965 

3.447 

3.020 

2.754 

LOG (N) 

2.326 

2.000 

1.722 

1.497 

1.312 

1.196 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

212. 

100; 

52.7 

31.4 

20.5 

15.7 

AMg CS-108 

Four-Component Systems 287 
SYSTEM 

AL203(11.97),MG0(15.14), 

CA0(27.20),SI02(45.70) (X) 

AL203(20.0) ,MG0(10.0), 

CAO (25. 0) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.130 

4.391 

3.764 

3.270 

2.845 

2.588 

LOG(N) 

2.228 

1.907 

1.634 

1.420 

1.236 

1.124 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

169. 

80.7 

43.1 

26.3 

17.2 

13.3 

A MgCS-1 09 

----------------------------------------------------------------------------- SYSTEM 

AL203(11.72) ,MG0(22.23), 

CAO (21. 30), SI02 (44. 75) (X) 

AL203(20.0) ,MG0(15.0), 

CAO (20. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.203 

3.584 

3.082 

2.653 

2.273 

AL203(11.49) ,MG0(29.04), 

CAO (15. 65) , SI02 ( 43. 83) (X) 

AL203(20.0),MG0(20.0), 

CAO (15. 0) , SI02 (45. 0) (%) 

LOG (N) 

1.825 

1.556 

1.338 

1.152 

0.987 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.472 

2.950 

2.526 

2.129 

SYSTEM 

AL203(12.50),MG0(28.41), 

CAO (11. 36), SI02 (47. 73) (X) 

AL203(20.0),MG0(25.0), 

CAO (10. 0) , SI02 ( 45. 0) (%) 

LOG (N) 

1.508 

1.281 

1.097 

0.925 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1450.00 5.804 2.434 1.057 

1500.00 5.640 2.044 0.888 

288 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

66.9 

36.0 

21.8 

14.2 

9.71 

AUTHOR 

AMgCS-110 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

32.2 

19.1 

12.5 

8.41 

AUTHOR 

AMgCS-111 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

11.4 

7.72 

AMgCS-112 
SYSTEM 

AL203(9.14),MGOl27.70), 

CA0(16.62) ,SI02 46.54) (X) 

AL203(15.0),MGO 25.0), 

CAO (15. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 1.611 0.700 

SYSTEM 

AL203(15.68),MG0(7.93), 

CA0(28.50) ,SI02(47.89) (X) 

AL203(25.0),MG0(5.0), 

CA0(25.0),SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.663 

4.047 

3.635 

3.105 

SYSTEM 

AL203(15.34),MG0(15.52), 

CAO (22. 30), SI02 (46. 84) (X) 

AL203(25.0),MG0(10.0), 

CA0(20.0),SI02(45.0) (%) 

LOG(N) 

2.025 

1.757 

1.579 

1.348 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

5.024 

4.331 

3.733 

3.408 

3.006 

AL203(15.01) ,MG0(22.78), 

CAO (16. 27) , SI02 ( 45. 84) (X) 

AL203(25.0) ,MG0(15.0), 

CAO (15. 0), SI02 (45. 0) (%) 

LOG(N) 

2.182 

1.881 

1.621 

1.480 

1.305 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.836 

4.124 

3.595 

3.105 

2.667 

LOG (N) 

2.100 

1.791 

1.561 

1.348 

1.158 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.01 

AUTHOR 

AMgCS-113 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

106. 

57.2 

37.9 

22.3 

AUTHOR 

AMgCS-114 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

152. 

76.0 

41.8 

30.2 

20.2 

AUTHOR 

AMgCS-115 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

126. 

61.8 

36.4 

22.3 

14.4 

AMgCS-116 

Four-Component Systems 289 
SYSTEM 

AL203(14.69) 1 MG0(29.74) 1 

CA0(10.68) 1 SI02(44.89) (X) 

AL203(25.0) IMG0(20.0) I 

CA0(10.0) ISI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.654 

3.945 

3.456 

2.996 

2.557 

SYSTEM AL203(16.03) MG0(29.15)~ 

CAO (5. 83) I SI02 (48. 98) (X) 

AL203(25.0) IMG0(25.0) I 

CAO (5. 0) I SI02 (45. 0) (%) 

LOG(N) 

2.021 

1.713 

1.501 

1.301 

1.111 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 3.421 1.486 

1450.00 5.804 2.833 1.230 

1500.00 5.640 2.361 1.025 

SYSTEM 

AL203(19.31) ,MG0(8.14), 

CA0(23.40) ,SI02(49.15) (X) 

AL203(30.0) ,MG0(5.0) I 

CA0(20.0) ,SI02(45.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.325 1.879 

1500.00 5.640 3.824 1.661 

SYSTEM 

AL203(0.0) ,CA0~45.63), 

MG0(7.06) ,SI02 47.32) (X) 

AL203(0.0) ,CAO 45.0), 

MG0(5.0) ,SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P. = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

105. 

51.7 

31.7 

20.0 

12.9 

AUTHOR 

(1/K) AMgCS-117 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

30.6 

17.0 

10.6 

AUTHOR 

AMgCS-118 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

75.6 

45.8 

AUTHOR 

AMgCS-119 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/K) 

T Z LN(N) LOG(N) N AMgCS-120 

1500.00 5.640 1.125 0.489 3.08 

290 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(0.0l,CA0(39.77), 

MG0(13.83 ,SI02(46.40) (X) 

AL203(0.0 ,CA0(40.0), 

MG0(10.0),SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N} 

1400.00 5.977 1.742 0.757 

1450.00 5.804 1.364 0.592 

1500.00 5.640 1.451 0.436 

SYSTEM 

AL203(0.0l,CA0(34.13), 

MGO (20. 35 , SI02 (45. 52) (X) 

AL203(0.0 ,CA0(35.0}, 

MG0(15.0),SI02(50.0} (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.115 

1.685 

1.319 

0.986 

SYSTEM 

AL203(0.0l,CA0(28.71), 

MGO (26. 62 , SI02 (44. 66} (X} 

AL203(0.0 ,CA0(30.0}, 

MG0(20.0},SI02(50.0} (%) 

LOG(N) 

0.919 

0.732 

0.573 

0.428 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.039 

1.629 

1.270 

0.959 

LOG(N) 

0.885 

0.708 

0.551 

0.417 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.71 

3.91 

2.86 

AUTHOR 

AMgCS-121 

MACHIN, YEE AND HANNA (1952} 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.29 

5.39 

3.74 

2.68 

AUTHOR 

AMgCS-122 

MACHIN, YEE AND HANNA (1952} 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7.68 

5.10 

3.56 

2.61 

AMgCS-123 

-----------------------------------------------------------------------------

SYSTEM 

AL203(0.0l,CA0(23.49), 

MGO (32. 67 , SI02 (43. 84} (X) 

AL203(0.0 ,CA0(25.0) I 

MG0(25.0} ,SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES} 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 1.324 0.575 

1500.00 5.640 1.030 0.447 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K} (1/K) 

N 

3.76 

2.80 

AMgCS-124 

Four-Component Systems 291 
SYSTEM 

AL203(2.91) ,CA0(47.66), 

MGO (0. 0), SI02 (49. 43) (X) 

AL203(5.0) ,CA0(45.0), 

MGO(O.O),SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 1.564 0.679 

SYSTEM 

AL203(2.85),CA0(41.51), 

MGO (7. 22), SI02 (48 .43) (X) 

AL203(5.0),CA0(40.0), 

MGO (5. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.272 0.987 

1450.00 5.804 1.875 0.814 

1500.00 5.640 1.560 0.678 

SYSTEM 

AL203(2.79) ,CA0(35.59), 

MG0(14.15) ,SI02 (47 .46) (X) 

AL203(5.0) ,CA0(35.0), 

MG0(10.0),SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.170 

2.653 

2.205 

1.805 

1.482 

SYSTEM 

AL203(2.74),CA0(29.92), 

MGO (20. 8) , SI02146. 54) (X) AL203(5.0) ,CAO 30.0), 

MG0(15.0),SI02 50.0) (%) MEASUREMENT METHOD 

LOG(N) 

1.377 

1.152 

0.958 

0.784 

0.643 

OSCILLATING-CYC. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.020 

2.534 

2.103 

1.723 

1.423 

LOG(N) 

1.312 

1.100 

0.913 

0.748 

0.618 

292 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z. = 10000. 0/T (K) (1/K) 

N 

4. 78 

AUTHOR 

AMgCS-125 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.70 

6.52 

4.76 

AUTHOR 

AMgCS-126 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

23.8 

14.2 

9.07 

6.08 

4.40 

AUTHOR 

AMgCS-127 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

20.5 

12.6 

8.19 

5.60 

4.15 

AMgCS-128 
SYSTEM 

AL203(2.69),CA0(24.45), 

MG0(27.21) ,SI02(45.64) (X) 

AL203(5.0),CA0(25.0), 

MG0(20.0),SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.161 

2.493 

2.089 

1.710 

1.369 

SYSTEM 

AL203(2.64),CA0(19.19), 

MG0(33.38) ,SI02(44.79) (X) 

AL203(5.0) ,CA0(20.0), 

MG0(25.0),SI02(50.0) (%) 

LOG(N) 

1.373 

1.083 

0.907 

0.743 

0.594 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 1.652 0.718 

1500.00 5.640 1.332 0.579 

SYSTEM 

AL203(5.97) ,CA0(43.40), 

MGO (0. 0) , SI02 (50. 63) (X) 

AL203(10.0) ,CA0(40.0), 

MGO (0. 0) , KSI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 2.955 1.283 

1450.00 5.804 2.493 1.083 

1500.00 5.640 2.108 0.915 

SYSTEM 

AL203(5.84),CA0(37.18), 

MGO (7. 39) , SI02 (49. 58) (X) 

AL203(10.0) ,CA0(35.0), 

MGO (5. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.499 

3.833 

3.300 

2.827 

2.389 

2.019 

LOG(N) 

1.954 

1.665 

1.433 

1.228 

1.037 

0.877 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

23.6 

12.1 

8.08 

5.53 

3.93 

AUTHOR 

AMgCS-129 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.22 

3.79 

AUTHOR 

AMgCS-130 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.2 

12.1 

8. 23 

AUTHOR 

AMgCS-131 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

89.9 

46.2 

27.1 

16.9 

10.9 

7.53 

AMgCS-132 

Four-Component Systems 293 
SYSTEM 

AL203(5.72) ,CAOl31.22), MG0(14.48),SI02 48.57) (X) 

AL203(10.0) ,CAO 30.0), 

MGO (10. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.317 

3.666 

3.170 

2.708 

2.295 

1.959 

LOG(N) 

1.875 

1.592 

1.377 

1.176 

0.997 

0.851 

SYSTEM 

AL203(5.61),eAOl25.50), 

MG0(21.28),SI02 47.60) (X) 

AL203(10.0) ,CAO 25.0), 

MGO (15. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-eYe. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4. 208 

3.520 

3.040 

2.573 

2.186 

1.904 

LOG(N) 

1.827 

1.529 

1.320 

1.117 

0.949 

0.827 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

75.0 

39.1 

23.8 

15.0 

9.92 

7.09 

AUTHOR 

AMgCS-133 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

67.2 

33.8 

20.9 

13.1 

8.90 

6.71 

AMgCS-134 

------------------------------------------------------------------------------ SYSTEM 

AL203(5.50),eAOl20.0), 

MGO (27. 82) , SI02 46. 67) (X) 

AL203(10.0) ,CAO 20.0), 

MG0(20.0),SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-eYe. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

2.970 

2.501 

2.094 

1.772 

SYSTEM 

AL203(5.39),eA0~14.71), 

MG0(34.11) ,SI02 45.78) (X) 

AL203(10.0),eAO 15.0), 

MGO (25. 0) , SI02 (50. 0) (%) 

LOG(N) 

1.290 

1.086 

0.910 

0.769 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 2.076 0.901 

1500.00 5.640 1.703 0.740 

294 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.5 

12.2 

8.12 

5.88 

AUTHOR 

AMgCS-135 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7.97 

5.49 

AMgCS-136 
SYSTEM 

AL203(9.17) ,CA0(38.92), 

MGO(O.O) ,SI02(51.90) (X) 

AL203(15.0) ,CA0(35.0), 

MGO(O.O),SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

5.342 

4.654 

4.045 

3.550 

3.086 

2.660 

AL203(8.98) ,CA0(32.66), 

MG0(7.57) ,SI02(50.80) (X) 

AL203(15.0) ,CA0(30.0), 

MG0(5.0) ,SI02(50.0) (%) 

LOG(N) 

2.320 

2.021 

1.757 

1.542 

1.340 

1.155 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

5.209 

4.524 

3.904 

3.450 

3.016 

2.721 

AL203(8.79) ,CA0~26.64), 

MG0(14.83) ,SI02 49.74) (X) 

AL203(15.0) ,CAO 25.0), 

MG0(10.0),SI02(50.0) (%) 

LOG (N) 

2.262 

1.965 

1.695 

1.498 

1.310 

1.182 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.075 

4.386 

3.780 

3.329 

2.923 

2.549 

LOG(N) 

2.204 

1.905 

1.641 

1.446 

1.270 

1.107 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

209. 

105. 

57.1 

34.8 

21.9 

14.3 

AUTHOR 

AMgCS-137 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

183. 

92.2 

49.6 

31.5 

20.4 

15.2 

AUTHOR 

AMgCS-138 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

160. 

80.3 

43.8 

27.9 

18.6 

12.8 

AMgCS-139 

Four-Component Systems 295 
SYSTEM 

AL203(8.61) ,CA0120.88), MG0(21.79) ,SI02 48.72) (X) 

AL203(15.0) ,CAO 20.0), 

MGO (15. 0) I SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.920 

4. 240 

3.632 

3.190 

2.785 

2.389 

AL203(8.44) ,CA0115.35), MG0(28.46) ,SI02 47.75) (X) 

AL203(15.0) ,GAO 15.0) I 

MG0(20.0),SI02(50.0) (%) 

LOG(N) 

2.137 

1.841 

1.577 

1.386 

1.210 

1.037 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.555 

3.063 

2.617 

2.252 

AL203(8.27) ,CA0110.03) I 

MG0(34.89) ,SI02 46.81) (X) 

AL203(15.0) ,CAO 10.0), 

MG0(25.0) ,SI02(50.0) (%) 

LOG(N) 

1.544 

1.330 

1.137 

0.978 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 2.534 1.100 

1500.00 5.640 2.104 0.914 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

137. 

69.4 

37.8 

24.3 

16.2 

10.9 

AUTHOR 

AMgCS-140 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

35.0 

21.4 

13.7 

9.51 

AUTHOR 

AMgCS-141 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.6 

8.2 

AMgCS-142 

------------------------------------------------------------------------------ SYSTEM 

AL203(8.11) ,CA014.92), MGO ( 41. 05) , SI02 45. 91) (X) 

AL203(15.0) ,CAO 5.0), 

MG0(30.0) ,SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 2.153 0.935 

296 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.61 

AMgCS-143 
SYSTEM 

AL203(12.55) ,CA0(34.22), 

MGO (0. 0) , SI02 (53. 23) (X) 

AL203(20.0) ,CA0(30.0), 

MGO(O.O) ,SI02(50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.271 

5.509 

4.836 

4. 261 

3.745 

3.408 

SYSTEM 

AL203(12.28),CA0(27.89), 

MG0(7.76),SI02(52.07) (X) 

AL203(20.0) ,CA0(25.0), 

MG0(5.0),SI02(50.0) (%) 

LOG (N) 

2.723 

2.393 

2.100 

1.851 

1.626 

1.480 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

6.184 

5.425 

4.745 

4.164 

3.619 

3.227 

LOG (N) 

2.686 

2.356 

2.061 

1.808 

1.572 

1.401 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

529. 

247. 

126. 

70.9 

42.3 

30.2 

AUTHOR 

AMgCS-144 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

485. 

227. 

115. 

64.3 

37.3 

25.2 

AMgCS-145 

------------------------------------------------------------------------------

SYSTEM 

AL203(12.01) ,CA0(21.84), 

MG0(15.19),SI02(50.96) (X) 

AL203(20.0),CA0(20.0), 

MG0(10.0),SI02(50.0) (%) MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.943 

5.182 

4.533 

3.985 

3.520 

3.100 

LOG (N) 

2.581 

2.250 

1.968 

1.731 

1.529 

1.346 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

381. 

178. 

93.0 

53.8 

33.8 

22.2 

AMgCS-146 

Four-Component Systems 297 
SYSTEM 

AL203(11.76) ,CA0(16.04) I 

MGO (22. 31) I SI02 (49. 89) (X) 

AL203(20.0) ,CA0(15.0) I 

MGO (15. 0) I SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.624 

4.898 

4.264 

3.735 

3.270 

2.833 

LOG(N) 

2.442 

2.127 

1.852 

1.622 

1.420 

1.230 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

277. 

134. 

71.1 

41.9 

26.3 

17.0 

AMgCS-147 

------------------------------------------------------------------------------

SYSTEM 

AL203(11.52) ,CA0(10.47) I 

MGO (29 .13) I SI02 ( 48. 87) (X) 

AL203(20.0) ,CA0(10.0) I 

MGO (20. 0) I SI02 (50. 0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

4.718 

4.055 

3.523 

3.063 

2.660 

AL203(11.29) ,CA0(5.13) I 

MG0(35.69) ,SI02(47.89) (X) 

AL203(20.0) ,CA0(5.0) I 

MG0(25.0) ,SI02(50.0) (%) 

MEASUREMENT METHOD 

LOG(N) 

2.049 

1.761 

1.530 

1.330 

1.155 

OSCILLATING-CYC. 

N (POISES) 

VISCOMETER 

T (DEGREES C) 

T Z 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

SYSTEM 

LN(N) 

3.965 

3.497 

3.011 

2.580 

AL203(16.10) ,CA0(29.27) I 

MGO (0. 0) I SI02 (54. 63) (X) 

AL203(25.0) ,CA0(25.0) I 

MGO(O.O),SI02(50.0) (%) 

LOG (N) 

1.722 

1.519 

1.307 

1.121 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 4.603 1.999 

1500.00 5.640 4.055 1.761 

298 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

112. 

57.7 

33.9 

21.4 

14.3 

AUTHOR 

AMgCS-148 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

52.7 

33.0 

20.3 

13.2 

AUTHOR 

AMgCS-149 

MACHIN, YEE AND HANNA (1952) 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

99.8 

57.7 

AMgCS-150 
SYSTEM AUTHOR 

AL203(15.74) ,CA0(22.59), 

MGO (7. 96) , SI02 (53. 41) (X) 

AL203(25.0) ,CA0(20.0), 

MGO (5. 0) , SI02 (50. 0) (%) 

MACHIN, YEE AND HANNA (1952) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 4.796 2.083 

1450.00 5.804 4.240 1.841 

1500.00 5.640 3.728 1.619 

SYSTEM 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

121. 

69.4 

41.6 

AUTHOR 

AMgCS-151 

AL203(15.39) ,CA0(16.79), 

MGO (15. 57) , SI02 (52. 24) (X) 

AL203(25.0) ,CA0(15.0), 

MG0(10.0) ,SI02(50.0) (%) 

MACHIN, YEE AND HANNA (1952) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.981 

5.147 

4.533 

3.976 

3.529 

LOG(N) 

2.598 

2.236 

1.968 

1.727 

1.533 

DERIVED FROM 

TABLE III 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

396. 

172. 

93.0 

53.3 

34.1 

AMgCS-152 

------------------------------------------------------------------------------ SYSTEM 

AL203(15.06),CA0(10.95), 

MGO (22. 86), SI02 (51.12) (X) 

AL203(25.0),CA0(10.0), 

AUTHOR 

MACHIN, YEE AND HANNA (1952) 

MGO (15. 0) , SI02 (50. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

OSCILLATING-CYC. VISCOMETER TABLE III 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1250.00 6.566 6.382 2.772 591. 

AMgCS-153 

1300.00 6.357 5.580 2.423 265. 

1350.00 6.161 4.883 2.121 132. 

1400.00 5.977 4.265 1.852 71.2 

1450.00 5.804 3.704 1.609 40.6 

1500.00 5.640 3.281 1.425 26.6 ------------------------------------------------------------------------- SYSTEM 

AL203 (14.75), CAO (5.36), 

MGO (29.84), SI02 (50.05) (X) 

AL203 (25.0), CAO (5.0), 

MOO (20.0), SI02 (50.0) (%) 

MEASUREMENT METHOD 

OSCILLATING-CYC. VISCOMETER 

N {POISES) 

T (DEGREES C) 

T 

1300. 

1350. 

1400. 

1450. 

1500. 

z 

6.357 

6.161 

5.977 

5.804 

5.640 

LN(N) 

5.308 

4.625 

4.006 

3.506 

3.045 

AUTHOR 

lVJACHIN, YEE AND HANNA ( 19 52) 

DERIVED FROM 

TABLE I I 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) AMgCS-154 

LOG(N) N 

2.305 202. 

2.009 102. 

1.740 54.9 

1.522 33.3 

1.322 21.0 

Four-Component Systems 299 
~ 

w 

V') 

-

0 

a.. 

.......... 

.,_ >-

-

V') 

0 

u 

V') 

-

> 

~ 

g 

4 ~------------~------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-85 

0 ~----~~----~------~------~------~-------

1200 1300 1400 1500 

TEMPERATURE (°C) 

300 Viscosity of Synthetic and Natural Melts and Glasses 
........... 

UJ 

V) 

-

0 

a.. 

-....... 

>- I--

-

V) 

0 

u 

V) 

-

> 

~ 

0 

...J 

4 ~----~--------------------~------~----~ 

3 

2 

1 

AI203- CaO- MgO- Si02 

MACHIN, YEE and HANNA (1952) 

~ /ACMgS-85 

ACMgff 

/ ACMgS-84 

0 ~----~------~------~----~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 301 
4 ----------------------~------~------~----~ 

AI203-Ca0-Mg0-Si02 .. 

MACHIN, YEE and HANNA (19.52) 

3 

.---.. 

w 

V') 

-

0 

Cl. 

.......,_ 

>- 1-

-

V') 2 0 

u 

V') 

-

> 

~ 

g 

ACMgS-87 

1 

0 ~----~------~------~------~------~--~~ 

1200 1300 1400 1500 

TEMPERATURE {°C) 

302 Viscosity of Synthetic and Natural Melts and Glasses 
.---... 

lU 

(./') 

0 

a.. 

-----

..,_ 

>-

-(./') 

0 

u 

(./') 

-

> 

l? 

0 

_J 

4 ~----~------~------~----~~----~------~ 

3 

2 

1 

AI20 3-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-87 

ACMgS-88 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 303 
.......... 

LU 

(./') 

0 

0.. 

>- 1-

-

4 ~~--~------~------~------~------~----~ 

3 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA /1952) 

(./") 2 0 

u 

(./") 

-

> ACMgS-90 

() 

g 

1 

0 ------~------~------~------~-------------- 1200 1300 1400 1500 

TEMPERATURE (°C) 

304 Viscosity of Synthetic and Natural Melts and Glasses 
4 ~----~------~------~----~------~----~ 

...--... 

lU 

V') 

0 

a.. 

-

>-

1-

3 

V') 2 

0 

u 

V') 

> 

0 

0 

___. 

1 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (19.52} 

ACMgS-90 

0 ~----~------~------L-----~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Com~nent Systems 305 
4 ----------------------~~------------~------~ 

..--.. 

lU 

V') 

0 

a.. 

>-

~ 

3 

V') 2 

0 

u 

V') 

> 

0 

g 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-92 

0 ~------~------~----~~----~------~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

306 Viscd~ity of Synthetic and Natural Melts and Glasses 
........._ 

LU 

V') 

-

0 

a.. 

>- 1-

4 

3 

V') 2 

0 

u 

V') 

> 

~ 

0 

~ 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-93 

ACMgS-92 

0 ~----~------~------~----~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 307 
..--... 

UJ 

U') 

0 

o_ 

.......... 

>- 1-

-

U') 

0 

u 

U') 

-

> 

() 

0 

__J 

4 ~----~~----~~----~------~------~-------, 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952} 

ACMgS-95 

ACMgS-96 

0 ~----~~----~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

308 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

UJ 

V) 

-

0 

a.. 

.......... 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

"' 0 

~ 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-95 

ACMgS-96 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 309 
4 ~----~~----~~------~----~------~------~ 

........... 

LU 

V) 

0 

~ 

>- 1-

3 

V) 2 

0 

u 

A1203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

V) ACMgS-99 

> ACMgS-101 

~ 

g 

1 

0 ~----~~----~~----~~----~------~--------

1200 1300 1400 1500 

TEMPERATURE (°C) 

31 0 Viscosity of Synthetic and Natural Melts and Glasses 
.....--.. 

lU 

(./) 

0 

a_ 

-

>- 1-

-

(./) 

0 

u 

(./) 

-

> 

0 

0 

_..J 

4 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952} 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 311 
..--.. 

UJ 

V') 

0 

a.. 

>-

t4 r-------~------~----~~----~------~------~ 

3 

AI203- CaO-MgO- Si02 

MACHIN, YEE and HANNA (1952) 

V') 2 ACMgS-104 

0 ACMgS-105 

u 

V') 

> 

0 

g 

1 

0 ~------~------~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

312 Viscosity of Synthetic and Natural Melts and Glasses 
..--... 

lU 

(./) 

0 

a.. 

-

>-

~ 

-(./) 

0 

u 

(./) 

-

> 

0 

0 

-1 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-104 

ACMgS-105 

ACMgS-106 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 313 
4 ~--------------------------------------~------~ 

~ 

lU 

V") 

0 

CL 

>- 1--

3 

V") 2 

0 

u 

V") 

> 

0 

g 

1 

A1 20 3- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-108 

ACMgS-109 

0 ~------~------~------~------------------------ 1200 1300 1400 1500 

TEMPERATURE (°C) 

314 Viscosity of Synthetic and Natural Melts and Glasses 
4 ~----~------~------~------~------~----~ 

>-

~ 

3 

V') 2 

0 

u 

V') 

> 

0 

0 

_, 

1 

0 

4.5 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA ( 1952) 

~ACMgS-112 

5.5 6.5 

ACMgS-108 

ACMgS-109 

75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 315 
4 ~------~----------------------~~----~----~ 

........... 

lU 

V') 

0 

a... 

>-

...... 

3 

V') 2 

0 

u 

V') 

> 

l? 

g 

1 

0 

1200 

AI203- CoO- MgO-Si02 

MACHIN, YEE and HANNA ( 1952) 

ACMgS-115 

ACMgS-116 

ACMgS-117 

1300 1400 

TEMPERATURE (°C) 

316 Viscosity of Synthetic and Natural Melts and Glasses 

1500 
4 ~----~~------------~----------------~----~ 

---- UJ 

(./) 

0 

a.. 

>- 1--

3 

(./) 2 

0 

u 

(./) 

> 

<-? 

0 

___. 

1 

AI203- CaO-MgO -Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-118 

ACMgS-115 

ACMgS-116 

ACMgS-117 

0 ~----~~----~~----~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 31 7 
4 ~----~------~------~----~~----~------~ 

...--.. 

lU 

V") 

0 

Cl.. 

-

>-

t3 

V") 2 

0 

u 

V") 

> 

0 

g 

1 

AI203 -Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-119 

0 ~----~------~------~------~----~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

318 Viscosity of Synthetic and Natural Melts and Glasses 
...--

lU 

V) 

0 

a_ 

...___,._ 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

0 

0 

___. 

4 ~----~~~----~~------~~------~~------~~----~ 

-

3 ~ 

2 ~ 

1~ 

AI203- CaO -MgO- Si02 

MACHIN, YEE and HANNA (1952) 

/ACMgS-119 

-

-

-

-

-

-

-

0 ~-----~~-----~~----~~~----~'~----~~~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1) 

Four-Component Systems 319 
__...._ 

lU 

V') 

0 

Cl.. 

........... 

>- 1--

-

V') 

0 

u 

V') 

-

> 

l? 

g 

4 ~----~----------------------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0- Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-121~ ACMgS-122 

ACMgS-123-_____;;::o.......: 

~~ 

0 ~----~------~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

320 Viscosity of Synthetic and Natural Melts and Glasses 
..--

LU 

V') 

-

0 

a.. 

--

>- 1-

-

V') 

0 

u 

V') 

-

> 

l? 

0 

__, 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

AI203-Co0-Mg0-Si02 

MACHIN, YEE and HANNA (19.52) 

ACMgS-121--:~~--ACMgS-122 

.,/---ACMgS-123 

ACMgS-124-

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 321 
........._ 

lU 

V) 

0 

a.. 

-

>- 1-

-

V) 

0 

u 

V) 

-

> 

0 

0 

--I 

4 ~--~--~------~----~~------~------~------, 

3 

2 

1 

0 

1200 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-128 

1300 1400 

TEMPERATURE (°C) 

1500 

322 Viscosity of Synthetic and Natural Melts and Glasses 
>- 1--

4 ~----~------~------~------~------~----~ 

3 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ll") 2 

0 

u 

ll") 

> 

l? 

0 

__. 

1 

ACMgS-128 

·H-------ACMgS-129 

ACMgS-127-~/• 

~ -ACMgS-130 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 323 
4 ~------~------~------~------~------~----~ 

........... 

UJ 

V') 

0 

o_ 

>- 1-

3 

V') 2 

0 

u 

V') 

> 

0 

g 

1 

0 

1200 

AI203- CoO-MgO-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-132 

ACMgS-133 

1300 1400 

TEMPERATURE (°C) 

324 Viscosity of Synthetic and Natural Melts and Glasses 

1500 
4 ~------~----~~----~------~------~------~ 

...--.. 

lU 

V') 

0 

Cl.. 

>-

....... 

3 

V') 2 

0 

u 

V') 

> 

~ 

0 

__. 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-132 

ACMgS-133 

ACMgS-134 

0 ------~~----~~----~------~------~--------

4.5 5.5 6.5 Z5 

10 000/T (KELVINS- 1

) 

Four-Component Systems 325 
__...._ 

LU 

V') 

0 

a... 

......__ 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

l? 

0 

__,J 

4 ~------~----------------------~------~-------, 

3 

2 

1 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA ( 1952) 

ACMgS-138 

ACMgS-141 

0 --------~------~------~------~------~------~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

326 Viscosity of Synthetic and Natural Melts and Glasses 
4 ~------~------~------~------~------~----~ 

___...._ 

UJ 

V') 

0 

Q.. 

>-

~ 

3 

V') 2 

0 

u 

V') 

> 

~ 

0 

_.J 

0 

4.5 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-140 

5.5 6.5 

ACMgS-137 

ACMgS-139 

75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 327 
4 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

0 ~------~------~------~------~------~-------

1200 1300 1400 1500 

TEMPERATURE (°C) 

328 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

LU 

V") 

-

0 

a.. 

-

>-

~ 

-

V") 

0 

u 

V") 

-

> 

() 

0 

.....J 

4 ~------~------~------------~------~------~ 

3 

2 

1 

0 

4.5 

AI203- Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (19.52) 

ACMgS-145 

ACMgS-147 

ACMgS-144 

ACMgS-146 

ACMgS-148 

5.5 6.5 

10 000/T (KELVINS- 1

) 

7.5 

Four-Component Systems 329 
__...... 

UJ 

V') 

0 

a... 

-

>- 1-

V') 

0 

u 

V') 

> 

l? 

g 

4 --------~----------------------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA /1952) 

ACMgS-153 

ACMgS-154 

0 ~------~------~------~------~------~----~ 

1200 1300 1400 1500 

TEMPERATURE {°C) 

330 Viscosity of Synthetic and Natural Melts and Glasses 
...--.. 

w 

V") 

0 

a_ 

-

.,_ >-

-

V") 

0 

u 

V") 

-

> 

0 

0 

__, 

4 ------~--------------~------~------~----~ 

3 

2 

1 

AI203-Ca0-Mg0-Si02 

MACHIN, YEE and HANNA (1952) 

ACMgS-153 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 75 

10 000/T (KELVINS- 1

) 

Four-Component Systems 331 
SYSTEM AUTHOR 

A1203(.13)K20(.04)Na20(.09)Si02(.75) (X) N' DALA et al. (1984) 

MEASUREMENT METHOD DER I VEO FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1. 0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN( N) LOG(N) N AKNS-1 

1523. 5.567 9.04 3.92 8433. 

1535. 5.530 8.96 3.89 7785. 

1547. 5.494 8.63 3.74 5597. 

1566. 5.437 8.59 3.73 5377. 

1578. 5.402 8.40 3.64 4447. 

1585. 5.382 8.06 3.50 3165. 

1611. 5.307 7.93 3.44 2779. 

1629. 5.257 7.64 3.17 2079. 

1632. 5.249 7.65 3.32 2100. 

1634. 5.243 7.59 3.29 1978. 

-----------------------------------------~--------------------------------------

SYSTEM AUTHOR 

A1203(.13)K20(.06)Na20(.06)Si02(.75) (X) N'DALA et a 1 • ( 1984) 

MEASUREMENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TARLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) {1/DEG. K) 

T z LN(N) LOG(N) N AKNS-2 

1513. 5.599 11.02 4.78 61083. 

1530. 5.546 11.00 4.77 59874. 

1595. 5.353 10.16 4.41 25848. 

1600. 5.339 10.17 4.41 26108. 

1601. 5.336 10.17 4.41 26108. 

1613. 5.302 9.93 4.31 20537. 

1616. 5.293 9.93 4.31 20537. 

1617. 5.291 9.76 4.23 17326. 

1621. 5.279 9.79 4.25 17854. 

1628. 5.260 9.77 4.24 17500. 

1630. 5.254 9.66 4.19 15677. 

332 Viscosity of Synthetic and Natural Melts and Glasses 
Five-Component Systems 

Five-Component Systems 333 
SYSTEM AL203(5.69) CA0(46.53) BA0(1.99)~ 

MGO (7 .19) I SI02l38. 60) (X) AL203(9.5) ICAO 42.75) IBA0(5.0) I 

MGO (4. 75) I SI02 38. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.332 

2.028 

1.686 

1.411 

LOG(N) 

1.013 

0.881 

0.732 

0.613 

AL203(5.71) 1 CA0(41.50) 1 BA0(2.0) 1 

MGO (7. 22) I SI02l43. 58) (X) AL203(9.5),CAO 38.0),BA0(5.0), 

MGO (4. 75) , SI02 42. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.425 

2.028 

1.723 

1.411 

LOG(N) 

1.053 

0.881 

0.748 

0.613 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.3 

7.6 

5.4 

4.1 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

11.3 

7.6 

5.6 

4.1 

ACBMgS-1 

ACBMgS-2 

---------------------------------------------------------------------------- SYSTEM 

AL203(5.73) 1 CA0(36.44) 1 BA0(2.00), 

MGO (7. 24) I SI02l48. 59) (X) AL203(9.5) 1 CAO 33.25) 1 BA0(5.0), 

MGO (4. 75) , SI02 47. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

3.250 

2.398 

1.988 

1.548 

LOG(N) 

1.412 

1.041 

0.863 

0.672 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

25.8 

11.0 

7.3 

4.7 

A CBMgS-3 

---------------------------------------------------------------------------- SYSTEM 

AL203(5.67) 1 CA0(51.52) 1 BA0(1.98), 

MG0(7.17) ,SI02l33.66) (X) AL203(9.5) ICAO 47.5) IBA0(5.0) I 

MG0(4.75) 1 SI02 33.25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1. 0 A'IM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) 

2.390 

2.186 

2.015 

LOG(N) N 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

1.033 10.8 

0.949 8.9 

0.875 7.5 

334 Viscosity of Synthetic and Natural Melts and Glasses 

ACBMgS-4 
SYSTEM 

AL203(5.61) ,CA0(30.61) ,BA0(1.96), 

MG0(14.20) ,SI02(47.61) (X) 

AL203(9.5) ,CA0(28.5) ,BA0(5.0), 

MGO (9. 5) , SI02 (47. 5) (%) 

MEASUREMENT ME'TIIOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

3.157 

2.342 

1.668 

0.693 

LOG(N) 

1.371 

1.017 

0.724 

0.301 

SYSTEM 

AL203(5.59),CA0(35.59),BA0(1.96), 

MG0(14.15) ,SI02(42.71) (X) 

AL203(9.5) ,CA0(33.25),BA0(5.0), 

MG0(9.5),SI02(42.75) (%) MEASUREMENT ME'TIIOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.262 

1.808 

1.411 

0.993 

LOG(N) 

0.982 

0.785 

0.613 

0.431 

SYSTEM 

AL203(5.57),CA0(40.54),BA0(1.95), 

MG0(14.10) ,SI02(37.83) (X) 

AL203(9.5) ,CA0(38.0) ,BA0(5.0), 

MGO (9. 5) , SI02 (38. 0) (%) 

MEASUREMENT ME'TIIOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.128 

1.723 

1.253 

0.788 

LOG(N) 

0.924 

0.748 

0.544 

0.342 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

23.5 

10.4 

5.3 

2.0 

AU'TIIOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

9.6 

6.1 

4.1 

2.7 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8.4 

5.6 

3.5 

2.2 

ACBMgS-5 

ACBMgS-6 

ACBMgS-7 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.56),CA0(45.45),BA0(1.94), 

MG0(14.10) ,SI02(37.83) (X) 

AL203(9.5) ,CA0(42.75),BA0(5.0). 

MGO (9. 5) , SI02 (33. 25) (%) 

MEASUREMENT ME'TIIOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 1.526 0.663 

1500.00 5.640 1.281 0.556 

1550.00 5.485 1.099 0.477 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.6 

3.6 

3.0 

ACBMgS-8 

Five-Component Systems 335 
SYSTEM 

AL203(5.48),CA0(29.91),BA0(1.92), 

MG0(20.81l,SI02(41.88) (X) AL203(9.5 ,CA0(28.5),BA0(5.0), 

MGO (14. 25 I SI02 (42. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.668 

1.386 

0.993 

0.788 

LOG(N) 

0.724 

0.602 

0.431 

0.342 

SYSTEM 

AL203(5.47),CA0(34.78),BA0(1.91), 

MG0(20.74l,SI02(37.10) (X) AL203(9.5 ,CA0(33.25),BA0(5.0), 

MGO (14. 25 I SI02 (38. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.370 

1.335 

0.993 

0.588 

LOG(N) 

1.029 

0.580 

0.431 

0.255 

AL203(5.45) ,CA0(39.62),BA0(1.91), 

MGO (20. 67l, SI02 (32. 36) (X) AL203(9.5 ,CA0(38.0),BA0(5.0), 

MGO (14. 25 , SI02 (33. 25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 1.131 0.491 

1500.00 5.640 0.742 0.322 

1550.00 5.485 0.405 0.176 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.3 

4.0 

2.7 

2.2 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.7 

3.8 

2.7 

1.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.1 

2.1 

1.5 

ACBMgS-9 

ACBMgS-10 

ACBMgS-11 

----------------------------------------------------------------------------- SYSTEM 

AL203(5.43) ,CA0(44.43) ,BA0(1.90), 

MG0(20.60l,SI02(27.64) (X) AL203(9.5 ,CA0(42.75) ,BA0(5.0), 

MG0(14.25 ,SI02(28.5) (%) MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 3.270 1.420 

1500.00 5.640 1.872 0.813 

1550.00 5.485 1.526 0.663 

336 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

26.3 

6.5 

4.6 

ACBMgS-12 
SYSTEM 

AL203(11.40) ,CA0(31.10),BA0(2.0), 

MGO (21. 63) , SI02 !33. 87) (X) AL203(19.0),CAO 28.5),BA0(5.0), 

MGO (14. 25) , SI02 33. 25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.460 

1550.00 5.485 

SYSTEM 

LN(N) 

2.322 

1.629 

1.308 

1.030 

LOG(N) 

1.009 

0.708 

0.568 

0.447 

AL203(11.32) ,CA0(41.18),BA0(1.98), 

MGO (21. 49) , SI02 !24. 03) (X) AL203(19.0) ,CAO 38.0) ,BA0(5.0), 

MGO (14. 25) , SI02 23. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.230 

1.435 

1.253 

1.030 

LOG(N) 

0.968 

0.623 

0.544 

0.447 

AL203(11.52) ,CA0(52.36) ,BA0(2.02), 

MGO (14. 57) , SI02 (19. 55) (X) 

AL203(19.0) ,CA0(47.5) ,BA0(5.0), 

MG0(9.5),SI02(19.0) (%) 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.2 

5.1 

3.7 

2.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.3 

4.2 

3.5 

2.8 

AUTHOR 

HOFMANN (1959) 

MEASUREMENT METHOD DERIVED FROM 

TORSION VISCOMETER TABLE II 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1450.00 5.804 3.235 1.405 25.4 

1500.00 5.640 1.825 0.792 6.2 

1550.00 5.485 1.548 0.672 4.7 

ACBMgS-13 

ACBMgS-14 

ACBMgS-15 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.60),CA0(35.65),BA0(4.14), 

MGO (7. 08) , SI02 (47. 53) (X) 

AL203(9.0) ,CA0(31.5),BA0(10.0), 

MGO (4. 5) , SI02 (45. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.785 

2.332 

1.856 

1.411 

LOG(N) 

1.210 

1.013 

0.806 

0.613 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

16.2 

10.3 

6.4 

4.1 

ACBMgS-16 

Five-Component Systems 337 
SYSTEM 

AL203(5.58) ,CA0(40.60),BA0(4.12), 

MGO (7. 06) , SI02 (42. 63) (X) 

AL203(9.0),CA0(36.0),BA0(10.0), 

MGO (4. 5), SI02 (40. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.518 

2.079 

1.758 

1.482 

LOG(N) 

1.093 

0.903 

0.763 

0.643 

SYSTEM 

AL203(5.56),CA0(45.52),BA0(4.11), 

MG0(7.03),SI02(37.77) (X) 

AL203(9.0),CA0(40.5),BA0(10.0), 

MGO (4. 5), SI02 (36. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.653 

2.303 

1.917 

1.548 

LOG(N) 

1.152 

1.000 

0.833 

0.672 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.4 

8.0 

5.8 

4.4 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

14.2 

10.0 

6.8 

4.7 

ACBMgS-17 

ACBMgS-18 

------------------------------------------------------------------------------ SYSTEM 

AL203(5.55) ,CA0(50.41) ,BA0(4.10), 

MGO (7. 01) , SI02 (32. 93) (X) 

AL203(9.0) ,CA0(45.0) ,BA0(10.0), 

MGO (4. 5), SI02 (31. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.728 

2.518 

2.322 

LOG(N) 

1.185 

1.093 

1.009 

AL203(9.46) ,CA0(51.60) ,BA0(6.99), 

MGO (23. 93) , SI02 (8. 03) (X) 

AL203(9.0) ,CA0(27.0),BA0(10.0), 

MGO (9. 0), SI02 (45. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.674 

2.163 

1.569 

0.788 

LOG(N) 

1.161 

0.940 

0.681 

0.342 

338 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

15.3 

12.4 

10.2 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

14.5 

8.7 

4.8 

2.2 

ACBMgS-19 

ACBMgS-20 
SYSTEM 

AL203(5o47),CA0(34o83),BA0(4o04), 

MGO (13 o 85) , SI02 ( 41o 8) (X) 

AL203(9o0) ,CA0(31o5) ,BA0(10o0), 

MGO (9 o 0) , SI02 (40 o 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400o00 5o977 

1450o00 5o804 

1500o00 5o640 

1550o00 5o485 

LN(N) 

2o370 

1o856 

1o482 

1o030 

LOG(N) 

1o029 

Oo806 

Oo643 

Oo447 

SYSTEM 

AL203(5o46),CA0(39o67),BA0(4o03), 

MGO (13 o 8) , SI02 (37 o 04) (X) 

AL203(9oO),CA0(36oO),BA0(10oO), 

MGO (9 o 0) , SI02 (36 o 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400o00 5o977 

1450o00 5o804 

1500o00 5o640 

1550o00 5o485 

SYSTEM 

LN(N) 

2o442 

1o974 

1o41JL 

0 0 69:~ 

LOG(N) 

1o061 

Oo857 

Oo613 

Oo301 

AL203(5o44) ,CA0(44o49),BA0(4o02), 

MG0(13o76),SI02(32o29) (X) 

AL203(9o0) ,CA0(40o5) ,BA0(10o0), 

MGO (9 o 0) , SI02 (31o 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1450o00 5o804 1o872 

1500.00 5.640 1.609 

1550.00 5.485 1.435 

LOG(N) 

0.813 

0.699 

0.623 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000 o 0/T (K) (1/K) 

N 

10.7 

6.4 

4.4 

2.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

11.5 

7.2 

4.1 

2.0 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.5 

5.0 

4.2 

ACBMgS-21 

ACBMgS-22 

ACBMgS-23 

-------------------------------------------------------------------------------

SYSTEM 

AL203(5.37) ,CA0(29.29),BA0(3.97), 

MGO (20. 37) , SI02 (41. 0) (X) 

AL203(9.0) ,CA0(27.0),BA0(10o0), 

MGO (13. 5) , SI02 (40. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1o649 

1.308 

0.916 

0.788 

LOG(N) 

0.716 

0.568 

0.398 

0.342 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.2 

3.7 

2.5 

2.2 

ACBMgS-24 

Five-Component Systems 339 
SYSTEM 

AL203(5.35),CA0(34.06),BA0(3.95), 

MG0(20.31),SI02(36.33) (X) 

AL203(9.0) ,CA0(31.5),BA0(10.0), 

MG0(13.5),SI02(36.0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

1.872 

1.435 

1.099 

0.742 

LOG(N) 

0.813 

0.623 

0.477 

0.322 

SYSTEM 

AL203(5.34),CA0(38.8),BA0(3.94), 

MGO (20. 24) , SI02 (31. 68) (X) 

AL203(9.0) ,CA0(36.0),BA0(10.0), 

MG0(13.5) ,SI02(31.5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 1.411 0.613 

1500.00 5.640 0.916 0.398 

1550.00 5.485 0.588 0.255 

SYSTEM 

AL203(5.32) ,CA0(43.51),BA0(3.93) I 

MG0(20.17),SI02(27.07) (X) 

AL203(9.0) ,CA0(40.5) ,BA0(10.0), 

MG0(13.5) ,~I02(27.0) (%) MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 

1450.00 5.804 2.639 1.146 

1500.00 5.640 2.380 1.033 

1550.00 5.485 2.054 0.892 

SYSTEM 

AL203(11.15) ,CA0(30.43),BA0(4.12), 

MGO (21.17) , SI02 (33 .13) (X) 

AL203(18.0) ,CA0(27.0),BA0(10.0), 

MG0(13.5),SI02(31.5) (%) MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.434 

1.917 

1.435 

0.993 

LOG(N) 

1.057 

0.833 

0.623 

0.431 

340 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

6.5 

4.2 

3.0 

2.1 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.1 

2.5 

1.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

14.0 

10.8 

7.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

11.4 

6.8 

4.2 

2.7 

ACBMgS-25 

ACBMgS-26 

ACBMgS-27 

ACBMgS-28 
SYSTEM 

AL203(11.08) ,CA0(40.3),BA0(4.09), 

MG0(21.02),SI02(23.51) (X) 

AL203(18.0),CA0(36.0),BA0(10.0), 

MGO (13. 5) , SI02 (22. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.303 

1.548 

1.361 

1.065 

LOG(N) 

1.000 

0.672 

0.591 

0.462 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10.0 

4.7 

3.9 

2.9 

ACBMgS-29 

------------------------------------------------------------------------------ SYSTEM 

AL203(11.26),CA0(51.21),BA0(4.16), 

MGO (14. 25) , SI02 (19 .12) (X) 

AL203(18.0) ,CA0(45.0) ,BA0(10.0), 

MGO (9. 0) , SI02 (18. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 1.946 0.845 

1550.00 5.485 1.649 0.716 

SYSTEM 

AL203(5.47),CA0(34.80),BA0(6.42), 

MGO (6. 91) , SI02146. 40) (X) AL203(8.5) ,CAO 29.75),BA0(15.0), 

MGO (4. 25), SI02 42. 5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

3.011 

2.251 

1.758 

1.308 

LOG(N) 

1.307 

0.978 

0.763 

0.568 

AL203(5.45) ,CA0(39.64),BA0(6.4), 

MGO (6. 89) , SI02141. 62) (X) AL203(8.5) ,CAO 34.0),BA0(15.0), 

MGO ( 4. 25) , SI02 38. 25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.603 

2.140 

1.792 

1.504 

LOG(N) 

1.130 

0.929 

0.778 

0.653 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7.0 

5.2 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

20.3 

9.5 

5.8 

3.7 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

13.5 

8.5 

6.0 

4.5 

ACBMgS-30 

ACBMgS-31 

ACBMgS-32 

Five-Component Systems 341 
SYSTEM 

AL203(5.43),CA0(44.45),BA0(6.37), 

MGO (6·. 87) , SI02 !36. 88) (X) AL203(8.5) ,CAO 38.25) ,BA0(15.0), 

MGO (4. 25), SI02 34. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.890 

2.549 

2.140 

1.758 

LOG(N) 

1.255 

1.107 

0.929 

0.763 

AL203(5.36) ,CA0(29.26),BA0(6.29), 

MG0(13.57) ,SI02(45.51) (X) 

AL203(8.5),CA0(25.5),BA0(15.0), 

MG0(8.5),SI02(42.5) (%) MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T 

1400.00 

1450.00 

1500.00 

1550.00 

SYSTEM 

z 

5.977 

5.804 

5.640 

5.485 

LN(N) 

2.955 

2.092 

1.482 

0.742 

LOG(N) 

1.283 

0.908 

0.643 

0.322 

AL203(5.35) ,CA0(34.02),BA0(6.27), 

MG0(13.53) ,SI02(40.83) (X) 

AL203(8.5) ,CA0(29.75),BA0(15.0), 

MGO (8. 5) , SI02 (38. 25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.485 

1.946 

1.548 

1.099 

LOG(N) 

1.079 

0.845 

0.672 

0.477 

AL203(5.33) ,CA0(38.76) ,BA0(6.25), 

MG0(13.48) ,SI02(36.18) (X) 

AL203(8.5) ,CA0(34.0) ,BA0(15.0), 

MGO (8. 5) , SI02 (34. 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.708 

2.241 

1.629 

0.833 

LOG(N) 

1.176 

0.973 

0.708 

0.362 

342 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

18.0 

12.8 

8.5 

5.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

19.2 

8.1 

4.4 

2.1 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

12.0 

7.0 

4.7 

3.0 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

15.0 

9.4 

5.1 

2.3 

ACBMgS-33 

ACBMgS-34 

ACBMgS-35 

ACBMgS-36 
SYSTEM 

AL203(5.31) ,CA0(43.47) ,BA0(6.23), 

MG0(13.44) ,SI02(31.55) (X) 

AL203(8.5) ,CA0(38.25),BA0(15.0), 

MGO (8. 5) , SI02 (29. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1450.00 5.804 2.251 0.978 

1500.00 5.640 1.988 0.863 

1550.00 5.485 1.887 0.820 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.5 

7.3 

6.6 

ACBMgS-37 

------------------------------------------------------------------------------

SYSTEM 

AL203(5.25) ,CA0(28.62) ,BA0(6.16) I 

MG0(19.9ll 1SI02(40.07) (X) 

AL203(8.5 ICA0(25.5) IBA0(15.0) I 

MGO (12. 75 I SI02 (38. 25) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

1.569 

1.224 

0.875 

0.588 

LOG(N) 

0.681 

0.531 

0.380 

0.255 

AL203(5.23) ICA0(33.28)1BA0(6.14) I 

MGO (19 .84l I SI02 (35 .5l (X) AL203(8.5 ICA0(29.75 IBA0(15.0) I 

MGO (12. 75 I SI02 (34. 0 (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

SYSTEM 

LN(N) 

2.028 

1.548 

1.194 

0.833 

LOG(N) 

0.881 

0.672 

0.519 

0.362 

AL203(5.21) CA0(37.92),BA0(6.12)~ 

MG0(19.78l 1 SI02(30.97) (X) 

AL203(8.5 ICA0(34.0) IBA0(15.0) I 

MGO (12. 75 I SI02 (29. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1450.00 5.804 1.668 0.724 

1500.00 5.640 1.099 0.477 

1550.00 5.485 0.788 0.342 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.8 

3.4 

2.4 

1.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

7.6 

4.7 

3.3 

2.3 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1. 0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

5.3 

3.0 

2.2 

ACBMgS-38 

ACBMgS-39 

ACBMgS-40 

Five-Component Systems 343 
SYSTEM 

AL203(5.2l,CA0(42.52),BA0(6.1), 

MGO (19. 72 , SI02 (26 .46) (X) 

AL203(8.5 ,CA0(38.25),BA0(15.0), 

MG0(12.75 ,SI02(25.5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 2.773 1.204 

1550.00 5.485 2.451 1.064 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

16.0 

11.6 

ACBMgS-41 

------------------------------------------------------------------------------ SYSTEM 

AL203(10.89) ,CA0(29.71) ,BA0(6.39), 

MG0(20.67) ,SI02(32.35) (X) 

AL203(17.0),CA0(25.5),BA0(15.0), 

MGO (12. 75) , SI02 (29. 75) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.485 

1.988 

1.482 

1.030 

LOG(N) 

1.079 

0.863 

0.643 

0.447 

SYSTEM 

AL203(10.79),CA0(39.25),BA0(6.33), 

MGO (20. 47) , SI02 !23 .16) (X) 

AL203(17.0),CAO 34.0),BA0(15.0), 

MG0(12.75) ,SI02 21.5) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

1550.00 5.485 

LN(N) 

2.485 

1.609 

1.459 

1.131 

LOG(N) 

1.079 

0.699 

0.633 

0.491 

SYSTEM 

AL203(10.99),CA0(49.99),BA0(6.45), 

MGO (13. 91) , SI02 (18. 66) (X) 

AL203(17.0),CA0(42.5),BA0(15.0), 

MGO ( 8 . 5) , S I 0 2 ( 17 . 0) (%) 

MEASUREMENT METHOD 

TORSION VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1500.00 5.640 2.197 0.954 

1550.00 5.485 1.758 0.763 

344 Viscosity· of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

12.0 

7.3 

4.4 

2.8 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

12.0 

5.0 

4.3 

3.1 

AUTHOR 

HOFMANN (1959) 

DERIVED FROM 

TABLE II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.0 

5.8 

ACBMgS-42 

ACBMgS-43 

ACBMgS-44 
.......... 

UJ 

V) 

-

0 

Cl.. 

.......... 

>- 1-

-

V) 

0 

u 

V) 

-

> 

() 

0 

-l 

4 ~----~--------------------~------------~ 

3 

2 

1 

Al20 3 - CaO-BaO-MgO- Si02 

HOFMANN (1959} 

ACBMgS-1 

ACBMgS-2 

ACBMgS-3 

0 ------~------~------~----~------~----~ 

1300 1400 1500 1600 

TEMPERATURE {°C) 

Five;.Component Systems 345 
.....--

UJ 

(./) 

0 

a.. 

-

>- 1-

4 

3 

(./) 2 

0 

u 

(./) 

> 

<) 

0 

_J 

1 

0 

4.5 

AI203- CoO- BoO- MgO- Si02 

HOFMANN (1959) 

ACBMgS-4 

ACBMgS-1 

ACBMgS-2 

ACBMgS-3 

5.5 6.5 

lO 000/T (KELVINS- 1

) 

346 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
.......... 

lU 

V') 

0 

a... 

>-

...... 

4 

3 

V') 2 

0 

u 

V') 

> 

0 

g 

1 

AI203- CoO- BoO- MgO- Si02 

HOFMANN (1959} 

ACBMgS-5 

ACBMgS-6 

ACBMgS-7 

0 ~----~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 347 
........... 

UJ 

V') 

0 

a.. 

>- 1-

4 

3 

V') 2 

0 

u 

V') 

-

> 

~ 

0 

__. 

1 

0 

4.5 

AI203- CoO- BaO-MgO- Si02 

HOFMANN (1959) 

ACBMgS-5 

ACBMgS-6 

ACBMgS-7 

ACBMgS-8 

5.5 6.5 

10 000/T (KELVINS- 1

) 

348 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
.--... 

UJ 

V') 

0 

a... 

>- 1-

4 ~----~----~~--------------~----~------~ 

3 

Al20 3 - CoO~ BoO- MgO- Si02 

HOFMANN (1959) 

V') 2 

0 

u 

V') 

> 

~ 

0 ACBMgS-12 

__. 

1 ACBMgS-10 

ACBMgS-9 

ACBMgS-11 

0 ~----~------~~----~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE {°C) 

Five-Component Systems 349 
......... 

UJ 

c./) 

-

0 

CL 

.......... 

.,_ >-

-

4 

3 

c./) 2 

0 

u 

c./) 

> 

l? 

0 

...J 

1 

Al20 3 - CaO- BaO -MgO- Si02 

HOFMANN (1959) 

ACBMgS-12 

ACBMgS-10 

ACBMgS-9 

0 ~----~------~------~------._------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS-1

) 

350 Viscosity of Synthetic and Natural Melts and Glasses 
---... 

u.J 

V) 

0 

a.. 

.......... 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

0 

0 

__,J 

4 

3 

2 

1 

Al20 3 - CaO- BaO -MgO- Si02 

HOFMANN {1959) 

ACBMgS-13 

ACBMgS-14 

0 ------~------~----~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 351 
...--

LU 

lf) 

0 

CL 

..__.. 

..,_ 

>-

-lf) 

0 

u 

lf) 

-

> 

~ 

0 

___. 

4 ~----~------~------~--~--~------.------. 

3 

2 

1 

Al 20 3- CaO- BaO-MgO- Si02 

HOFMANN (1959} 

0 ~----~------_.------~------~--------------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

352 Viscosity of Synthetic and Natural Melts and Glasses 
>-

..... 

4 ~----~------~----~------~--~~----~ 

3 

AI203- CoO- BoO-MgO- Si02 

HOFMANN (1959) 

(./) 2 

0 

u 

(./) 

> 

l? 

g ACBMgS-15 

1 

0 ~----~------~----~------~----~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 353 
...--

w 

V') 

0 

a_ 

>-

~ 

4 

3 

V') 2 

0 

u 

V') 

> 

l? 

0 

___, 

1 

A120 3- Ca0-Ba0-Mg0-Si02 

HOFMANN /1959) 

ACBMgS-15 

0 ~----~------~------~------~------~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

354 Viscosity of Synthetic and Natural Melts and Glasses 
~ 

lU 

ll) 

-

0 

0... 

>-

~ 

4 

3 

ll) 2 

0 

u 

ll) 

-

> 

~ 

g 

1 

AI203- CoO- BoO- MgO- Si02 

HOFMANN (1959) 

ACBMgS-16 

ACBMgS-18 

ACBMgS-17 

ACBMgS-19 

0 ~----~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 355 
_........._ 

LU 

V') 

0 

a... 

----

>- 1-

-

V') 

0 

u 

V') 

-

> 

(j 

0 

....J 

4 

3 

2 

1 

AI203- CoO -BaO-MgO- Si02 

HOFMANN (1959) 

ACBMgS-16 

ACBMgS-18 

ACBMgS-17 

0 ~------~----~~--~~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

356 Viscosity of Synthetic and Natural Melts and Glasses 
.---... 

lU 

U') 

0 

a.. 

-

>- 1-

-

U') 

0 

u 

U') 

-

> 

0 

0 

___. 

4 

3 

2 

1 

Al20 3 - CoO- BoO -MgO- Si02 

HOFMANN {19.59) 

ACBMgS-20 

ACBMgS-22 

ACBMgS-21 

0 ------~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 357 
.......... 

UJ 

V") 

0 

a... 

-

>-

I-

-

V") 

0 

u 

V") 

-

> 

<-' 0 

_J 

4 ~------~----~~----~------~------~------~ 

3 

2 

1 

AI203- CoO- BoO- MgO- Si02 

HOFMANN (19.59) 

ACBMgS-20 

ACBMgS-22 

ACBMgS-21 

ACBMgS-23 

0 ~----~~----~~----~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

358 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

UJ 

(/) 

0 

Cl.. 

----

...,_ 

>-

-

(/) 

0 

u 

(/) 

-

> 

0 

0 

--l 

4 ~----~--------------~----~~----~------~ 

3 

2 

1 

AI203- CoO- BaO-MgO- Si02 

HOFMANN {1959} 

ACBMgS-25 

ACBMgS -26 

ACBMgS-27 

0 ~----~------~------~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 359 
.......... 

UJ 

tl') 

0 

a.. 

.,_ >-

4 

3 

Al20 3 - CoO- BaO-MgO- Si02 

HOFMANN ( 1959} 

tl') 2 

0 

u 

tl') 

> 

0 

0 

__, 

1 

/ACBMgS-27 

ACBMgS-24 

0 ~----~~----~------~------~------~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

360 Viscosity of Synthetic and Natural Melts and Glasses 
.......-.. 

UJ 

V') 

0 

a.. 

.__... 

>-

~ 

-

V') 

0 

u 

V') 

-

> 

~ 

g 

4 ~----~------~----~------~------~~--_, 

3 

2 

1 

Al2 0 3 - CoO- BoO- MgO- Si02 

HOFMANN (1959} 

ACBMgS-28 

ACBMgS-29 

0 ~----~------~----~------~------~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 361 
,.......... 

lU 

V') 

0 

a.. 

__.. 

>-

1--

-

V') 

0 

u 

V') 

-

> 

0 

0 

___. 

4 

3 

2 

1 

AI203- CoO- BoO- MgO- Si02 

HOFMANN (1959) 

ACBMgS-28 

ACBMgS-29 

0 ~----~------~------~------~------~------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS-1

) 

362 Viscosity of Synthetic and Natural Melts and Glasses 
~ 

UJ 

V) 

0 

CL 

....__ 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

<-' 

0 

__. 

4 ~----~------~----~------~----~----~ 

3 

2 

1 

AI203- CoO- BoO -MgO- Si02 

HOFMANN (1959} 

ACBMgS-30------

0 ~----~------~----~----~~----~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 363 
~ 

UJ 

lf) 

0 

Q.. 

...........-

.,_ >-

-lf) 

0 

u 

lf) 

-

> 

l? 

0 

_,J 

4 ~--------------------~----~------~------~ 

3 

2 

1 

Al20 3 - CaO- BaO-MgO- Si02 

HOFMANN (1959) 

/ACBMgS-30 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

364 Viscosity of Synthetic and Natural Melts and Glasses 
_...., 

UJ 

V) 

0 

a.. 

...__ 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

l? 

0 

....J 

4 ~----~--------------------~------------~ 

3 

2 

1 

Al20 3 - CaO- BaO-MgO- Si02 

HOFMANN (1959) 

ACBMgS-31 

ACBMgS-33 

ACBMgS-32 

0 ~----~------~------~----~------~----~ 

1300 1400 1500 1600 

TEMPERATURE {°C) 

Five-Component Systems 365 
..........._ 

LU 

ll) 

-

0 

a... 

...__... 

>- Ill) -

0 

u 

ll) 

-

> 

() 

0 

__. 

4 ~----~~----~------~------~------~------~ 

3 

2 

1 

A120 3 - CoO- BoO -MgO- Si02 

HOFMANN (1959) 

ACBMgS-32 

ACBMgS-33 

ACBMgS-31 

0 ~----~------~------~------~------~----~ 

4.5 5.5 . 6.5 7.5 

10 000/T (KELVINS- 1

) 

366 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

lU 

V') 

0 

a.. 

>-

t4 ------------------------------------~------~ 

3 

AI203- CoO- BoO -MgO- Si02 

HOFMANN (1959) 

V') 2 

0 

u 

V') 

> 

0 

0 

_J 

1 

ACBMgS-34 

ACBMgS-36 

ACBMgS-35 

ACBMgS-37 

0 ~----~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE {°C) 

Five-Component Systems 367 
.......... 

w 

V') 

-

0 

Cl.. 

>-

..... 

-

4 ~----~~----~------~------~------~------~ 

3 

AI203 - CoO- BoO-MgO- Si02 

HOFMANN (1959) 

V') 2 

0 

u 

V') 

-

> 

~ 

9 

1 

ACBMgS-37 

ACBMgS-34 

ACBMgS-36 

ACBMgS-35 

0 ~----~------~------~------~------~-------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

368 Viscosity of Synthetic and Natural Melts and Glasses 
.......... 

UJ 

V") 

0 

Cl.. 

-.......... 

>-

....... 

-

V") 

0 

u 

V") 

-

> 

0 

0 

_,J 

4 ~----~----------------------------~------~ 

3 

2 

1 

AI203- CoO- BaO-MgO- Si02 

HOFMANN (1959) 

ACBMgS-41..________ 

ACBMgS-39 

ACBMgS-38 

0 ------~------~------~------~----~------~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 369 
............ 

UJ 

(/') 

0 

a.. 

___.. 

>- 1-

-(/') 

0 

u 

(/') 

-

> 

() 

g 

4 

3 

2 

1 

0 

4.5 

Al20 3 - CoO- BaO -MgO- Si02 

HOFMANN (1959) 

/ACBMgS-41 

ACBMgS-39 

ACBMgS-38 

5.5 6.5 

10 000/T (KELVINS- 1

) 

370 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
........... 

UJ 

V') 

-

0 

a... 

........... 

>- 1-

-

V') 

0 

u 

V') 

-

> 

0 

g 

4 ~----~------~----~------~------~----~ 

3 

2 

1 

AI203- CaO- BaO- MgO- Si02 

HOFMANN {19.59) 

0 ~----~------~----~------~------~------

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 371 
..--.. 

UJ 

V) 

0 

a.. 

___. 

>-

...... 

-

V) 

0 

u 

V) 

-

> 

() 

0 

__, 

4 

3 

2 

1 

0 

4.5 

A120 3 - CoO- BoO -MgO- Si02 

HOFMANN (1959) 

5.5 6.5 

10 000/T (KELVINS- 1

) 

372 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
........... 

UJ 

V') 

0 

a.. 

-

>-

~ 

-

V') 

0 

u 

V') 

-

> 

0 

0 

__, 

4 ~----~------~----~------~----~----~ 

3 

2 

1 

Al20 3 - CoO- BoO- MgO- Si02 

HOFMANN (1959) 

ACBMgS-44~ 

0 ------~------~----~----~~----~----~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Five-Component Systems 373 
...--

lU 

V') 

-

0 

a.. 

____.. 

._ >-

-

V') 

0 

u 

V') 

-

> 

() 

0 

~ 

4 

3 

2 

1 

AI203- CaO- BaO-MgO- Si02 

HOFMANN (1959) 

/ACBMgS-44 

0 ~----~------~------~----~~----~------~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

374 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUTHOR 

Al20j(.08)Ca0(.07)K20(.02)Na20(.06)Si02(.77) (X) N'OALA et al. (1984) 

MEASURE r.£NT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1. 0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN(N) LOG(N) N ACKNS-1 

1376. 6.064 10.48 4.55 35596. 

1417. 5.917 10.13 4.39 25084. 

1472. 5.730 9.50 4.12 13359. 

1475. 5.720 9.35 4.06 11498. 

1516. 5.589 9.05 3.93 8518. 

1520. 5.577 8.99 3.90 8022. 

1577. 5.405 8.43 3.66 4582. 

1604. 5.327 8.12 3.52 3361. 

1607. 5.319 8.06 3.50 3165. 

1609. 5.313 8.04 3.49 3102. 

1625. 5.268 7.77 3.37 2368. 

1632. 5.249 7.74 3.36 2298. 

1636. 5.238 7.71 3.34 2230. 

-------------------------------------------------------------------------------- SYSTEM AUTHOR 

Al203(.18)Ca0(.09)K20(.04)Na20(.03)Si02(.66) (X) N'DALA et al. (1984) 

~ASURE MENT METHOD DERIVED FROM 

ROTATIONAL VISCOMETER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z = 10000.0/T(K) (1/DEG. K) 

T z LN(N) LOG(N) N ACKNS-2 

1375. 6.060 9.91 4.30 20130. 

1392. 6.006 9.66 4.19 15677. 

1417. 5.917 9. 31 4.04 11047. 

1424. 5.892 9.12 3.96 9136. 

1497. 5.649 8.35 3.62 4230. 

1550. 5.485 7.56 3.28 1919. 

1556. 5.4o7 7.49 3.25 1790. 

1558. 5.461 7.47 3.24 1754. 

1630. 5.254 6.63 2.87 757. 

1632. 5.249 6.61 2.87 742. 

1642. 5.221 6.41 2.78 607. 

1651. 5.197 6.40 2.77 601. 

Five-Component Systems 375 

Six-Component Systems 

Six-Component Systems 377 
SYSTEM 

AL203(20.75),CA0(13.84) ,MG0(10.49), 

BA0(1.84) ,SR0(6.13) ,SI02(46.95) (X) 

AL203(30.0),CA0(11.0),MG0(6.0), 

BA0(4.0),SR0(9.0),SI02(40.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

AUTHOR 

HOFMAIER (1968) 

DERIVED FROM 

ABB. 6 

N (POISES) P = 1. 0 A'IM. 

T (DEGREES C) T Z 

1496.9 5.650 

1578.9 5.400 

1680.1 5.120 

1772.0 4.890 

1877.5 4.650 

1999.7 4.400 

2052.6 4.300 

LN(N) 

3.730 

2.924 

2.187 

1.382 

0.829 

0.230 

0.000 

LOG(N) 

1.62 

1.27 

0.95 

0.60 

0.36 

0.1 

0.000 

378 Viscosity of Synthetic and Natural Melts and Glasses 

Z = 10000. 0/T (K) (1/K) 

N 

41.687 

18.621 

8.913 

3.981 

2.291 

1.259 

1.0 

ACMgBSS-1 
V'J 

j;(" 

h 

0 

3 

"8 

:I 

11) 

a 

!.1'1 

-< 

;-

3 

"' 

w 

....... 

1./:J 

_...... 

UJ 

c./') 

-

0 

a.. 

___. 

>-

~ 

-

c./') 

0 

u 

c./') 

-

> 

~ 

0 

-J 

3 

I 

I 

2 

I 

1 

01 

-1 

1450 

I I I ' I I . I . . 

AI203-Ca0-Mg0-Ba0-Sr0-Si02 

HOFMAIER {1968) 

ACMgBSS-1 

--..... • ACMgBSS-2 

1550 1650 1750 1850 1950 2050 

TEMPERATURE {°C) 
,........ 

UJ 

U") 

-

0 

a... 

___. 

...,_ 

>-

-

U") 

0 

u 

U") 

-

> 

~ 

0 

-I 

3 ~----~--------------~------~------~----~ 

2 

1 

0 

-1 

3.5 

AI203-Ca0-Mg0-Ba0-Sr0-Si02 

HOFMAIER (1968) 

4.5 5.5 

10 000/T (KELVINS- 1

) 

ACMgBSS-1 

ACMgBSS -2 

6.5 

380 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

AL203(4.92) ,MG0~12.28) ,CA0{22.88), FE0(4.64) ,FE203 0.02 ,SI02(55.25) (X) 

AL203(8.45) ,MGO 8.34 ,CA0(21.62), 

FEO (5. 61) , FE203 0. 06l , SI02 (55. 92) (%) 

MEASUREMENT METHOD 

AUTHOR 

BILLS (1963) 

DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

5.158 

4.518 

3.806 

3.272 

2.908 

2.466 

LOG(N) 

2.240 

1.962 

1.653 

1.421 

1.263 

1.071 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

173.8 

91.6 

44.98 

26.36 

18.32 

11.78 

SYSTEM AUTHOR 

AL203{4.71),MG0!11.77),CA0(21.92), BILLS (1963) 

FE0(8.64) ,FE203 0.04),SI02(52.92) (X) . AL203(8.02) ,MGO 7.92) ,CA0(20.53), 

FE0(10.36),FE203(0.10),SI02(53.10) (%) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

4. 747 

4.004 

3.454 

2.977 

2.489 

LOG(N) 

2.062 

1.739 

1.500 

1.293 

1.081 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

115.3 

54.83 

31.62 

19.63 

12.05 

SYSTEM AUTHOR 

AL203(6.55),MG0(9.20),CA0(29.70), BILLS (1963) 

FE0(5.68) ,FE203(0.02) ,SI02!48.85l (X) AL203(11.04) ,MG0(6.13) ,CAO 27.53 , FE0(6.74) ,FE203(0.05) ,SI02 48.51 (%) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

4.495 

3.850 

3.254 

2.772 

2.282 

LOG(N) 

1.952 

1.672 

1.413 

1.204 

0.991 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

89.54 

46.99 

25.88 

16.00 

9.795 

AMgCFFS-1 

AM gCFFS-2 

A Mg CFFS- 3 

Six-Component Systems 381 
SYSTEM 

AL203(11.03) ,MG0(11.75) ,CA0(29.56), 

FE0(3.30),FE203(0.02),SI02!44.34l (X) AL203(18.26) ,MG0(7.69) ,CAO 26.91 , FE0(3.85) ,FE203(0.05) ,SI02 43.24 (%) 

AUTHOR 

BILLS (1963) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

4.287 

3.691 

3.108 

2.636 

2.204 

LOG(N) 

1.862 

1.603 

1.350 

1.145 

0.957 

AL203(5.61) ,MG0(14.02) ,CA0(26.13), 

FE0(16.23) ,FE203(0.09) ,SI02(37.91) 

AL203(7.57) ,MG0(7.47) ,CA0(19.37), 

FE0(15.41) ,FE203(0.19) ,SI02(30.10) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

72.78 

40.09 

22.39 

13.96 

9.057 

AUTHOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) 

T Z LN(N) LOG(N) N 

1250.00 

1300.00 

1350.00 

1400.00 

1450.00 

SYSTEM 

6.566 

6.357 

6.161 

5.977 

5.804 

4. 283 

3.645 

2.959 

2.53 

2.077 

1.860 

1.583 

1.285 

1.100 

0.902 

72.44 

38.28 

19.28 

12.59 

7.980 

AL203(6.02) ,MG0(8.81) ,CA0(28.46), 

FE0(9.60),FE203(0.04) ,SI02(46.81) (X) 

AL203(10.50),MG0(5.83),CA0(26.18), 

FE0(11.31),FE203(0.11),SI02(46.13) (%) 

MEASUREMENT METHOD 

AUTHOR 

BILLS (1963) 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

4.048 

3.465 

2.927 

2.464 

1.950 

1.596 

LOG(N) 

1.758 

1.505 

1.271 

1.070 

0.847 

0.693 

382 Viscosity of Synthetic and Natural Melts and Glasses 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

57.28 

31.99 

18.66 

11.75 

7.031 

4.932 

A MgCFFS-4 

AMgC FFS-5 

AMgCFFS-6 
SYSTEM 

AL203(10.55) IMG0(11.23) ICA0(28.24) I 

FE0(7.58) FE203(0.04)~SI02!42.36l (X) AL203(17.33) IMG0(7.30)1CAO 25.53 I 

FE0(8.78) 1FE203(0.09) 1SI02 41.03 (%) 

AUTHOR 

BILLS (1963) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

3.822 

3.288 

2.749 

2.270 

1.840 

LOG(N) 

1.660 

1.428 

1.194 

0.986 

0.799 

AL203(6.02) IMG0(8.44)1CA0(27.27) I 

FE0(13.35) ,FE203(0.07) ,SI02(44.85) 

AL203(9.99) 1MG0(5.54) ,CA0(24.90), 

FE0(15.62) ,FE203(0.19) ,SI02(43.88) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

3.772 

3.033 

2.519 

2.164 

1.667 

LOG(N) 

1.638 

1.317 

1.094 

0.940 

0.724 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

45.71 

26.79 

15.63 

9.683 

6.295 

AUTHOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

43.45 

20.75 

12.42 

8.710 

5.297 

SYSTEM AUTHOR 

AL203(10.00) ,MG0~10.66) ,CA0(26.79), BILLS (1963) 

FE0(12.29) ,FE203 0.08l,SI02(40.18) (X) AL203(16.30) ,MGO 7.64 ,CA0(24.03), 

FEO (14 .12) , FE203 0. 20 , SI02 (38. 61) (%) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

1500.00 5.640 

LN(N) 

3.594 

2.959 

2.413 

2.077 

1.664 

1.317 

LOG(N) 

1.561 

1.285 

1.048 

0.902 

0.732 

0.572 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

36.39 

19.28 

11.17 

7.980 

5.284 

3.733 

AMgCFFS-7 

AMgCFFS-8 

AMg CFFS-9 

Six-Component Systems 383 
SYSTEM 

AL203(4.25) IMG0(10.63) ICA0(19.79) I 

FE0(17.44) 1 FE203(0.11) 1 SI02(47.78) 

AL203(7.11) 1 MG0(7.02) 1 CA0(18.19) 1 

FE0(20.53) 1 FE203(0.28) 1 SI02(47.05) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

3.795 

3.136 

2.487 

1.840 

1.338 

LOG(N) 

1.648 

1.362 

1.080 

0.799 

0.581 

AL203(5.65) IMG0(7.94) ICA0(25.63) I 

FE0(18.52) FE203(0.10)~SI02(42.16) 

AL203(9.29) 1 MG0(5.16) 1 CA0(23.18) 1 

FE0(21.45) 1 FE203(0.26) 1 SI02(40.84) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

3.325 

2.650 

1.992 

1.593 

1.121 

LOG(N) 

1.444 

1.151 

0.865 

0.692 

0.487 

AUTHOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

44.46 - 23.01 

12.02 

6.295 

3.811 

AUTIIOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

27.80 

14.16 

7.328 

4.920 

3.069 

SYSTEM AUTIIOR AL203(9.49) MG0(10.11l CA0(26.79)~ BILLS (1963) 

FE0(16.69) 1 FE203l0.11 1 SI02(38.16) (X) AL203(15.37) 1 MGO 6.47 1 CA0(22.65) 1 

FE0(19.03)~FE203 0.28 1 SI02(36.40) (%) MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

3.178 

2.540 

1.945 

1.621 

1.156 

LOG(N) 

1.380 

1.103 

0.835 

0.704 

0.502 

384 Viscosity of Synthetic and Natural Melts and Classes 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

23.99 

12.68 

6.998 

5.058 

3.177 

(1/K) 

AMgCFFS-10 

AMgCFFS-11 

AMgCFFS-12 
SYSTEM 

AL203(3.96) IMG0(9.90) ICA0(18.45) I 

FE0(23.01) 1 FE203(0.14) 1 SI02(44.54) 

AL203(6.55) IMG0(6.46) ICA0(16.76) I 

FE0(26.78) 1 FE203(0.37) 1 SI02(43.35) 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN(N) 

3.357 

2.632 

1.980 

1.423 

0.880 

LOG(N) 

1.458 

1.143 

0.860 

0.618 

0.382 

AUTHOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

28.71 

13.90 

7.244 

4.150 

2.410 

SYSTEM AUTHOR 

AL203(8.86) IMG0(9.44) ICA0(25.44) I BILLS (1963) 

FE0(22.16) 1 FE203l0.17l 1 SI02(35.62) (X) AL203(14.22)~MGO 5.99 CA0(20.96)~ 

FEO (25. 06) I FE203 0. 41 I SI02 ( 33. 68) (%) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

SYSTEM 

LN(N) 

2.754 

2.160 

1.669 

1.204 

0.734 

LOG(N) 

1.196 

0.938 

0.725 

0.523 

0.321 

AL203(5.41) 1 MG0(7.09) 1 CA0(24.50) 1 

FE0(22.05) 1 FE203(0.15) 1 SI02(40.30) 

AL203(8.83) 1 MG0(4.90) 1 CA0(22.01), 

FE0(25.38) 1 FE203(0.36) 1 SI02(38.78) 

MEASUREMENT METHOC 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

1450.00 5.804 

LN,'N) 

3.021 

2. 2J..7 

1.547 

0.914 

0.368 

LOG(N) 

1.312 

0.963 

0.672 

0.397 

0.16 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1 15.70 

8.670 

5.309 

3.334 

2.094 

AUTHOR 

BILLS (1963) 

(X) 

(%) DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

20.51 

9.18 

4.699 

2.495 

1.445 

AMgCFFS-13 

AMgCFFS-14 

AMgCFFS-15 

Six-Component Systems 385 
SYSTEM 

AL203(5.05) ,MG0(7.09),CA0(22.90), 

FE0(27.07) ,FE203(0.22) ,SI02(37.67) 

AUTHOR 

BILLS (1963) 

(X) 

AL203(8.17) ,MG0(4.54) ,CA0(20.39) I 

FE0(30.87),FE203(0.56),SI02(35.92) (%) MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

2.689 

1.913 

1.193 

0.260 

LOG(N) 

1.168 

0.831 

0.518 

0.113 

386 Viscosity of Synthetic and Natural Melts and Glasses 

DERIVED FROM 

TABLE 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

14.72 

6.776 

3.296 

1.297 

AMgCFFS-16 
.....--.-. 

lU 

V') 

0 

Cl.. 

........... 

>- 1--

-

V') 

0 

u 

V') 

-

> 

0 

g 

4 

3 

2 

1 

Al20 3- MgO- CaO- FeO- Fe20 3 -Si02 

8/L LS (196J) 

AMgCFFS-1 

AMgCFFS-2 

AMgCFFS-4 

AMgCFFS-6 

AMgCFFS-8 

AMgCFFS-9 

AMgCFFS-12 

AMgCFFS-14 

0 --------~------~------~------~------~-------

1200 1300 1400 1500 

TEMPERATURE (°C) 

Six-Component Systems 387 
........... 

lU 

(./') 

-

0 

a.. 

........... 

>-

~ 

-(./') 

0 

u 

(./') 

-

> 

0 

0 

~ 

4 

3 

2 

1 

0 

4.5 

AI203-Mg0-Ca0- FeO- Fe203- Si02 

BILLS (1963) 

AMgCFFS-6 

AMgCFFS-9 / 

AMgCFFS-10 

AMgCFFS-13 

AMgCFFS-14 

AMgCFFS-15 AMgCFFS-16 

5.5 6.5 

10 000/T (KELVINS- 1

) 

AMgCFFS-1 

AMgCFFS-2 

AMgCFFS-3 

AMgCFFS-4 

AMgCFFS-6 

AMgCFFS-8 

AMgCFFS-9 

AMgCFFS-11 

AMgCFFS-12 

AMgCFFS-15 

AMgCFFS-14 

388 Viscosity of Synthetic and Natural Melts and Glasses 

7.5 
Seven-Component Systems 

Seven-Component Systems 389 
SYSTEM 

AL203(9.04),CA0(49.55),MG0(5.58), 

MN0(0.34) ,FE(0.11),S(2.09), 

SI02 (33. 30) (X) 

AL203(15.15) ,CA0(45.70),MG0(3.70), 

MN0(0.4),FE(0.1),S(1.1), 

SI02 (32. 9) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1500.00 5.640 

1538.00 5.522 

1574.00 5.414 

1615.00 5.297 

1668.00 5.152 

1690.00 5.094 

1738.00 4.973 

LN(N) 

0.916 

0.652 

0.405 

0.140 

-0.073 

-0.236 

-0.288 

LOG(N) 

0.398 

0.283 

0.176 

0.061 

-0.032 

-0.102 

-0.125 

390 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

HOFMAIER (1968) 

DERIVED FROM 

ABB. 13 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.5 

1.92 

1.5 

1.15 

0.93 

0.79 

0.75 

ACMgMnFSS-1 
SYSTEM 

(AL203 + FE203) (0. 38) , CAO (9. 61) , MGO (0. 23) , (NA20 + K20) (14. 8) , SI02 (74. 98) (X) 

(AL203 + FE203) (0.75),CA0(8.64), 

MGO (0 .15), (NA20 + K20) (17. 76), 

SI02 (7 2. 27) (%) 

MEASUREMENT METHOD 

CONCENTRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

685.00 10.438 

750.00 9.775 

780.00 9.497 

850.00 8.905 

905.00 8.489 

1000.00 7.855 

1080.00 7.391 

1230.00 6.653 

1320.00 6.277 

1465.00 5.754 

LN(N) 

17.269 

14.852 

13.816 

11.858 

10.707 

8.750 

7.599 

5.872 

5.181 

4.145 

LOG(N) 

7.50 

6.45 

6.00 

5.15 

4.65 

3.80 

3.30 

2.55 

2.25 

1.80 

AUTHOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N (APPROX.) 

3.16*10E7 

2.82*10E6 

1.00*10E6 

1.41*10E5 

4.47*10£4 

6309.57 

1995.26 

354.81 

177.83 

63.10 

AFCMgNKS-1 

Seven-Component Systems 391 
w 

1.0 

t.) 

< c;;· 

,., 

0 

~ "' 

a 

VI 

-< :I 

:r 

!l 

;::;· 

AI 

:I 

Q. 

z 

a:. 

!:; 

e:. 

~ ·w - ~ V) 

"' 0 AI 

:I 

Q. a_ 

C1 

~ 

"' >- "' 1'1> ~ "' 

V) 

0 

u 

V) 

> 

0 

0 

_J 

9 ~--~~~~--~--~--~--~--~--~--~--~--~--~--~--~--~~ 

7 

5 

3 

(AI203 + Fe203) (0.75) +CoO ( 8.64) + MgO (0.15) 

+ (Na20 + K20)(17.76) + Si02 {72.27) 

LILLIE (1929) 

AFCMgNKS-1 

1 --~~~--~--~--~------~--~--~~~~--~----------~----~ 

650 750 850 950 1050 1150 1250 1350 1450 

TEMPERATURE (°C} 
- r-- Lf) I 

~ Lf) V) 

0 

- 00 z 

0 

C> ~ ~ 

+ -r-..... 

UJ 

~ 

-N 

~ . ..() N 

00 r-..... 

- - ~ 0 N 

0 ~ 

0 (). 

u V') ....... 

...._ 

....... 

........... 

0 

Lf) 0 

0 " 0 

r--

+ + l..t.J 

U)~ ........ 

......., 

......., 

~" ........ 

......., 

Or-

----Mo 0 N N~ 

Q) 

u. + 

+ 0 

M N 

0 0 

..!:'Z 

<( - - + 

(3SIOd) AliSO)SI/\ 901 

Seven-Component Systems 393 

Minerals 

Minerals 395 
SYSTEM AUTHOR 

KUSHIRO (1976a) 

DERIVED FROM 

TABLE 2 

N aAISi2Q6.,(JADEITE) 

MEASUREMENT METHOD 

FALLING SPHERE VISCOMETRY 

N (POISES) 

T = 1350 C Z = 10000.0/T(K) (1/K) 

P (KBAR) LN (N) 

1. 11.127 

5. 10.571 

5. 10.434 

7.5 10.240 

10. 9.547 

15. 9. 071 

20.7 8.810 

24. 8.575 

SYSTEM 

LOG (N) 

4.833 

4.591 

4.531 

4.447 

4.146 

3.940 

3.826 

3.724 

QUARTZ (SI02) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T_ Z LN(N) 

1100.00 7.283 31.475 

1220.00 6.698 . 29.633 

1300.00 6.357 27.680 

1400.00 5.977 24.556 

1440.00 5.838 23.103 

SYSTEM 

WOLLASTONITE (CASI03) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N ~POISES) T DEGREES C) 

T z LN(N) 1550.00 5.485 1.004 

1600.00 5.339 0.875 

1650.00 5.200 0.867 

N 

6.8*10E4 

3.9*10E4 

3.4*10E4 

2.8*10E4 

1.4*10E4 

8.7*10E3 

6.7*10E3 

5.3*10E3 

AUTHOR 

BIRCH AND DANE ( 1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

LOG(N) 

13.669 

12.869 

12.021 

10.665 

10.033 

LOG(N) 

0.436 

0.380 

0.377 

Z = 10000.0/T(K) (1/K) 

N 

p = 

z = 

4.67*10E13 

7.40*10E12 

1.05*10E12 

4.62*10E10 

1.08*10E10 

AUTHOR 

BIRCH AND DANE 

DERIVED FROM 

TABLE 10-1 

1.0 ATM. 

(1942) 

10000.0/T(K) (1/K) 

N 

2.73 

2.40 

2.38 

396 Viscosity of Synthetic and Natural Melts and Glasses 

M-1 

M-2 

M-3 
10 ~--~------------~------------~ 

>-

1- 104 

(./') 

0 

u 

(./') 

> 

'""' ',~ ~\ 

\~ 

\ \ ' \ 

\\ 

\\ 

\ 

KUSHIRO 1976a 

JADEITE 

NaAI Si2 0 6 

1350°( 

e Piston Cylinder 

o Gas Media 

' ' ' ' 

10 ~--~--~----~--~----~--~--~ 

0 5 10 15 20 25 30 35 

PRESSURE {Kbar) 

Minerals 397 
SYSTEM 

DIOPSIDE (CA MG (SI03)2) 

MEASUREMENT METHOD 

(EROM LITERATURE) 

N (POISES) T (DEGREES C) . T Z LN(N) 1280.00 6.439 4.663 

1300.00 6.357 3.497 

1400.00 5.977 3.258 

1500.00 5.640 0.615 

1600.00 5.339 0.182 

SYSTEM 

ANORTHITE (CA AL2 SI2 08) 

MEASUREMENT METHOD 

(EROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1450.00 5.804 4.710 

1500.00 5.640 4.094 

,1600.00 5.339 3.219 

LOG(N) 

2.025 

1.519 

1.415 

0.267 

0.079 

LOG(N) 

2.045 

1.778 

1.398 

398 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

106. 

33. 

26. 

1.85 

1.2 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

111. 

60. 

25. 

M-4 

M-5a 
_....._ 

w 

V) 

0 

0... 

~ 

>-

~ 

-

V) 

0 

u 

V) 

-

> 

0 

0 

--1 

4 ~----~----~------~----~------~----~ 

3 

2 

1 

WOLLASTONITE 

BIRCH and DANE (1942) 

• • 

0 ~----~----~------~----~------~----~ 

1400 1500 1600 1700 

TEMPERATURE (°C) 

Minerals 399 
----- w 

(./') 

-

0 

a.. 

-...... 

>- 1-

(./') -

0 

u 

(./') 

-

> 

<-' 0 

__, 

4 ~----~------~----~------~------~----~ 

3 

2 

1 

WOLLASTONITE 

BIRCH and DANE /1942) 

0 ~----_.------~----~------~------~----~ 

4 5 . 6 7 

10 000/T (KELVINS- 1

) 

400 Viscosity of Synthetic and Natural Melts and Glasses 
...--.. 

UJ 

V') 

0 

a... 

---

>- ...,_ 

-

V') 

0 

u 

V') 

-

> 

0 

0 

--l 

4~----~----~------~----~----~----~ 

3 

2 

1 

ANORTHITE 

8/HCH and DANE (1942/ 

M-5 

0 ~----~----~------~----~----~----~ 

1400 1500 1600 1700 

TEMPERATURE (°C) 

Minerals 401 
----- UJ 

V') 

-

0 

a.. 

___. 

>-

t-

-

V') 

0 

u 

V') 

-

> 

0 

0 

--' 

4 ~--------------------~----~~----~------~ 

3 

2 

1 

ANORTHITE 

BIRCH and DANE (1942} 

M-5 

0 ~----~------~------~----~~----~------~ 

4 5 6 7 

10 000/T (KELVINS- 1

) 

402 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

K2 SI03 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

875.00 8.711 3.795 

906.00 8.482 3.619 

LOG(N) 

1.648 

1.572 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

44.5 

37.3 

M-6 

---------------------------------------------------.---------------------------

SYSTEM 

ORTHOCLASE (K AL SI3 08) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

. T Z LN (N) 1250.00 6.566 20.723 

1400.00 5.977 16.118 

1450.00 5.804 15.202 

SYSTEM 

ALBITE (NA AL SI3 08) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

LOG(N) 

9.000 

7.000 

6.602 

LOG(N) 

1150.00 

1400.00 

7.027 20.723 9.000 

5.977 10.597 4.602 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.0*10E9 

1.0*10E7 

4.0*10E6 

AUTHOR 

BIRCH AND DANE ( 19 4 2 ) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.0*10E9 

4.0*10E4 

M-7 

M-8 

Minerals 403 
UJ 

~ 

:J 

(./") 

(./") 

w 

~ 

a... 10 

1 2 

Ca251.5 

1630°( 

M-5b 

KUSHIRO ( 1981) 

L n "f'J 

3 4 

~ 

~ 

ee 

' I 

Ca254 e 

16sooc I 

5 6 

e 

I 

Co2 56 

1650°( 

7 

15~--~--~--~----~--~--~--~ 

1 2 3 4 5 6 

VISCOSITY, Ln ("f'J) 

404 Viscosity of Synthetic and Natural Melts and Glasses 
,........_ 

Q) 

Cl) 

·-0 

c. 

>-

!::::: 1 03 

V') 

0 

u 

(/) 

-

> 

Kushiro (1976a) 

10 ~--~--~--~--~--~--

0 5 10 15 20 25 

PRESSURE (Kbar) 

Minerals 405 

Two-Component Mineral Systems 

Two-Component Mineral Systems 407 
SYSTEM 

DIOPSIDE (100. 0) , ALBITE (0. 0) (X) 

DIOPSIDE(100.0) ,ALBITE(O.O) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1391.00 6.010 

1400.00 5.977 

1415.00 5.924 

1425.00 5.889 

LN(N) 

4.421 

4.382 

4.298 

4.224 

LOG(N) 

1.92 

1.903 

1.867 

1.834 

SYSTEM 

DIOPSIDE(82.88),ALBITE(17.11) (X) 

DIOPSIDE (80. 0) , ALBITE (20. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1354.00 6.146 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

4.628 

4.534 

4.449 

4.358 

LOG (N) 

2.01 

1.969 

1.932 

1.893 

DIOPSIDE (64. 50) , ALBITE ( 35. 50) (X) 

DIOPSIDE (60. 0) ,ALBITE (40. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1275.00 6.460 

1300.00 6.357 

1310.00 6.317 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

LN(N) 

6.509 

6.070 

5.651 

5.411 

5.296 

5.079 

4.868 

4.684 

4.513 

LOG(N) 

2.827 

2.636 

2.454 

2.350 

2.300 

2.206 

2.114 

2.034 

1.960 

408 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

83.2 

80.0 

73.6 

68.3 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

102.3 

93.2 

85.5 

78.1 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

671. 

433. 

284. 

224. 

200. 

161. 

130. 

108. 

91.2 

DA-1 

DA- 2 

DA-3 
SYSTEM 

DIOPSIDE (44. 67) ,ALBITE (55. 33) (X) 

DIOPSIDE (40. 0) ,ALBITE (60. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1225.00 6.676 

1250.00 6.566 

1260.00 6.523 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

9.178 

8.581 

8.100 

7.898 

7.785 

7.404 

6.966 

6.621 

6.370 

6.093 

5.743 

LOG(N) 

3.986 

3.727 

3.518 

3.430 

3.381 

3.215 

3.025 

2.876 

2.767 

2.646 

2.494 

DIOPSIDE ~23. 24) ,ALBITE (76. 76) (X) 

DIOPSIDE 20.0) ,ALBITE(80.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T z LN(N) LOG(N) 

1150.00 7.027 12.653 5.495 

1175.00 6.906 12.177 5. 288 

1185.00 6.859 11.973 5.200 

1200.00 6.789 11.670 5.068 

1225.00 6.676 11.159 4.846 

1250.00 6.566 10.652 4.626 

1275.00 6.460 10.192 4.426 

1300.00 6.357 9.921 4.309 

1325.00 6.258 9.393 4. 079 

1350.00 6.161 9.092 3.949 

1375.00 6.068 8.725 3.789 

1400.00 5.977 8.376 3.638 

1425.00 5.889 8.063 3.502 

SYSTEM 

DIOPSIDE (0. 0) ,ALBITE (100. 0) (X) 

DIOPSIDE(O.O),ALBITE(100.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1100.00 7.283 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

LN(N) 

17.338 

13.908 

13.479 

12.982 

12.555 

12.087 

11.645 

LOG(N) 

7.530 

6.040 

5.854 

5.638 

5.453 

5.249 

5.057 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE !,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

p 

z 

N 

9680. 

5330. 

3300. 

2690. 

2400. 

1640. 

1060. 

751. 

584. 

443. 

312. 

AUTHOR 

KOZU AND KANI 

DERIVED FROM 

TABLE !,II 

= 1.0 ATM. 

(1934) 

= 10000.0/T(K) (1/K) 

N 

3.13*10E5 

1.94*10E5 

1.58*10E5 

1.17*10E5 

7.02*10E4 

4.23*10E4 

2.67*10E4 

2.04*10E4 

1.20*10E4 

8890. 

6150. 

4340. 

3180. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE !,II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3.39*10E7 

1.10*10E6 

7.14*10E5 

4.35*10E5 

2.83*10E5 

1.78*10E5 

1.14*10E5 

DA-4 

DA-5 

DA-6 

Two-Component Mineral Systems 409 
-

UJ 

V> 

-

0 

CL 

-

>- ..,._ 

V> 

0 

u 

V> 

-

> 

() 

0 

__J 

6 

4 

2 

DA-6 

DA-5 

DIOPSIDE- ALBITE 

KOZU and KANt /1934) 

0 ~----~-----L----~------~----~----~----~----~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 

41 0 Viscosity of Synthetic and Natural Melts and Glasses 
__...._, 

lU 

V) 

0 

a.. 

-....... 

>-

t-

-

V) 

0 

u 

V) 

-

> 

~ 

0 

--1 

8 ~----~------~--------------------~----~ 

6 

4 

2 

0 

5 

DIOPSIDE- ALBITE 

KOZU and KANI ( 1934) 

DA-2 

"'DA-1 

6 7 

DA-6 

DA-5 

8 

10 000/T (KELVINS- 1

) 

Two-Component Mineral Systems 411 
SYSTEM 

ALBITE (100. 0) ,ANORTHITE (0. 0) (X) 

ALBITE(100.0),ANORTHITE(O.O) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1100.00 7.283 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

17.338 

13.908 

13.479 

12.982 

12.555 

12.087 

11.645 

LOG(N) 

7.530 

6.040 

5.854 

5.638 

5.453 

5.249 

5.057 

ALBITE (80. 93) , ANORTHITE (19. 07) (X) 

ALBITE (80. 0) ,ANORTHITE (20. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1330.00 6.238 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N} 

13.963 

13.253 

12.685 

12.120 

11.996 

11.650 

11.110 

10.676 

10.222 

LOG(N) 

6.064 

5.756 

5.509 

5.264 

5.210 

5.060 

4.825 

4.637 

4.439 

ALBITE (61. 41) , ANORTHITE ( 38. 59) (X) 

ALBITE (60. 0) I ANORTHITE (40. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T z LN(N) LOG(N) 1325.00 6.258 10.306 4.476 

1350.00 6.161 9.854 4. 280 

1375.00 6.068 9.387 4.077 

1400.00 5.977 8.961 3.892 

1415.00 5.924 8.700 3.778 

1425.00 5.889 8.532 3.706 

412 Viscosity of Synthetic and Natural Melts and (;lasses 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

3.39*10E7 

1.10*10E6 

7.14*10E5 

4.35*10E5 

2.83*10E5 

1.78*10E5 

1.14*10E5 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

p = z = 

1.16*10E6 

5.70*10E5 

3.23*10E5 

1.84*10E5 

1.62*10E5 

1.15*10E5 

6.68*10E4 

4.33*10E4 

2.75*10E4 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

1.0 ATM. 

10000.0/T(K) (1/K) 

N 

2.99*10E4 

1.90*10E4 

1.19*10E4 

7.79*10E3 

6.00*10E3 

5.08*10E3 

AI-An-1 

AI-An-2 

AI-An-3 
SYSTEM 

ALBITE ( 41. 42) , ANORTIIITE (58. 58) (X) 

ALBITE (40. 0) ,ANORTIIITE (60. 0) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1425.00 5.889 

1450.00 5.804 

1470.00 5.737 

1480.00 5.705 

1500.00 5.640 

SYSTEM 

LN(N) 

7.373 

6.913 

6.585 

6.474 

6.127 

LOG(N) 

3.202 

3.002 

2.860 

2.812 

2.661 

ALBITE (20. 96) , ANORTIIITE (79. 03) (X) 

ALBITE (20. 0) ,ANORTIIITE (80. 0) (%) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1475.00 5.721 

1500.00 5.640 

1515.00 5.593 

1525.00 5.562 

1550.00 5.485 

SYSTEM 

LN(N) 

5.466 

5.225 

5.112 

5.051 

4.884 

LOG(N) 

2.374 

2.269 

2.220 

2.194 

2.121 

ALBITE (0. 0) ,ANORTIIITE (100. 0) (X) 

ALBITE(O.O) ,ANORTHITE(100.0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1555.00 5.470 

1565.00 5.441 

1575.00 5.411 

LN(N) 

4.720 

4.672 

4.578 

4.476 

LOG (N) 

2.05 

2.029 

1.988 

1.944 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

1590. 

1010. 

724. 

648. 

458. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

236. 

186. 

166. 

156. 

132. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1. 0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

112. 

107. 

97.3 

87.9 

AI-An-4 

AI-An-5 

AI-An-6 

Two-Component Mineral Systems 41 3 
~ ~ 

< <ii' 

I"') 

0 

~. 

-< 

a 

IJ'l 

-< 

= :r 

~ ;::;· 

Ql 

= c.. 

z _........, e:. UJ 5; (./') e!. 

~ - ~ 0 "' Ql o_ 

= c.. 

C'l - ~ >-

"' tl) 1-- "' (./') 

0 

u 

(./') 

-

> 

~ 

0 

__J 

8 

I~ 

I 

6 

L 

I 

4 

I 

2 

0 

1100 

~ 

1200 

ALBITE -ANORTHITE 

KOZU and KANI ( 1934} 

--....... '""eAL-AN-1 

.........._ ---eAL-AN-2 

-.._AL-AN-3 

AL-AN-4~ 

AL-AN-5~ 

Al-AN-6/ 

1300 1400 1500 1600 

TEMPERATURE (°C) 
8 ~----~------~------~------~------~----~ 

>- I6 

V') 4 

0 

u 

V') 

> 

0 

0 

__. 

2 

0 

5 

ALBITE -ANORTHITE 

KOZU and KANI ( 19.14) 

/AL-AN-4 

/.AL-AN-5 

AL-AN-6 

6 7 

AL-AN-1 

8 

10 000/T (KELVINS- 1

) 

Two-Component Mineral Systems 415 
SYSTEM 

ANORTHITE (100. 0) , DIOPSIDE (0. 0) (X) 

ANORTHITE(100.0),DIOPSIDE(O.O) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1550.00 5.485 

1555.00 5.470 

1565.00 5.441 

1575.00 5.411 

SYSTEM 

LN(N) 

4.720 

4.672 

4.578 

4.476 

LOG(N) 

2.05 

2.029 

1.988 

1.944 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

112. 

107. 

97.3 

87.9 

AUTHOR 

ANORTHITE (75. 69) , DIOPSIDE (24. 31) (X) KOZU AND KANI (1934) 

ANORTHITE (80. 0) , DIOPSIDE (20. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1425.00 5.889 

1450.00 5.804 

1475.00 5.721 

1480.00 5.705 

1500.00 5.640 

1525.00 5.562 

SYSTEM 

LN(N) 

5.132 

4.966 

4.800 

4.789 

4.689 

4.584 

LOG(N) 

2.229 

2.157 

2.085 

2.080 

2.037 

1.991 

Z = 10000.0/T(K) (1/K) 

N 

169. 

143. 

122. 

120. 

109. 

97.9 

AUTHOR 

ANORTHITE (53. 87) , DIOPSIDE (46 .13) (X) KOZU AND KANI (1934) 

ANORTHITE (60. 0) , DIOPSIDE ( 40. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1390.00 6.013 

1400.00 5.977 

1425.00 5.889 

LN(N) 

9.781 

8.679 

7.829 

5.745 

4.902 

4.674 

4.645 

4.555 

LOG(N) 

4.248 

3.769 

3.400 

2.495 

2.129 

2.030 

2.018 

1.978 

416 Viscosity of Synthetic and Natural Melts and Glasses 

Z = 10000. 0/T (K) (1/K) 

N 

17700. 

5880. 

2510. 

313. 

134. 

107. 

104. 

95.1 

An-Di-1 

An-Di- 2 

An-Di-3 
SYSTEM AUTHOR 

ANORTHITE (34.16) ,DIOPSIDE (65.84) (X) KOZU AND KANI (1934) 

ANORTHITE ( 40. 0) , DIOPSIDE (60. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1250.00 6.566 

1275.00 6.460 

1278.00 6.447 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

6.011 

5.153 

5.020 

4.999 

4.817 

4.724 

4.608 

4.509 

4.403 

LOG(N) 

2.611 

2.238 

2.180 

2.171 

2.092 

2.052 

2.001 

1.958 

1.912 

Z = 10000. 0/T (K) (1/K) 

N 

408. 

173. 

151. 

148. 

124. 

113. 

100. 

90.8 

81.7 

AUTHOR 

ANORTHITE (16. 29) , DIOPSIDE (83. 71) (X) KOZU AND KANI (1934) 

ANORTHITE (20. 0) , DIOPSIDE (80. 0) (%) 

MEASUREMENT METHOD DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

4.628 

4.512 

4.413 

4.306 

LOG(N) 

2.010 

1.960 

1.917 

1.870 

ANORTHITE (0. 0) , DIOPSIDE (100. 0) (X) 

ANORTHITE(O.O),DIOPSIDE(100.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1391.00 6.010 

1400.00 5.977 

1415.00 5.924 

1425.00 5.889 

LN(N) 

4.421 

4.382 

4.298 

4.224 

LOG(N) 

1.92 

1.903 

1.867 

1.834 

Z = 10000.0/T(K) (1/K) 

N 

102. 

91.1 

82.5 

74.1 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

83.2 

80.0 

73.6 

68.3 

An-Di-4 

An-Di-5 

An-Di-6 

Two-Component Mineral Systems 417 
ANORTHITE- DIOPSIDE 

KOZU and KANI (1934) 

4 

-

UJ 

V) 

0 

CL 

._. 

~ 

V) 3 0 

u 

V) 

-

> 

C) 

0 

_...J 

AN-DI-1 

2 

AN-DI-5 ' 

1 ~----~----~----~----~~----~----~----~----~ 

1200 1300 1400 1500 1600 

TEMPERATURE (°C') 

418 Viscosity of Synthetic and Natural Melts and Glasses 
5 ~----~------~----~------~------~----~ 

..--.. 

UJ 

ll') 

0 

a.. 

-

>- 1--

4 

ll') 3 

0 

u 

ll') 

> 

l? 

0 

___. 

2 

1 

4.5 

ANORTHITE- DIOPSIDE 

KOZU and KANI (1934) 

\ ~AN-DI-5 

AN-DI-6 

5.5 6.5 

10 000/T (KELVINS- 1

) 

AN-DI-4 

Z5 

Two-Component Mineral Systems 419 
SYSTEM 

ORTHOCLASE (100. 0) , ALBITE (0. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1400.00 5.977 18.421 8.00 

1450.00 5.804 15.202 6.602 

SYSTEM 

ORTHOCLASE (80. 0) , ALBITE (20. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1400.00 5.977 14.346 6.230 

1450.00 5.804 13.459 5.845 

SYSTEM 

ORTHOCLASE (60. 0) ,ALBITE (40. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1350.00 6.161 14.509 6.301 

1400.00 5.977 13.541 5.881 

1450.00 5.804 12.676 5.505 

SYSTEM 

ORTHOCLASE (40. 0) ,ALBITE (60. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1350.00 6.161 14.221 6.176 

1400.00 5.977 13.369 5.806 

1450.00 5.804 12.429 5.398 

420 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

BIRCH AND DANE ( 19 4 2) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.0*10E8 

4.0*10E6 

AUTHOR 

BIRCH AND DANE ( 1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.7*10E6 

7.0*10E5 

AUTHOR 

BIRCH AND DANE ( 1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2.0*10E6 

7.6*10E5 

3.2*10E5 

AUTHOR 

BIRCH AND DANE ( 1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.5*10E6 

6.4*10E5 

2.5*10E5 

Or-Ab-1 

Or-Ab-2 

Or-Ab-3 

Or-Ab-4 
SYSTEM 

ORTHOCLASE (20. 0) I ALBITE (80. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN (N) LOG (N) 1350.00 6.161 16.118 7.000 

1400.00 5.977 13.017 5.653 

1450.00 5.804 12.101 5.255 

SYSTEM 

ORTHOCLASE (0. 0) I ALBITE (100. 0) (%) 

MEASUREMENT METHOD 

(FROM LITERATURE) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1300.00 6.357 13.911 6.041 

1350.00 6.161 12.972 5.633 

1400.00 5.977 12.101 5.255 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.0*10E7 

4.5*10£5 

1.8*10E5 

AUTHOR 

BIRCH AND DANE (1942) 

DERIVED FROM 

TABLE 10-1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1.1*10E6 

4.3*10E5 

1.8*10E5 

Or-Ab-5 

Or-Ab-6 

Two-Component Mineral Systems 421 
SYSTEM 

DIOPSIDE-ANORTHITE 

DIOPSIDE(100) ANORTHITE(O) (WT.%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z 

1375. 6.067 

1400. 5.977 

1450. 5.803 

1500. 5.640 

1550. 5.485 

1600. 5.339 

SYSTEM 

DIOPSIDE-ANORTHITE 

LN(N) 

2.50 

2.28 

1.89 

1.56 

1.28 

1.07 

DIOPSIDE(90) ANORTHITE(10) (WT.%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN{ N) 

1300. 6.357 3.54 

1350. 6.161 3.05 

1400. 5.977 2.59 

1450. 5.803 2.20 

1500. 5.640 1.84 

1550. 5.485 1.49 

422 Viscosity of Synthetic and Natural Melts and Glasses 

LOG(N) 

1.086 

0.992 

0.821 

0.678 

0.559 

0.465 

LOG(N) 

1.539 

1.327 

1.12R 

0.957 

0.800 

0.648 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-1 

12. 

9. 

6. 

4. 

3. 

2. 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T{K) {1/0EG. K) 

N o·i-An-2 

34. 

21. 

13. 

9. 

6. 

4. 
SYSTElvi AUTHOR 

DIOPSIDE-ANORTHITE SCARFE et al. (1983) 

DIOPSIDE (80) ANORTHITE (20) (WT. %) 

IVIEASUREMENT METHOD 

ROTATIONAL VISCOJ.\IIETER 

N (POISES) p = 

DERIVED FROM 

TABLE 1 

1. 0 ATM. 

T (DEGREES C) Z =10000.0/T(K) (1/DEG K) 

T z LN(N) LOG(N) N Di-An-3 

1250.00 6.565 4.39 1.909 81 . 

1300.00 6.357 3.82 1.660 46. 

1350.00 6.161 3.32 1.442 28. 

1400.00 5.977 2.84 1.237 17 . 

1450.00 5.803 2.43 1.057 1 1 . 

1500.00 5.640 2.06 0.898 8 . 

1550. 00 5.485 1.74 0.759 6 . 

1600.00 5.339 1.46 0.636 4. 

-----------------------------------------------------------------------

SYSTEM AUTHOR 

DIOPSIDE-ANORTHITE SCARFE et al. (1983) 

DIOPSIDE (58) ANORTHITE (42) (WT. %) 

1VIEASUREMENT l'v1ETHOD DERIVED FROM 

ROTATIONAL VISCONffiTER TABLE 1 

N (POISES) P = 1.0 ATM. 

T (DEGREES C) Z =10000.0/T(K) (1/DEG K) 

T z LN(N) LOG(N) N Di-An-4 

1175.00 6.906 6.58 2.859 722. 

1225.00 6.675 5.68 2.468 294. 

1275.00 6.459 4.91 2.134 136. 

1350.00 6.161 3.96 1.721 53 . 

1400.00 5.977 3.49 1.518 33. 

1450.00 5.803 3.06 1.329 21 . 

1500. 00 5.640 2.63 1. 146 14. 

1550.00 5.485 2.27 0.990 10. 

1600.00 5.339 1.95 0.851 7 . 

Two-Component Mineral Systems 423 
SYSTEM 

DIOPSIDE-ANORTHITE 

DIOPSIDE(50) ANORTHITE(50) (WT.%) 

MEASURE ~NT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) 

1200. 6.788 6.55 

1250. 6.565 5.65 

1300. 6.357 4.90 

1325. 6.257 4.57 

1350. 6.161 4.26 

1400. 5.977 3.75 

1450. 5.803 3.29 

1500. 5.640 2.85 

1550. 5.485 2.47 

1600. 5.339 2.20 

SYSTEM 

OIOPSIDE-ANORTHITE 

DIOPSIDE(40) ANORTHITE(60) (WT.%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) 

1350. 6.161 4.63 

1375. 6.067 4.33 

1400. 5.977 4.04 

1450. 5.803 3.57 

1500. 5.640 3.15 

1550. 5.485 2.74 

1600. 5.339 2.36 

424 Viscosity of Synthetic and Natural Melts and Glasses 

LOG(N) 

2.846 

2.457 

2.132 

1.989 

1.854 

1.630 

1.432 

1.240 

1.074 

0.956 

LOG(N) 

2.015 

1.883 

1.756 

1.553 

1.370 

1.194 

1.029 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-5 

701. 

286. 

135. 

97. 

71. 

43. 

27. 

17. 

12. 

9. 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-6 

104. 

76. 

57. 

36. 

23. 

16. 

11. 
SYSTEM 

DIOPSIDE-ANORTHITE 

DIOPSIDE(30) ANORTHITE(70) (WT.%) 

MEASUREMENT ~THOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z 

1300. 6.357 

1350. 6.161 

1400. 5.977 

1425. 5.889 

1450. 5.803 

1500. 5.640 

1550. 5.485 

1600. 5.339 

SYSTEM 

DIOPSIDE-ANORTHITE 

LN(N) 

5.929 

5.199 

4.559 

4.255 

3.983 

3.525 

3.126 

2.714 

DIOPSIDE(20) ANORTHITE(80) (WT.%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) 

1250. 6.565 7.23 

1300. 6.357 6.28 

1350. 6.161 5.48 

1400. 5. 977, 4.83 

1450. 5.803 4.22 

1475. 5.720 4.00 

1500. 5.640 3.74 

1525. 5.561 3.50 

1550. 5.485 3.30 

1600. 5.339 2.88 

LOG(N) 

2.575 

2.258 

1.980 

1.848 

1.730 

1.531 

1.358 

1.179 

LOG(N) 

3.140 

2.730 

2.384 

2.098 

1.836 

1.738 

1.625 

1.522 

1.434 

1.252 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-7 

376. 

181. 

95. 

70. 

54. 

34. 

23. 

15. 

AUTHOR 

SCARFE et al. (1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-8 

1380. 

537. 

242. 

125. 

69. 

55. 

42. 

33. 

27. 

18. 

Two-Component Mineral Systems 425 
SYSTEM 

DIOPSIDE-ANORTHITE 

DIOPSIDE(O) ANORTHITE(100) (WT.%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T z LN(N) 

1375. 6.067 5.910 

1400. 5.977 5.530 

1425. 5.889 5.171 

1450. 5.803 4.837 

1475. 5.720 4.531 

1500. 5.640 4.239 

1525. 5.561 3.939 

1550. 5.485 3.741 

1575. 5.411 3.483 

1600. 5.339 3.29Q 

1625. 5.268 3.069 

426 Viscosity of Synthetic and Natural Melts and Glasses 

LOG(N) 

2.567 

2.402 

2.246 

2.101 

1.968 

1.841 

1.711 

1.625 

1.513 

1.433 

1.333 

AUTHOR 

SCAR FE et a 1 • ( 1983) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/DEG. K) 

N Di-An-9 

369. 

252. 

176. 

126. 

93. 

69. 

51. 

42. 

33. 

27. 

22. 
5 

10 

M 

0 

N 

-

<( 

~ 15 

UJ 

__. 

0 

~ 

20 

25 

DIOPSIDE 

+ 

30o.o 1.0 2.0 3.0 

VISCOSITY, LOG (7]) (poise) 

Two-Component Mineral Systems 427 
u 

0 

UJ 

0! 

:::> 

Di58 

1200 

Di20 

1300 

~ 1400 ~ 

UJ 

a.. 

~ UJ 

1-

1500 

1600 

DIOPSIDE 

+ 

ANORTHITE 

SYSTEM 

1700~--~~~--~--~--~--~--~~ 

0.0 1.0 2.0 3.0 4.0 

VISCOSITY, LOG (7]) (poise) 

428 Viscosity of Synthetic and Natural Melts and Glasses 
Three-Component Mineral Systems 

Three-Component Mineral Systems 429 
SYSTEM 

DIOPSIDE(65.15) ,ALBITE(17.93), 

ANORTHITE(16.90) (X) 

DIOPSIDE(60.0) ,ALBITE(20.0), 

ANORTHITE(20.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1225.00 6.676 

1250.00 6.566 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

6.258 

5.880 

5.499 

5.131 

4.931 

4.790 

4.676 

4.579 

4.479 

LOG(N) 

2.718 

2.554 

2.388 

2.228 

2.141 

2.080 

2.031 

1.989 

1.945 

DIOPSIDE(45.15) ,ALBITE(37.28), 

ANORTHITE(17.57) (X) 

DIOPSIDE(40.0) ,ALBITE(40.0), 

ANORTHITE (20. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1175.00 6.906 

1200.00 6.789 

1225.00 6.676 

1250.00 6.566 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

8.999 

8.418 

7.974 

7.481 

7.152 

6.722 

6.376 

6.032 

5.726 

5.446 

5.162 

LOG (N) 

3.908 

3.656 

3.463 

3.106 

3.106 

2.919 

2.769 

2.620 

2.487 

2.365 

2.242 

DIOPSIDE(45.63) ,ALBITE(18.84), 

ANORTHITE(35.52) (X) 

DIOPSIDE(40.0),ALBITE(20.0), 

ANORTHITE(40.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1250.00 6.566 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

LN(N) 

7.476 

6.582 

6.145 

5.768 

5.387 

5.163 

4.884 

4.738 

LOG(N) 

3.247 

2.859 

2.669 

2.505 

2.340 

2.242 

2.121 

2.058 

430 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

522. 

358. 

245. 

169. 

138. 

120. 

107. 

97.4 

88.2 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

8100. 

4530. 

2900. 

1770. 

1276. 

830. 

587. 

417. 

307. 

232. 

174. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1770. 

722. 

466. 

320. 

219. 

175. 

132. 

114. 

Di-AI-An-1 

Di-AI-An-2 

Di-AI-An-3 
SYSTEM 

DIOPSIDE(23.50) ,ALBITE(58.22), 

ANORTHITE(18.29) (X) 

DIOPSIDE(20.0) ,ALBITE(60.0), 

ANORTHITE (20. 0) (%) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1175.00 6.906 11.661 5.064 

1200.00 6.789 11.121 4.830 

1225.00 6.676 10.486 4.554 

1250.00 6.566 9.844 4.275 

1275.00 6.460 9.381 4.074 

1300.00 6.357 8.926 3.876 

1325.00 

1350.00 

1375.00 

1400.00 

1425.00 

SYSTEM 

6.258 

6.161 

6.068 

5.977 

5.889 

8.494 

8.086 

7.709 

7.326 

7.103 

3.689 

3.512 

3.348 

3.182 

3.085 

DIOPSIDE(23.76) ,ALBITE(39.23), 

ANORTHITE(37.00) (X) 

DIOPSIDE(20.0) ,ALBITE(40.0), 

ANORTHITE(40.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1275.00 6.460 

1300.00 6.357 

1325.00 6.258 

1350.00 6.161 

1375.00 6.068 

1400.00 5.977 

1425.00 5.889 

SYSTEM 

LN(N) 

9.449 

8.228 

7.593 

7.199 

6.773 

6.433 

5.996 

LOG(N) 

4.104 

3.573 

3.298 

3.126 

2.941 

2.794 

2.604 

DIOPSIDE(24.03) ,ALBITE(19.85), 

ANORTHITE(56.13) (X) 

DIOPSIDE(20.0) ,ALBITE(20.0), 

ANORTHITE(60.0) (%) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1375.00 6.068 

1400.00 5.977 

1415.00 5.889 

1430.00 5.872 

1450.00 5.804 

1465.00 5.754 

LN(N) 

6.221 

5.879 

5.662 

5.439 

5.263 

5.068 

LOG(N) 

2.702 

2.553 

2.459 

2.362 

2.286 

2.201 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.16*10E5 

6.76*10E4 

3.58*10E4 

1.88*10E4 

1.19*10E4 

7520. 

4880. 

3250. 

2230. 

1520. 

1220. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.27*10E4 

3740. 

1980. 

1340. 

874. 

622. 

402. 

AUTHOR 

KOZU AND KANI (1934) 

DERIVED FROM 

TABLE I,II 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

503. 

358. 

288. 

230. 

193. 

159. 

Di-AI-An-4 

Di-AI-An-5 

Di-AI-An-6 

Three-Component Mineral Systems 431 
4.5 

-

LU 

c./) 

0 

CL 01-Al-AN-2 

-

>-

...... 

0 3.5 

u 

c./) 

-· > 

0 

9 

2.5 

01-Al-AN-1 

DIOPSIDE -ALBITE- ANORTHITE 

KOZU and KANI /1934) 

1.5 L...-..----L...-..-----1~-.. _ ____. __ ----l. __ --J,. __ ~ __ __._ __ ___. 

1100 1200 1300 

TEMPERATURE (°C) 

432 Viscosity of Synthetic and Natural Melts and Glasses 

1400 1500 
...--.. 

UJ 

V') 

0 

a.. 

-

>- r-

-

5.5 r-----.----......-------.-----.----..-------, 

DIOPSIDE -ALBITE -ANORTHITE 

KOZU and KANt (1934) 

4.5 

DI-AL-AN-2 

0 3.5 

u 

V') 

> 

l') 

0 

~ 

2.5 

DI-Al-AN-6 

DI-AL-AN-3 

1.5 ..__ __ ---~. ___ __,__ ___ ...~....-__ ___,~i.--__ ___._ ___ _, 

5 6 ' 7 8 

10 000/T (KELVINS- 1

) 

Three-Component Mineral Systems 433 

Basalts 

Basalts 435 
SYSTEM 

OLIVINE BASALT 

(VOGELSBURG, GERMANY) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1175. 6.906 

1215. 6.720 

1253. 6.553 

1292. 6. 390 

1330. 6.238 

SYSTEM 

OLIVINE BASALT 

LN(N) 

7.224 

5.704 

4.700 

3.496 

2.398 

(AYRESHIRE, SCOTLAND) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1138. 7.087 

1180. 6.882 

1220. 6.698 

1260. 6. 523 

1300. 6. 357 

1338. 6. 207 

1378. 6. 057 

1418. 5.914 

LN(N) 

6.507 

5.799 

5.273 

4.663 

4.127 

3.584. 

2.890 

2.303 

LOG(N) 

3.146 

2.477 

2.041 

1.519 

1.041 

LOG(N) 

2.826 

2.519 

2.290 

2.025 

1.792 

1.556 

1.255 

1.000 

436 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1400. 

300. 

110. 

33. 

11. 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

670. 

330. 

195. 

106. 

62. 

36. 

18. 

10. 

B-1 

B-2 
---.. 

>- ~ 

~ c ~ c __. ...... 

E '-

<( ~ 

V') Q) ~ 

co 

<((_I) ~ 

~ ... 

w C) 

~ ~ z ::l - ...Q "'b >...!! ~ .....J Q) 

0 C) 

~ ~ ~ - ~ 

-I 

co 

0 

ll) 

~ r--

0 

ll) 

M 

r--

0 

ll) 

N 

r--

0 

ll) 

r--

r--

0 

_........ 

u 

0 

........... 

w 

~ 

:::> 

~ ~ 

w 

Q.. 

~ w 

.,_ 

~----~----~----~----~----~----~----~--~ll) o52 r-

(3SIOd) A!ISO)SIA 901 

Basalts 437 
,.._ 

.UJ 

(./') 

0 

a_ 

...........-

>-

t-

-

V) 

0 

u 

(./') 

-

> 

0 

0 

__. 

4 ~----~--------------~----~~----~------~ 

3 

2 

1 

OLIVINE BASALT 

(Vogelsburg, Germany) 

EULER and WINKLER (19.57) 

B-1 

0 ~----~------~------~----~~----~------~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

438 Viscosity of Synthetic and Natural Melts and Glasses 
= Slol 

~ "' 

""' l.o.l 

~ 

.....--

LU 

(./') 

0 

Cl.. 

__... 

>-

t-

-(./") 

0 

u 

(./') 

-

> 

() 

0 

__. 

4 

I I I ' I I 

OLIVINE BASALT 

(Ayreshire, Scotland) 

EULER and WINKLER (1957) 

I 

3 

I B-2 

2 

1 

o~--~--~--~----~--~------------~--~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
__........ 

UJ 

V') 

-

0 

a.. 

___.. 

>- I-

-

V') 

0 

u 

V') 

-

> 

0 

0 

_, 

4~----~--------------~----~------~----~ 

3 

2 

1 

0 

5 

OLIVINE BASALT 

(Ayreshire, Scotland) 

EULER and WINKLER (1957/ 

6 7 

10 000/T (KELVINS- 1

) 

B-2 

8 

440 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

BASALT (SCHONEN, SWEDEN) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T z LN(N) 

1110. 7.231 7.409 

1150. 7.027 6.620 

1190. 6.835 6.174 

1230. 6.653 5.784 

1264. 6.506 5.394 

1305. 6.337 4.852 

1342. 6.192 4.394 

1383. 6.039 3.850 

1421. 5.903 3.401 

1468. 5.744 2.996 

SYSTEM 

OLIVINE-ANDESITE BASALT 

(GOTTENBURG, GERMANY) 

SAMPLE N0.1 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1225. 6.675 

1262. 6.515 

1300. 6.357 

1340. 6.200 

1380. 6. 050 

1418. 5.914 

1462. 5.764 

LN(N) 

5.858 

5.459 

5.011 

4.585 

4.127 

3.496 

2.996 

SYSTEM 

OLIVINE-ANDESITE BASALT 

(GOTTENBURG, GERMANY) 

SAMPLE N0.2 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1090. 7. 337 

1110. 7. 231 

1130. 7.128 

1150. 7.027 

1190. 6.835 

LN(N) 

7.601 

7.313 

6.908 

6.579 

6.194 

LOG(N) 

3.217 

2.875 

2.681 

2.512 

2.342 

2.107 

1.908 

1.672 

1.477 

1.301 

LOG(N) 

2.544 

2.371 

2.176 

1.991 

1.792 

1.519 

1.301 

LOG(N) 

3.301 

3.176 

3.000 

2.857 

2.690 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

p = 1.0 ATM. 

z = 10000. 0/T (K) (1/K) 

N 

1650. 

750. 

480. 

325. 

220. 

128. 

81. 

47. 

30. 

20. 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

350. 

235. 

150. 

98. 

62. 

33. 

20. 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2000. 

1500. 

1000. 

720. 

490. 

B-3 

B-4 

B-5 

Basalts 441 
(""') 

I 

co 

(3SIOd) AliSOJSI/\ 901 

442 Viscosity of Synthetic and Natural Melts and Glasses 

0 

1.1') 

M ----- ,..... u 

0 

1.1') 

o2 

0 
~ 

w 

ll) 

0 

a.. 

-

>-

...... 

-

ll) 

0 

u 

ll) 

-

> 

~ 

0 

_J 

4~------------------~------~----~----~ 

3 

2 

1 

BASALT 

(Schonen, Sweden) 

EULER and WINKLER {1957) 

B-3 

o~----~------~----~-----~~----~-------~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

Basalts 443 
"" 4 "" "" 

< fii' 

l"l 

0 

~. 

~ 

a. 

Vl 

-< 

~ 

~ 

a 

;:;· 

AI 3 ~ 

c.. 

z ...--... c 

~ w ... U") --.. B-4 e:!.. I ~ - !-

Ill 0 AI a... ~ 

c.. 

C') ---

>- £j 

Ill 

Ill 

t- ~ 

Ill 

U") 2 0 

u 

U") 

> 

~ 

0 

__. 

1~ OLIVINE- ANDESITE BASALT 

(Gottenburg, Germany) 

EULER and WINKLER (1957) 

0 ~--~--~--~----~--~--~----~--~--~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
_..--.. 

UJ 

U") 

0 

0-. 

__... 

>-

~ 

-

U") 

0 

u 

U") 

-

> 

l? 

0 

__. 

4~----~----~------------~------~----~ 

3 

2 

1 

13-4 

OLIVINE- ANDESITE BASA\LT 

(Gottenburg, Germany) 

EULER and WINKLER (1957) 

o~----~----~------~----~------~----~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

Basalts 445 
0 

ll) 

M __..._.. ,..... 

u 

0 

........... 

w ...,_ 0::: __, :::::> 

<( ......... V') >- ~ 0 ~ <( c ~ ll) 0::: 

co 0 ....... N w E '- ,..... a_ 

w ~ 

1.1") 

...,_ Q) ~ ~ - ~ ....., I w V') 

~ co 

w ... 1-

0 C) 

~ ~ z :l 

<( ..c "'b 

c ~ 0 I Q) t) l.f') 

w: ~ ,..... 

z 0 ,..... 

>- -~ ~ 

""" __, 

0 

0 

1.1) 

N ,..... o2 

(3SIOd) A!ISOJSII\ ~01 

446 Viscosity of Synthetic and Natural Melts and Glasses 
,........, 

UJ 

V) 

0 

a.. 

-

._ >-

-

V) 

0 

u 

V) 

-

> 

~ 

0 

__. 

4~----~----~------~----~------~----~ 

3 

2 

1 

OLIVINE -ANDESITE BASA.LT 

(Gottenburg, Germany) 

EULER and WINKLER (1957) 

B-5 

0 ~----~~--~------~----~------~----~ 

5 6 7 8 

10 000/T (KELVINS-1

) 

Basalts 447 
SYSTEM 

OLIVINE BASALT 

(GEMBUDO) MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

OLIVINE BASALT 

(KONOURA) 

LN(N) 

10.543 

8.065 

6.486 

5.691 

5.170 

4.918 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

ANDESITIC BASALT 

(MOTOMURA) 

LN(N) 

6.596 

5.819 

5.151 

4.915 

4.785 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) T (DEGREES C) 

T 

1150.00 

1200.00 

1250.00 

1300.00 

1350.00 

1400.00 

z 

7.027 

6.789 

6.566 

6.357 

6.161 

5.977 

SYSTEM 

NEPHELINE BASALT 

(NAGAHAMA) 

LN(N) 

11.283 

10.347 

6.294 

5.557 

5.209 

4.931 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

5.247 

4.763 

4.578 

4.479 

4.379 

LOG(N) 

4.579 

3.503 

2.817 

2.472 

2.245 

2.136 

LOG(N) 

2.864 

2.527 

2.237 

2.135 

2.078 

LOG(N) 

4.900 

4.494 

2.734 

2.414 

2.262 

2.142 

LOG(N) 

2.279 

2.069 

1.988 

1.945 

1.902 

448 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

KANI (1934b) 

DERIVED FROM 

TABLE VII 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

37897.00 

3180.60 

656.15 

296.15 

175.83 

136.68 

AUTHOR 

KANI (1934b) 

DERIVED FROM 

TABLE VII 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

731.82 

336.59 

172.67 

136.37 

119.73 

AUTHOR 

KANI (1934b) 

DERIVED FROM 

TABLE VII 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

79470.00 

31168.00 

541.51 

259.12 

182.94 

138.55 

AUTHOR 

KANI (1934b) 

DERIVED FROM 

TABLE VII 

P = 1.0 ATM. 

Z = 10000.0/T(K)' (1/K) 

N 

190.00 

117.14 

97.34 

88.11 

79.76 

B-6 

B-7 

B-8 

B-9 
,........_, 

lU 

V') 

0 

a.. 

......__ 

>- 1--

-

V') 

0 

u 

V') 

-

> 

~ 

0 

_.. 

5 .-------~------~----------------------~------~ 

4 

3 

2 

B-8 

B-6 

-ANDESTIC BASALT 

(Motomura) 

OLIVINE BASALT--

(Gembudo) 

OLIVINE BASALT 

(Konoura) 

B-9 

NEPHELINE BASALT/ 

(Nagahama) 

BASALTS 

KANI ( 1934b) 

1 --------~------~------_.------~--------~----~ 

1100 1200 1300 1400 

TEMPERATURE (°C) 

Basalts 449 
....--.. 

UJ 

V) 

0 

a.. 

......._. 

>- I-

-

V) 

0 

u 

V) 

-

> 

0 

0 

_J 

5 ~------~----------------------------------------

4 

3 

2 

1 

5 

BASALTS 

KANI (1934b) 

B-8 

B-6 

ANDESTIC BASALT--

(Motomura) 

--OLIVINE BASALT 

(Gembudo) 

-OLIVINE BASALT 

(Konoura) 

B-9 

-NEPHELINE BASALT 

(Nagahama) 

6 7 8 

10 000/T (KELVINS- 1

) 

450 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

BASALT 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1350. 6.161 3.689 

AUTHOR 

KUSHIRO ET AL. (1976a) 

DERIVED FROM 

TABLE I GRAPH 

P = 15.0 KBAR 

Z = 10000.0IT(K) (1IK) 

LOG(N) N 

1.602 40. 10. 

1375. 6.068 3.219 1.398 25. 7. 

SYSTEM 

BASALT 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1375. 6.068 3.219 

1400. 5.977 2.708 

SYSTEM 

BASALT 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1500. 5.640 2.079 

LOG(N) 

1.398 

1.176 

LOG(N) 

0.903 

AUTHOR 

KUSHIRO ET AL. (1976a) 

DERIVED FROM 

TABLE I GRAPH 

P = 20.0 KBAR 

Z = 10000. OIT (K) (1IK) 

N 

25. 6. 

15. 4. 

AUTHOR 

KUSHIRO ET AL. (1976a) DERIVED FROM . -

TABLE I GRAPH 

P = 30.0 KBAR 

Z = 10000. OIT (K) (1IK) 

N 

8. 2. 

B-10a 

B-10b 

B-10c 

Basalts 451 
SYSTEM 

COLUMBIA RIVER BASALT 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1130.00 7.128 

1195.00 6.812 

1240.00 

1295.00 

1365.00 

1385.00 

1400.00 

1443.00 

6.609 

6.378 

6.105 

6.031 

5.977 

5.828 

LN(N) 

7.483 

8.980 

6.171 

5.411 

4.605 

4.375 

4.214 

3.684 

LOG(N) 

3.25 

2.90 

2.68 

2.35 

2.00 

1.90 

1.83 

1.60 

452 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MURASE AND MCBIRNEY 

DERIVED FROM 

GRAPH (D) 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1778. 

794.3 

478. 

223.9 

100. 

79.43 

67.61 

39.81 

(1973) 

8-11 
4 ~--------~----------------~--------~ 

B-11 

3 

.......... 

w 

V') 

0 

CL 

....._..... 

>- 1-

V') 2 0 

u 

V') 

> 

0 

g 

1 BASALT 

(Columbia River Basalt) 

MURASE and MCBIRNEY ( 197.1) 

o~----~--~----~----~----~----~----~ 

1100 1200 1300 1400 

TEMPERATURE {°C) 

Basalts 453 
.......... 

lU 

U') 

0 

a.. 

........... 

>-

~ 

-

U') 

0 

u 

U') 

-

> 

0 

0 

......J 

4 ~----~------~------~------~------~----~ 

3 

2 

1 

B-11 

BASALT 

(Columbia River Basalt) 

MUHASE and MCBIHNEY ( 197.1) 

0 ~----~------~------~------~------~----~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

454 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

OLIVINE THOLEIITE 

(KILAUEA 1961) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1186. 6.854 

1215. 6.720 

1233. 6.640 

1252. 6.557 

1267. 6.494 

1318. 6.285 

1364. 6.109 

1411. 5.938 

1507. 5.618 

1604. 5.328 

LN(N) 

5.819 

5.408 

5.153 

4.914 

4.749 

4.174 

3.745 

3.304 

2.552 

1.883 

LOG (N) 

2.527 

2.348 

2.238 

2.134 

2.063 

1.813 

1.627 

1.435 

1.108 

0.818 

AUTHOR 

THIS REPORT 

DERIVED FROM 

DATA POINTS 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

336.7 

223.1 

172.9 

136.2 

115.5 

64.97 

42.32 

27.22 

12.83 

6.57 

B-12 

Basalts 455 
-r--

--() 

0. 

w r--

1- ._ 

0 

w Q) 

__. ::J 

0 0 

I ~ 

1- ._ 

w ::J 

0 z E 

> ::J 

0 __. E 0 Q) 

0 

I 

-

).... 

§ 

" V) 

...... 

~ 

t2 

~ 

N 

I 

co 

0 

ll') 

--() 

r--

0 

ll') 

ll') 

r--

0 

ll') 

~ r--

0 

V") 

("") 

r--

0 

~-----L------~----~------~------~----~------------~ ll') r--

or--

(3SIOd) A!ISO)SI/\ 901 

456 Viscosity of Synthetic and Natural Melts and Glasses 

..--.. 

u 

0 

--- lU 

~ 

:::::> 

~ ~ 

LU 

CL 

~ lU 

1-
.....--.. 

UJ 

V) 

0 

a_ 

-

._ >-

-

V) 

0 

u 

V) 

-

> 

0 

0 

___. 

4~----~----~------~----~------~----~ 

3 

2 

1 

OLIVINE THOLEIITE 

(Halemaumau, Kilauea, 1961) 

PRESENT STUDY 

B-12 

0 ~----~----~------~----~------~-----

5 6 7 8 

10 000/T (KELVINS- 1

) 

Basalts 457 
SYSTEM 

HAWAIIAN THOLEIITIC BASALT 

MAKAOPUHI LAVA LAKE 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1160.00 6.978 

1165.00 6.954 

1170.00 6.930 

1190.00 6.835 

1200.00 6.789 

1210.00 6.743 

1220.00 6.698 

1235.00 6.631 

1300.00 6.357 

LN(N) 

7.550 

6.768 

6.565 

6.659 

6.174 

5.768 

5.481 

5.416 

5.298 

4.554 

LOG(N) 

3.279 

2.940 

2.851 

2.892 

2.681 

2.505 

2.380 

2.352 

2.301 

1.978 

458 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

SHAW (1969) 

DERIVED FROM 

GRAPH (D) 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1900. 

870. 

810. 

780. 

480. 

320. 

240. 

225. 

200. 

95. 

B-13 
..--.. 

LU 

V") 

0 

a... 

--

>-

~ 

-

V') 

0 

u 

V') 

-

> 

l? 

0 

_.J 

4~----~------~----~----~~----~----~ 

3 

2 

1 

• 

B-13 

OLIVINE THOLEIITE 

(Makaopuhi Lava Lake, Kilauea) 

SHAW (1969) 

0 ~----~------~----~------~----~----~ 

1100 1200 1300 1400 

TEMPERATURE {°C) 

Basalts 459 
....--

UJ 

ll') 

-

0 

a.. 

--

>- Ill') -

0 

u 

ll') 

-

> 

~ 

0 

__. 

4~----~------~----~------~------~----~ 

3 

2 

1 

B -13 

OLIVINE THOLEIITE 

(Makaopuhi Lava Lake, Kilauea) 

SHAW (1969) 

0 ~------------~----~------~------~------

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

460 Viscosity of Synthetic and Natural Melts and Glasses 
0~~----~,--~--~--~--~--~ 

~ 10 ~ 

0 

_o 

~ 

UJ 

a::= 

::::> 

V) 20 

V) 

UJ 

~ 

a.. 

30 

\ 

\ 

L. .d \ 1qu1 US---_.\ 

\\ 

\ ' \ \, 

K USHIRO eta I. 

1976a 

7] (poise} ~ \,\ P ( ~. cm~3) 

50--------/(" ·\~ \ ' ,·fP. 

35 ~ 0., \~ 

3 0-----_,/'\ "? ..Q 

20 '" \' ,, ~ KILAUEA 1921 ' '"'-. v> 

OLIVINE THOLEIITE \~ . ·~o \' 

10 ', ~lo 

1000 1100 1200 1300 1400 1500 1600 

TEMPERATURE (°C} 

Basalts 461 
~ 

'-

0 

...0 

5 

10 

~ 15 

w 

Ck: 

:::> 

~ 20 

w 

Q::: 

Q.. 

25 

30 

FUJII and KUSHIRO 

(1977a) 

.33 

.29 

7] (poise) 

31 21 

e e 

Liquidus~ 

Kl LAUEA 1921 

OLIVINE 

THOLEIITE 

1100 1200 1300 1400 1500 

TEMPERATURE (°C) 

462 Viscosity of Synthetic and Natural Melts and Glasses 
w 

~ 

:::J 

V') 

V') 

w 

~ 

0~--~----~~--~--~----~ 

Liquidus 

"-----. 

FUJII and KUSHIRO (1977b) 

8-14 

.170 

7] (poise) 

a... 10 

ABYSSAL 

OLIVINE 

THOLEIITE 

240 .\79 

15~--~----~--~----~--~ 

1100 1200 1300 

TEMPERATURE (°C) 

Basalts 463 
1100 

1200 

u 

0 

............ 

...---....----...---....----. 7. 5 

ALKALI 

/

OLIVINE 

BASALT 

OLIVINE 

NEPHELI NITE 7.0 

J 

UJ 

~ 

::::> 

6.5 Q 

~ 1300 ~ 

UJ 

a.. 

~ UJ 

I- 1400 

1500 

SODA) 

MEL I LITE 

B-15 

SCARFE(1981) 

4 3 2 1 0 

6.0 

5.5 

VISCOSITY, LOG (TJ) (poise) 

464 Viscosity of Synthetic and Natural Melts and Glasses 

I-

~ 

0 

,..--
5 

20 

OLIVINE 

NEPHELI NITE 

~ 

B-15 

SCARFE(1981) 

I. I~+-! ~\ 

\ SODA 

\ MEL I LITE 

ALKALI 

OLIVINE 

~BASALT 

0.0 1.0 2.0 

VISCOSITY, LOG (7]) (poise) 

Basalts 465 
-

w 

V) 

0 

Q.. 

-0 

s::-

0 

C) 

0 

__, 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

@ KANI (1934b) 

r81 KANI ( 1934b) 

~ KANI (1934b) 

~ KANI (1934b) 

6 EULER AND WINKLER 

(1957) 

© OLIVINE BASALT (GEMBUDO, JAPAN) 

~ OLIVINE BASALT (KONOURA, JAPAN) 

~ ANDESITIC BASALT (MOTOMURA, JAPAN) 

~ NEPHELENE BASALT (NAGAHAMA, JAPAN) 

6 OLIVINE BASALT (VOGELSBURG, GERMANY) 

D OLIVINE BASALT (AYRESHIRE, SCOTLAND) 

~ BASALT (SCHONEN, SWEDEN) 

EB OLIVINE ANDESITIC BASALT 

(GOTTENBURG, GERMANY) 

rn OLIVINE ANDESITIC BASALT 

(GOTTENBURG, GERMANY) 

0 OLIVINE THOLEIITE 

(MAKAOPUHI, KILAUEA, HAWAII) 

i:. COLUMBIA RIVER BASALT (OREGON, U.S.A.) 

• OLIVINE THOLEIITE 

(HALEMAUMAU, KILAUEA, HAWAII) 

o EULER AND WINKLER ( 1957) 

~ EULER AND WINKLER ( 1957} 

EB EULER AND WINKLER (1957) 

EE EULER AND WINKLER (1957} 

0 SHAW (1969) 

i:. MURASE AND MC BIRNEY ( 1973} 

• PRESENT STUDY 

3.0 

2.5 

2.0 

-fJ) 

_, • 

1.5 < u 

fJ) 

< CL 

-0 

s::-

1.0 0 ...-

C) 

0 

_, 

0.5 

0.0 

-0.5 

LJ_L_L_L_.L-.l~__L_L_l...____j_l_____L_L_J..._j_L____L__i_L-J._L-L-~.L-J.---':"=-:::-'-~~ - 1. 0 

o.~ 000 1100 1200 1300 1400 1500 1800 

TEMPERATURE (°C) 

466 Viscosity of Synthetic and Natural Melts and Glasses 
Andesites 

Andesites 467 
SYSTEM 

ANDESITE 

(OLD RED SANDSTONE LAVA; 

EDINBURGH, SCOTLAND) 

MEASUREMENT METIIOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T z LN(N) 

1260. 6.523 8.294 

1300. 6.357 7.783 

1340. 6.200 7.223 

1380. 6.050 6.918 

1415. 5.924 6.579 

1455. 5.787 6.153 

1498 5.646 5.704 

SYSTEM 

HYPERSTHENE ANDESITE 

(OLD RED SANDSTONE LAVA; 

EDINBURGH, SCOTLAND) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1260. 6.523 

1300. 6.357 

1340. 6. 200 

1380. 6. 050 

1418. 5.914 

1458. 5.777 

1493. 5.663 

LN(N) 

8.006 

7.459 

6.960 

6.672 

6.273 

5.829 

5.438 

LOG(N) 

3.602 

3.380 

3.137 

3.004 

2.857 

2.672 

2.477 

LOG(N) 

3.477 

3.255 

3.021 

2.898 

2.724 

2.531 

2.362 

468 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 8 

p = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4000. 

2400. 

1370. 

1010. 

720. 

470. 

300. 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3000. 

1800. 

1050. 

790. 

530. 

340. 

230. 

A-1 

A-2 
> &. 

I'D 

= ~ 

~ 

0'1 

"" 

.....--.. 

w 

(/') 

-

0 

a... 

..__... 

>-

1-

(/') -

0 

u 

(/') 

-

> 

e> 

g 

4~--~--~--~----~--~--~----~--~--~ 

3 

2 

1L 

A-1 

ANDESITE 

(Old Red Sandstone lava, Edinburgh, Scotland) 

EULER and WINKLER (1957) 

o~--~--~--~--~~--~--~--~----~--~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
4~----~--------------~----~~----~------~ 

A-1 

3 

~ 

w 

U") 

0 

a.. 

-

>- I--

-

U") 2 0 

u 

U") 

-

> 

~ 

0 

---' 

1 

ANDESITE 

(Old Red Sandstone Lava, Edinburgh, Scotland) 

EULER and WINKLER (1957} 

o~----~------~------~----~~----~------~ 

5 6 7 8 

10 000/T (KELVINS- 1

) · 

470 Viscosity of Synthetic and Natural Melts and Glasses 
> ::I 

c.. 

t'l) 

~. 

;-

"' 

.f;oo 

::::.: 

4--------~----~------~----~--~--~--~ 

........... 

w 

c..f) 

-

0 

a... 

..._... 

>-

t3 

(./') 2 

0 

u 

(./') 

> 

~ 

g 

1 

A-2 

HYPERSTHENE ANDESITE 

(Old Red Sandstone lava, Edinburgh, Scotland) 

EULER and WINKLER {1957) 

o~--~--~--~----~--~--~--~----~--~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
.......... 

UJ 

tl") 

-

0 

a... 

........... 

..,_ >-

-tl") 

0 

u 

tl") 

-

> 

~ 

0 

__. 

4 ~----~--------------------~------~----~ 

3 

2 

1 

A-2 

HYPERSTHENE ANDESITE 

(Old Red Sandstone Lava, Edinburgh, Scotland) 

EULER and WINKLE!? (1957} 

0 ~----~------~------~----~------------~ 

5 6 7 8 

10 000/T {KELVINS- 1

) 

472 Viscosity of Synthetic and Natural Melts and ,Glasses 
SYSTEM 

ANDESITE (CRATER LAKE, ORE.) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1250. 6.566 8.065 3.502 

1350. 6.161 6.975 3.029 

SYSTEM 

ANDESITE (CRATER LAKE, ORE.) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1350. 6.161 6.745 2.929 

SYSTEM 

ANDESITE (CRATER LAKE, ORE.) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1350. 6.161 6.791 2.949 

AUTHOR 

KUSHIRO ET AL. (1976b) 

DERIVED FROM 

TABLE I GRAPH 

P=7.5KBAR 

Z = 10000. OIT (K) (1IK) 

N 

3180. 

1070. 

AUTHOR 

KUSHIRO ET AL. (1976b) 

DERIVED FROM 

TABLE I GRAPH 

P = 15.0 KBAR 

Z = 10000.0IT(K) (1IK) 

N 

850. 

AUTHOR 

KUSHIRO ET AL. (1976b) 

DERIVED FROM 

TABLE I GRAPH 

P = 20.0 KBAR 

Z = 10000. OIT (K) (1IK) 

N 

890. 

A-3a 

A-3b 

A-3c 

Andesites 473 
5 ~----~------~------~------~------~------~ 

4 

.........._ 

UJ 

ll') 

0 

a_ 

__... 

>-

Ill') 3 0 

u 

ll') 

-

> 

~ 

0 

__J 

2 

ANDESITE 

KUSHIRO, YODER and MYSEN ( 1976h) 

1 ~----~------~------~------~------~------~ 

0 4 8 12 16 20 24 

PRESSURE ( Kbar) 

474 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

MOUNT HOOD ANDESITE 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z 

1115.00 7.205 

1165.00 6.954 

1210.00 6.743 

1260.00 6.523 

1310.00 6.317 

1355.00 6.143 

1400.00 5.977 

1408.00 5.949 

1455.00 5.787 

-w 

V) 

-

0 

a.. 

...__ 

>-

~ 

V) 

0 

u 

V) 

> 

() 

0 

---1 

LN(N) 

11.47 

10.48 

9.556 

8.750 

8.060 

7.483 

6.908 

6.862 

6.332 

LOG(N) 

4.98 

4.55 

4.15 

3.80 

3.50 

3.25 

3.00 

2.98 

2.75 

2 ANDESITE 

AUTHOR 

MURASE AND MCBIRNEY 

DERIVED FROM 

GRAPH (D) 

P = 1.0 A'IM. 

Z = 10000.0/T(K) (1/K) 

N 

9.55E4 

3.55E4 

1.41E4 

6.31E3 

3.16E3 

1.78E3 

1.00E3 

9.55E2 

5.62E2 

(Mount Hood, Washington) 

MURASE and MCBIRNEY (1973) 

(197 3) 

A-4 

1 ------~------------~----~------~------------------~ 1100 1200 1300 1400 1500 

TEMPERATURE (°C) 

Andesites 475 
.....--

UJ 

c./) 

0 

a.. 

----

>-

...... 

-

c./) 3 0 

u 

c./) A-4 -

> 

0 

0 

__, 

2 

ANDESITE 

(Mount Hood, Washington) 

MURASE and MCBIRNEY ( 1973) 

1 ~----~------~------~------~------~----~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

476 Viscosity of Synthetic and Natural Melts and Glasses 
0~--~--~--~----~--~ 

5 

~ 10 

0 

_a 

~ ........... 

UJ 15 ~ 

:::::> 

(./) 

(./) 

UJ 20 ~ 

a.. 

25 

30 

' \ 7] (poise) 

\ ~230 e1380 

\ 

\ 

\ 

\ 

\ e 1090 

\ Liquidus_..-/"'\ 

KUSHIRO etal. 1976a 

CRATER LAKE 

ANDESITE 

\\ e1160 

\ 

\ 

1000 1100 1200 1300 1400 1500 

TEMPERATURE (°C) 

Andesites 477 

Rhyolites 

Rhyolites 479 
SYSTEM 

RHYOLITE GLASS 

P(H20)=0.0 BARS 

MEAS.UREMENT METHOD 

COMPO. -CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

735.00 9.921 29.934 

785.00 9.452 28.782 

835.00 9.025 24.407 

SYSTEM 

RHYOLITE GLASS 

P(H20)=1.72 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN (N) 

735.00 9.921 26.019 

785.00 9.452 26.019 

SYSTEM 

RHYOLITE GLASS 

P(H20)=3.45 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN (N) 

635.00 11.013 32.236 

735.00 9.921 25.559 

785.00 9.452 25.559 

SYSTEM 

RHYOLITE GLASS 

LOG(N) 

13.0 

12.5 

10.6 

LOG(N) 

11.3 

11.3 

LOG(N) 

14.0 

11.1 

11.1 

P(H20)=10.3 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

635.00 11.013 28.322 

735.00 9.921 23.717 

785.00 9.452 23.717 

SYSTEM 

RHYOLITE GLASS 

P(H20)=20.7 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

635.00 11.013 26.019 

735.00 9.921 23.256 

785.00 9.452 22.796 

LOG(N) 

12.3 

10.3 

10.3 

LOG(N) 

11.3 

10.1 

9.9 

480 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 15.2 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

1.0*10E13 

3.16*10E12 

3.98*10E10 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 15.2 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

2.0*10E11 

2.0*10£11 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 15.2 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

1.0*10E14 

1.26*10E11 

1.26*10E11 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 15.2 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

2.00*10E12 

2.00*10E10 

2.00*10E10 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 15.2 BARS 

Z = 10000.0/T(K) (1/K) 

N 

2.0*10E11 

1.26*10E10 

7.94*10£09 

R-1 

R-2 

R-3 

R-4 

R-5 
SYSTEM 

RHYOLITE GLASS 

P(H20)=0.0 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

735.00 9.921 28.782 12.5 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 36.4 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

3.16*10E12 

R- 6 

------------------------------------------------------------------------------

SYSTEM 

RHYOLITE GLASS 

P(H20)=1.72 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

635.00 11.013 31.085 

735.00 9.921 26.710 

LOG(N) 

13.5 

11.6 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 36.4 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

3.16*10E13 

3.98*10E11 

R-7 

------------------------------------------------------------------------------

SYSTEM 

RHYOLITE GLASS 

P(H20)=3.45 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN (N) 

635.00 11.013 29.243 

735.00 9.921 25.559 

LOG (N) 

12.7 

11.1 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 36.4 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

5.01*10E12 

1.26*10E11 

R-8 

------------------------------------------------------------------------------

SYSTEM 

RHYOLITE GLASS 

P(H20)=10.3 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

535.00 12.376 31.085 

635.00 11.013 27.401 

735.00 9.921 24.407 

SYSTEM 

RHYOLITE GLASS 

P(H20)=20.7 BARS 

MEASUREMENT METHOD 

COMPO.-CURVE CALCULATION 

N (POISES) 

T (DEGREES C) 

T Z 

485.00 13.193 

535.00 12.376 

635.00 11.013 

735.00 9.921 

LN(N) 

32.236 

28.782 

24.868 

23.486 

LOG (N) 

13.5 

11.9 

10.6 

LOG(N) 

14.0 

12.5 

10.8 

10.2 

AUTHOR 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 36.4 BARS 

Z = 10000. 0/T (K) (1/K) 

N 

3.16*10E13 

7.94*10E11 

3.98*10E10 

AUTHOR 

R-9 

FRIEDMAN, LONG AND SMITH (1963) 

DERIVED FROM 

TABLE 2 

P = 36.4 BARS 

Z = 10000.0/T(K) (1/K) 

N 

1.0*10E14 

3.16*10E12 

6.31*10E10 

1.58*10E10 

R- 10 

Rhyolites 481 
~ 

= N 

< ;;;· 

I") 

Q 

!!!. 

-< 

a 

til 

-< ::I 

:r 

a 

;:;· 

Ill 

::I 

Q. 

z 

a 

~ 

e!. 

~ 

Ill 

~ 

Ill 

::I 

Q. 

C'l 

~ 

~ Ill 

16------~--~--~--~-.---r--~--r-~r-~--~ 

.......-... 

w 14 (./') -

0 

a.. 

.__..... 

>-

1--

(./') 12 0 

u 

(./') 

> 

<-' g 10 

R-3 

R-4 

R-5 

RHYOLITIC OBSIDIAN 

{Bandelier Rhyolite Tuff, 

Jemez Mts., New Mexico) 

FRIEDMAN, LONG and SMITH (196.1) 

R -1 

a~~--~--~~--~--~~--~--~~------

400 500 600 700 BOO 900 1000 

TEMPERATURE (°C) 
~ 

:r 

l 

i 

.a:. 

= IN 

16 ~~~~--~--~--~------~--~--~--~-------

........._ 

w 14 

V') 

-

0 

a.. 

.....__... 

>- 1-

-

V') 12 0 

u 

V') 

-

> 

~ 

g 10 

R-3 

R-4 

R-5 

RHYOLITIC OBSIDIAN 

(Bandelier Rhyolite Tuff, 

Jemez Mts.1 New Mexico) 

FRIEDMAN, LONG and SMITH {1963) 

8 ~--~~~~~~--~--~--~--~--~--~--~--~ 

9 10 11 12 13 14 15 

10 000/T (KELVINS-1) 
~ 

= ~ 

<ij• < 16 t"l 

0 

Cll 

~ 

a RHYOLITIC OBSIDIAN VI 

-< 

a 

(Bandelier Rhyolite Tuff, :::r !!. 

;:::;· 

Jemez Mts., New Mexico) Col ............ = w 14 \ Q. 

z ll') FRIEDMAN, LONG and SMITH (196.3) Col 

c 0 ... 

e!.. 

~ a_ ttl 

- ...__ Cll 

Col 

Q. = >- ~ 1--

iii 

(./") Cll 12 Cll 

ttl 

Cll 0 I " ~ ""'-.. •R-7 u 

ll') L " - ~ 'R-8 

> --------=: R- 9 8 10 I R-10 

~ 

a~~--~--~~--~--~~--~--~~--~~ 

400 500 600 700 800 900 1000 

TEMPERATURE (°C) 
;111::1 

::r 

-< 2.. 

oc 

olio 

U1 = 

16------~--~~---.--.---.--.---.--~-.--~ 

~ 

w 14 ll) 

0 

a.. 

__... 

>-

f--

ll) 12 8 I 

c./) - L-

> 

~ 10 I 

R-7 

R-8 

R-9 

R-10 RHYOLITIC OBSIDIAN 

(Bandelier Rhyolite Tuff, 

Jemez Mts., New Mexico) 

FRIEDMAN, LONG and SMITH (1963) 

s------~--~----------~~~~------~-------

9 10 11 12 13 14 15 

10000/T {KELVINS1) 
SYSTEM 

NEWS ERRY RHY_O_UTE OBSIDIAN 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

1120.00 7.719 16.81 

1175.00 6.906 15.59 

1290.00 6.398 13.42 

LOG(N) 

7.3 

6.77 

5.85 

486 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MURASE AND MCBIRNEY 

DERIVED FROM 

GRAPH (D) 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.99E7 

5.88E6 

6.76E5 

(1973) 

R-11 
.---... 

w 

c.l) 

0 

a.. 

.......... 

>-

..... 

-

c.l) 

0 

u 

c.l) 

> 

<-? 

0 

.....J 

8~----~------~------~----~------~----~ 

7 

6 

5 

RHYOLITIC OBSIDIAN 

(Newberry Crater, Oregon) 

MURASE and MCBIRNEY ( 1973) 

R-11 

4~----~------~------~----~------~----~ 

1050 1150 1250 1350 

TEMPERATURE {°C) 

Rhyolites 487 
.---... 

LU 

c./) 

-

0 

a.. 

..........._. 

>-

...... 

-

c./) 

0 

u 

c./) 

-

> 

() 

0 

_,J 

8~----~------~------~----~~----~------~ 

7 

6 

5 

RHYOLITIC OBSIDIAN 

(Newberry Crater, Oregon) 

MURASE and MCBIRNEY /1973) 

R -11 

4 ~----~------~------~----~~-------------

5 6 7 8 

10 000/T (KELVINS- 1

) 

488 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

RHYOLITIC OBSIDIAN 

(JEMEZ MNTS . , NEW MEXICO) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T 

800. 

850. 

SYSTEM 

z 

9.320 

8.905 

RHYOLITIC OBSIDIAN 

LN(N) 

14.852 

14.207 

(JEMEZ MINS . , NEW MEXICO) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

p 

z 

X (H20) 

LOG(N) 

6.45 

6.17 

AUTHOR 

SHAW (1963) 

DERIVED FROM 

TABLE 2 = 2000 BARS = 10000. 0/T (K) (1/K) = 0.043 

N 

2.82*10E6 

1.48*10E6 

AUTHOR 

SHAW (1963) 

DERIVED FROM 

TABLE 2 

P = 2000.0 BARS 

Z = 10000. 0/T (K) (1/K) 

X(H20)= 0.062 

T Z LN(N) LOG(N) N 

700.@ 10.277 15.012 6.52 3.31*10E6 

750.@ 9.775 13.929 6.05 1.12*10E6 

800.@ 9.320 12.824 5.57 3.71*10E5 

800.* 9.320 12.965 5.63 4.27*10E5 

850.@ 8.905 12.090 5.25 1.78*10E5 

@ MEASUREMENT MADE WITH PLATINUM SPHERE 

* MEASUREMENT MADE WITH SILVER SPHERE 

SYSTEM 

RHYOLITIC OBSIDIAN 

(JEMEZ MINS . , NEW MEXICO) 

MEASUREMENT METHOD 

FALLING SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

800. 9.320 14.966 

AUTHOR 

SHAW (1963) 

DERIVED FROM 

TABLE 2 

P = 1000.0 BARS 

Z = 1 0 0 0 0 . 0 /T (K) ( 1 /l() 

X(H20)= 0.043 

LOG(N) N 

6.51 3.16*10£6 

850. 

900. 

8.905 14.414 6.26 

8.525 13.540 5.88 

1.82*10E6 

7.59*10£5 

R-12 

R-13 

R-14 

Rhyolites 489 
8 ------------------------------------~----~ 

........... 

w 

V) 

0 

a.. 

>-

....... 

7 

V) 6 

0 

u 

V) 

> 

l? 

g 

5 

4 

650 

RHYOLITIC OBSIDIAN 

P= 2 Kbar, X H

2

o= 0.043 

(Jemez Mts., New Mexico) 

SHAW (1963) 

R-12~ 

750 850 

TEMPERATURE (°C) 

490 Viscosity of Synthetic and Natural Melts and Glasses 

950 
8 ~----~----~------------~------~----~ 

---- LU 

V') 

0 

a.. 

--

>-

...... 

7 

V') 6 

0 

u 

V') 

> 

l? 

0 

--' 

5 

RHYOLITIC OBSIDIAN 

P= 2 Kbar, X H2o= 0.043 

(Jemez Mts., New Mexico) 

SHAW (1963) 

/R-12 

4 ~----~----~------~----~------~----~ 

7.5 8.5 9.5 10.5 

10 000/T (KELVINS- 1

) 

Rhyolites 491 
..--.. 

lU 

V) 

0 

Q.. 

......... 

.,_ >-

-

V) 

0 

u 

V) 

-

> 

0 

0 

__. 

8 ~----~--------------------~~----~------~ 

7 

6 

5 

4 

650 

RHYOLITIC OBSIDIAN 

P= 2Kbar, XH 2o = 0.062 

(Jemez Mts., New Mexico) 

SHAW (1963) 

/SILVER SPHERE (e) 

e 

• 

PLATINUM SPHEREL c 

d 

750 850 

TEMPERATURE (°C) 

950 

492 Viscosity of Synthetic and Natural Melts and Glasses 
8 ~----~----------------------------------~ 

...--.. 

w 

V") 

0 

a.. 

>-

~ 

7 

V") 6 

0 

u 

V") 

> 

0 

0 

_J 

5 

RHYOLITIC OBSIDIAN 

P= 2Kbar, XH

2

o = 0.062 

{Jemez Mts., New Mexico} 

SHAW (196.1) 

SILVER SPHERE \e 

• 

c 

0 

\PLATINUM SPHERE (a-d) 

4 ~----~------~------~----~------~----~ 

7.5 as ~s 10.5 

10 000/T (KELVINS- 1

) 

Rhyolites 493 
........... 

LU 

lf) 

0 

a_ 

........... 

>- 1-

-lf) 

0 

u 

lf) 

-

> 

0 

0 

....J 

8 ~----~--------------------~------~----~ 

7 

6 

5 

RHYOLITIC OBSIDIAN 

P = 1 Kbar, X H2o = 0.043 

(Jemez Mts., New Mexico) 

SHAW (1963) 

4 ~----~------~------~----~------~----~ 

650 750 850 950 

TEMPERATURE (°C) 

494 Viscosity of Synthetic and Natural Melts and Glasses 
....--.. 

UJ 

V) 

0 

a_ 

.....__ 

.,_ >-

-

V) 

0 

u 

V) 

-

> 

<-' 0 

___. 

8 ~------------------------~~----~----~ 

7 

6 

5 

RHYOLITIC OBSIDIAN 

P=lKbar, XH2o =0.043 

(Jemez Mts., New Mexico) 

SHAW (1963) 

4 ~----~------~----~----~~----~----~ 

Z5 8.5 9.5 10.5 

10 000/T (KELVINS- 1

) 

Rhyolites 495 

Additional Igneous Melts 

Additional Igneous Melts 497 
SYSTEM 

NEPHELINE-LEUCITE TEPHRITE 

(BRUCH, MICHELS, EIFEL, 

GERMANY) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N ~POISES) T DEGREES C) 

T 

1101. 

1144. 

1188. 

1224. 

1261. 

1300. 

1340. 

1378. 

1416. 

1462. 

SYSTEM 

KERSANTIT 

z 

7.278 

7.057 

6.845 

6.680 

6.519 

6.357 

6.200 

6.057 

5.921 

5.764 

LN(N) 

7.650 

7.170 

6.551 

6.215 

5.913 

5.501 

5.043 

4.635 

4.190 

3.538 

(SCHWARTZWALD, GERMANY) 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1186. 6.854 

1225. 6.675 

1264. 6.506 

1302. 6.349 

1341. 6.196 

1378. 6. 057 

1420. 5.907 

1462. 5.764 

SYSTEM 

LN(N) 

8.071 

7.601 

7.244 

6.802 

6.273 

6.087 

5.704 

5.136 

OLIVINE DOLERITE 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1180. 6.882 

1220. 6.698 

1260. 6.523 

1295. 6.378 

1338. 6.207 

LN(N) 

6.380 

5.298 

4.007 

3.135 

2.303 

LOG (N) 

3.322 

3.114 

2.845 

2.699 

2.568 

2.394 

2.190 

2.013 

1.829 

1.556 

LOG(N) 

3.505 

3.301 

3.146 

2.954 

2.724 

2.643 

2.447 

2.230 

LOG(N) 

2.771 

2.301 

1.740 

1.362 

1.000 

498 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM 

TABLE 2 

p = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

2100. 

1300. 

700. 

500. 

370. 

245. 

155. 

103. 

66. 

36. 

AUTHOR 

EULER AND WINKLER ( 195 7) 

DERIVED FROM 

TABLE 8 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

3200. 

2000. 

1400. 

900. 

530. 

440. 

300. 

170. 

AUTHOR 

EULER AND WINKLER (1957) 

DERIVED FROM _ TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

590. 

200. 

55. 

23. 

10. 

IM-1 

IM-2 

IM-3 
> c. 

~ s· 

= a 

a; 

= 

~ c 

"' 

~ 

~ 

"' 

"" I.C 

I.C 

~ 

w 

c.l) -

0 

a... 

.......... 

>-

t--

4~--~--~----~--~--~----~--~--~--~ 

3 

NEPHELINE- LEUCITE TEPHRITE 

(Bruch, Michels, Eifel, Germany) 

EULER and WINKLER (1957) 

0 2 

u 

c.l) -

> 

() 

g 

1 

o~--~--~--~----~--~--~--~----~--~ 

1050 1150 1250 1350 1450. 

TEMPERATURE {°C) 
.,....._ 

UJ 

(./) 

0 

0... 

-...... 

>- 1-

-(./) 

0 

u 

(./) 

-

> 

~ 

0 

__. 

4 ------~----------------------------------~ 

3 

2 

l 

NEPHELINE- LEUCITE TEPHRITE 

(Bruch, Michels, Eifel, Germany) 

EULER and WINKLER (1957) 

IM-1 

0 ~----~------~------~----~------~------

5 6 7 8 

10 000/T {KELVINS- 1

) 

500 Viscosity of Synthetic and Natural Melts and Glasses 
t 

~ s· 

= e!.. 

a; 

= 

~ c: 

'll 

~ ~ 

~ 

~ 

:: 

............ 

UJ 

t/) 

0 

a.. -

>-

1--

4----~------~----~--~--~----~--------

IM-2 

3 

t/) 2 

0 

u 

t/) 

> 

t) 

g 

1 

KERSANTITE 

(Schwartzwald, Germany) 

EULER and WINKLER (1957} 

0~--~--~--~----~--~--~--~----~--~ 

1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
..--.. 

lU 

(./') 

0 

a.. 

.......... 

>-

1--

-(./') 

0 

u 

(./') 

-

> 

() 

0 

-I 

4 ~----~--------------~------~------~----~ 

3 

2 

1 

IM-2 

KERSANTITE 

{Schwartzwald, Germany) 

EULER and WINKLER (1957/ 

0 ~----~------~------~------~------~----~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

502 Viscosity of Synthetic and Natural Melts and Glasses 
~ 0 

1.1") w 

.,.._ ~ ~ ....... ..... - '-

Ck: 

w 

__, ~ 

0 ~ 0 ~ 

w ~ z "b 0 

§ 1.1") 

> M ............_ 

~ ..... __, u 

0 0 

~ - ~ w 

~ 

:::) 

0 ~ 1.1") ~ 

N w ..... a... 

~ w 

1-

N 

{3SIOd) AliSOJSIA 901 

Additional Igneous Melts 503 
.....-...-

UJ 

(./') 

0 

a... 

-

>- 1-

-(./') 

0 

u 

(./') 

-

> 

l? 

0 

....J 

4 ~----~--------------~----~~----~------~ 

3 

2 

1 

OLIVINE DOLERITE 

EULER and WINKLER (1957} 

IM-3 

0 ~----~------~------~----~~----~------~ 

5 6 7 8 

10 000/T (KELVINS- 1

) 

504 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

SKAERGAARD INTRUSION 

MEASUREMENT METHOD 

RESTRAINED SPHERE 

N (POISES) T (DEGREES C) T Z 

1200.00 6.789 

1240.00 6.609 

1290.00 6.398 

1335.00 6.219 

1408.00 5.949 

1445.00 5.821 

1494.00 5.659 

LN(N) 

7.483 

5.895 

4.951 

6.793 

3.569 

3.339 

3.062 

LOG(N) 

3.25 

2.56 

2.15 

2.95 

1.55 

1.45 

1.33 

AUTHOR 

MURASE AND MCBIRNEY 

DERIVED FROM 

GRAPH (D) 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

1778. 

363.1 

141.3 

89.13 

35.48 

28.18 

2.~ .. 38 

(1973) 

IM-4 

Additional Igneous Melts 505 
.........._ 

LU 

V") 

-

0 

a... 

...__.... 

>-

..... 

-lf) 

0 

u 

V") 

-

> 

0 

g 

4 ~----~--------------~----~------~----~ 

3 

2 

1 

\\SKAERGAARD" LIQUID 

(XcRYSTAL ~ 0.35) 

(Skaergaard, Greenland) 

MURASE and MCBIRNEY (197J) 

IM-4 

0 ~----~------~------~----~------~----~ 

1200 1300 1400 1500 

TEMPERATURE (°C) 

506 Viscosity of Synthetic and Natural Melts and Glasses 
....--.. 

LU 

ll) 

-

0 

a.. 

-....... 

....,_ 

>-

-

ll) 

0 

u 

ll) 

-

> 

~ 

0 

__. 

4 ~----~----~~----~----~------~----~ 

3 

2 

1 

''SKAERGAARD" LIQUID 

{X cRYSTAL~ 0.35) 

{Skaergaard, Greenland) 

MURASE and MCBIRNEY ( 1973) 

IM-4 

0 ~----~------~----~----~~----~----~ 

4.5 5.5 6.5 7.5 

10 000/T (KELVINS- 1

) 

Additional Igneous Melts 507 
SYSTEM 

SYNTHETIC LUNAR SAMPLE 

IN AIR (SLS,A) 

MEASUREMENT METHOD 

COUNTER-BALANCED SPHERE 

N (POISES) 

T (DEGREES C) T Z 

1390.00 6.013 

1400.00 5.977 

1440.00 5.838 

1455.00 5.787 

1490.00 5.672 

LN(N) 

2.303 

2.303 

1.727 

1.612 

1.497 

LOG(N) 

1.000 

1.000 

0.75 

0.70 

0.65 

AUTHOR 

MURASE AND MCBIRNEY (1970) 

DERIVED FROM 

FIG. 1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N (APPROX.) 

10.00 

10.00 

5.62 

5.01 

4.47 

IM-5 

----------------------------------------------------------------------------- SYSTEM 

SYNTHETIC LUNAR SAMPLE 

IN ARGON (SLS, B) 

MEASUREMENT METHOD 

COUNTER-BALANCED SPHERE 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 1395.00 5.995 1.842 

1425.00 5.889 1.612 

1448.00 5.811 1.566 

LOG(N) 

0.80 

0.70 

0.68 

508 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

MURASE AND MCBIRNEY (1970) 

DERIVED FROM 

FIG. 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N (APPROX.) 

6.31 

5.01 

4.79 

IM-6 
.,........_ 

w 

l/) 

-

0 

a.. 

...__.... 

>-

._.. 

V') 

0 

u 

l/) 

-

> 

() 

g 

3 ~----~------~----~~----~------~----~ 

2 

1 

SYNTHETIC LUNAR MELT 

MURASE and MCBINNEY (1970} 

0 ~----~------~------~----~~----~------~ 

1300 1400 1500 1600 

TEMPERATURE (°C) 

Additional Igneous Melts 509 
_......... 

w 

ll) 

-

0 

a.. 

.......... 

>-

..,_ 

-

ll) 

0 

u 

ll) 

-

> 

<:) 

0 

__. 

3 ~----~~----~------~------~----~------~ 

2 

1 

SYNTHETIC LUNAR MELT 

MUHASE and MCBIHNEY (1970) 

AIR ATMOSPHERE\riM-S 

AIM-6 

\RGON ATMOSPHERE 

0 ~----~------~------~----~~----~------~ 

1300 1400 1500 1600 

10 000/T (KELVINS- 1

) 

510 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM AUTHOR 

SPRUCE PINE PEGMATITE BURNHAM (1963) 

WITH 8.8 WT. % H20 

(SPRUCE PINE, N. CAROLINA) 

MEASUREMENT METHOD DERIVED FROM 

RESTRAINED SPHERE TABLE (ABS.) 

N (POISES) P = 4800 TO 7400 BARS ** 

T (DEGREES C) Z = 10000. 0/T (K) (1/K) I M- 7 

T Z LN(N) LOG(N) N 

700. 10.277 14.077 6.113 1.3*10E6 

800. 9.319 11.775 5.113 1.3*10E5 

900. 8.525 10.239 4.447 2.8*10E4 

** THE APPARENT VISCOSITY WAS PRESSURE-INDEPENDENT OVER THIS RANGE. 

Additional Igneous Melts 511 
0.2 

~ 

0 0.4 

N 

<( 

0 

u 

w 0.6 ___. 

0 

~ 

0.8 

1.0 

10 Kbar 

1650 °( 

\. 

8 10 12 

1 atm 

'---1650°( 

KUSHIRO( 1981) 

0 2 4 6 8 10 12 

VISCOSITY, Ln (7]) 

512 Viscosity of Synthetic and Natural Melts and Glasses 
Standard Glasses 

Standard Glasses 513 
SYSTEM 

SS 710 (SAMPLE 1) 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N ~POISES) T DEGREES C) 

T z LN(N) 855.1 8.864 12.805 

881.4 8.663 12.100 

901.4 8.515 11.587 

907.4 8.472 11.506 

946.8 8.198 10.587 

1000.4 7.853 9.523 

1102.9 7.268 7.905 

1112.4 7.218 7.767 

1202.5 6.777 6.675 

1306.1 6.333 5.607 

1306.7 6.330 5.630 

1412.3 5.934 4.743 

SYSTEM 

SS 710 (SAMPLE 2) 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

905.1 8.488 

1025.3 7.702 

1124.6 7.155 

1198.5 6.796 

1248.0 6.575 

1315.6 6.295 

1411.1 5.938 

SYSTEM 

LN(N) 

11.511 

9.095 

7.587 

6.730 

6.194 

5.563 

4.794 

SS 710 (SAMPLE 3) 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

900.3 8.523 

945.7 8.205 

1019.1 7.739 

1054.6 7.543 

1103.5 7.265 

1200.6 6.786 

1212.0 6.734 

1298.4 6.364 

1402.4 5.969 

LN(N) 

11.617 

10.594 

9.245 

8.637 

7.893 

6.705 

6.569 

5.699 

4.861 

LOG(N) 

5.561 

5.255 

5.032 

4.997 

4.598 

4.136 

3.433 

3.373 

2.899 

2.435 

2.445 

2.060 

LOG(N) 

4.999 

3.950 

3.295 

2.923 

2.690 

2.416 

2.082 

LOG(N) 

5.045 

4.601 

4.015 

3.751 

3.428 

2.912 

2.853 

2.475 

2.111 

514 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

NAPOLI'"!'ANO AND HAWKINS (1964) 

DERIV~:D FROM 

TABil:; 3 

p = 1.0 ATM. 

z = 10000.0/T(K) (1/K) 710-1 

N 

3.64*10E 5 

1.80*10E 5 

1.08*10E 5 

9.93*10E 4 

3.96*10E 4 

1.37*10E 4 

2710.00 

2360.00 

793.00 

272.00 

279.00 

115.00 

AUTHOR 

NAPOLITANO AND HAWKINS (1964) 

DERIVED FROM 

TABLE 3 

P = 1.0 ATM. 

Z = 10 0 0 0 . 0 /T (K) ( 1 /K) 7 1 0 - 2 

N 

9.98*10E 4 

8910.00 

1970.00 

838.00 

490.00 

261.00 

121.00 

AUTHOR 

NAPOLITANO AND HAWKINS (1964) 

DERIVED FROM 

TABLE 3 

P = 1.0 ATM. 

Z = 10 0 0 0 . 0 /T (K) ( 1 /K) 7 1 0 - 3 

N 

1.11*10E 5 

3.99*10E 4 

1.04*10E 4 

5640.00 

2680.00 

817.00 

713.00 

299.00 

129.00 
SYSTEM 

SS 710 (SAMPLE 4) 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N ~POISES) T DEGREES C) 

T Z LN(N) 

904.7 8.491 11.582 

963.4 8.088 10.226 

996.5 7.877 9.586 

1103.1 7.267 7.914 

1123.0 7.163 7.635 

1214.8 6.721 6.569 

1315.7 6.294 5.611 

1414.5 5.926 4.776 

SYSTEM 

SS 710 (SAMPLE 5) 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

903.0 8.503 

954.4 8.147 

963.5 8.087 

1054.8 7.531 

1104.5 7.260 

1149.9 7.028 

1194.3 6.815 

1250.4 6.564 

1250.8 6.563 

1338.5 6.205 

1399.8 5.978 

1402.7 5.968 

LN(N) 

11.511 

10.493 

10.157 

8.609 

7.898 

7.285 

6.786 

6.173 

6.180 

5.321 

4.847 

4.794 

LOG(N) 

5.030 

4.441 

4.163 

3.437 

3.316 

2.853 

2.437 

2.074 

LOG(N) 

4.999 

4.557 

4.411 

3.739 

3.430 

3.164 

2.947 

2.681 

2.684 

2.311 

2.105 

2.082 

AUTHOR 

NAPOLITANO AND HAWKINS (1964) 

DERIVED FROM 

TABLE 3 

p = 1.0 A'IM. 

z = 10000.0/T(K) (1/K) 710-4 

N 

1.07*10E 5 

2.76*10E 4 

1.46*10E 4 

2740.00 

2070.00 

713.00 

274.00 

119.00 

AUTHOR 

NAPOLITANO AND HAWKINS (1964) 

DERIVED FROM 

TABLE 3 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 7 1 0-5 

N 

9.98*10E 4 

3.61*10E 4 

2.58*10E 4 

5480.00 

2690.00 

1460.00 

885.00 

480.00 

483.00 

205.00 

127.00 

121.00 

Standard Glasses 515 
:!! 

0'1 

~ 

~ ;:::;: 

-< 

a 

~ 

g:. = 

~. I") 

tlol 

= c. 

z 

~ c 

iil 

-

~ -w ~ l/) 

"' tlol 

= c. 

C1 

~ 

"' "' 

~ 

0 

Q_ 

>-

J6 ~--~--~----~----~--~----~--~~--~----~--~----~----~ 

5 

Na- Ca- Si02 GLASS 

NBS Standard Glass No. 710 (Samples No. 1-5) 

NAPOLITANO and HAWKINS (1964) 

0 4 

u 

l/) 

> 

l') 

g 

3 

2 ~--~--~----~--~~--~----~--~----~--~----~--~~--~ 

850 950 1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
-w 

V) 

0 

a... 

-

>- ....._ 

5 

l/') 4 

0 

u 

l/') 

> 

<:) 

g 

3 

Na- Ca- Si02 GLASS 

NBS Standard Glass No. 710 (Samples No.1-5) 

NAPOLITANO and HAWKINS (1964) 

2 ----------~----------~----------------~--~ 

5 6 7 8 9 

10 000/T (KELVINS-1) 

Standard Glasses 517 
SYSTEM 

SRM 710 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

FIBER ELONGATION 

N ~POISES) T DEGREES C) 

T 

519.2 

529.4 

538.4 

548.9 

556.6 

558.3 

560.2 

564.7 

565.7 

569.4 

571.6 

574:6 

575.8 

580.4 

585.2 

590.6 

600.1 

603.2 

609.8 

618.7 

626.5 

628.4 

633.9 

639.6 

648.0 

SYSTEM 

SRM 710 

z 

12.623 

12.463 

12.324 

12.167 

12.054 

12.029 

12.002 

11.937 

11.923 

11.871 

11.840 

11.798 

11.781 

11.718 

11.652 

11.587 

11.453 

11.413 

11.328 

11.215 

11.117 

11.094 

11.027 

10.958 

10.858 

LN(N) 

34.649 

32.674 

31.785 

30.820 

29.860 

29.597 

29.360 

28.750 

28.736 

28.347 

28.098 

27.778 

27.631 

27.180 

26.814 

26.307 

25.480 

25.107 

24.665 

24.030 

23.357 

23.180 

22.837 

22.413 

22.073 

(SODA-LIME SILICA GLASS) 

MEASUREMENT METHOD 

BEAM BENDING 

N ~POISES) 

T rfDEGREES ~) 

510.8 12.758 

518.5 12.634 

525.3 12.527 

536.1 12.359 

540.4 12.294 

548.0 12.180 

554.9 12.079 

562.8 11.965 

563.0 11.962 

569.5 11.869 

579.8 11.726 

589.5 11.594 

595.6 11.513 

600 0 0 11 .. 455 

610.0 11.325 

619.9 11.199 

629.4 11.082 

640.0 10.953 

660.0 10.718 

LN(N) 

35.324 

34.513 

33.279 

31.845 

31.391 

30.620 

29.828 

28.957 

28.950 

28.211 

27.286 

26.505 

25.847 

25.648 

24.387 

23.627 

23.157 

22.729 

21.209 

LOG(N) 

15.048 

14.190 

13.804 

13.385 

12.968 

12.854 

12.751 

12.486 

12.480 

12.311 

12.203 

12.064 

12.000 

11.804 

11.645 

11.425 

11.066 

10.904 

10.712 

10.436 

10.144 

10.067 

9.918 

9.734 

9.586 

LOG(N) 

15.341 

14.989 

14.453 

13.830 

13.633 

13.298 

12.954 

12.576 

12.573 

12.252 

11.850 

11.511 

11.225 

11.139 

10.591 

10.261 

10.057 

9.871 

9.211 

518 Viscosity of Synthetic and Natural Melts and Glasses 

p 

z 

AUTHOR 

NAPOLITANO, SIMMONS, 

BLACKBURN AND CHIDESTER 

DERIVED FROM 

TABLE 1 

= 1. 0 A'IM. 

= 10000.0/T(K) (1/K) 

N 

1.12*10E15 

1.55*10E14 

6.37*10E13 

2.43*10E13 

9.29*10E12 

7.14*10E12 

5.64*10E12 

3.06*10E12 

3.02*10E12 

2.05*10E12 

1.60*10E12 

1.16*10E12 

1.00*10E11 

6.37*10E11 

4.42*10E11 

2.66*10E11 

1.16*10E11 

8.02*10E10 

5.15*10E10 

2.73*10E10 

1.39*10E10 

1.17*10E10 

8.28*10E9 

5.42*10E9 

3.85*10E9 

AUTHOR 

NAPOLITANO, SIMMONS, 

BLACKBURN, AND CHIDESTER 

DERIVED FROM 

TABLE 2 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.19*10E15 

9.75*10E14 

2.84*10E14 

6.76*10E13 

4.30*10E13 

1.99*10El3 

8.99*10E12 

3.77*10E12 

3.74*10E12 

1.79*10E12 

7.08*10E11 

3.24*10E11 

1.68*10E11 

1.38*10Ell 

3.90*10El0 

1.82*10E10 

1.14*10El0 

7.43*10E 9 

1.63*10E 9 

(1974) 

710-6 

(1974) 

710-7 
.-.... 

w 

V') 

-

0 

Cl.. 

............ 

>-

..... 

-

V') 

0 

u 

V') 

-

> 

() 

g 

17~----~----~~----~----~------~----~ 

15 

13 

11 

Na - Ca - Si02 GLASS 

NBS Standard Glass No. 710 (Nos. 710-6, 710 -7) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974) 

9 ~----~----~------~----~------~----~ 

500 600 700 800 

TEMPERATURE (°C) 

Standard Glasses 519 
~ 

LU 

V) 

-

0 

a.. 

....._.. 

>- IV) -

0 

u 

V) 

-

> 

l? 

0 

...J 

17 ~----~------~----~------~------~----~ 

15 

13 

1 1 

Na- Ca- Si02 GLASS 

NBS Standard Glass No. 710 (Nos. 710-6, 710-7) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974) 

9 ~----~------~----~------~------~----~ 

10 11 12 13 

10 000/T (KELVINS- 1

) 

520 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

SRM 711 (BAR NO. 50) 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z 

788.8 9.418 

805.8 9.270 

865.3 8.785 

908.2 8.466 

924.0 8.354 

979.8 7.982 

1046.9 7.576 

1119.4 7.182 

1158.2 6.987 

1217.5 6.709 

1266.7 6.495 

1297.9 6.366 

1320.1 6.277 

SYSTEM 

LN(N) 

11.658 

11.278 

10.023 

9.233 

8.980 

8.124 

7.251 

6.424 

6.035 

5.469 

5.080 

4.826 

4.665 

SRM 711 (BAR NO. 130) 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

912.0 8.439 

970.7 8.041 

1032.2 7.662 

1089.9 7.337 

1126.7 7.144 

1203.6 6.772 

1240.2 6.609 

1298.3 6.364 

1349.0 6.165 

LN(N) 

9.169 

8.248 

7.426 

6.724 

6.353 

5.616 

5.296 

4.835 

4.458 

LOG(N) 

5.063 

4.898 

4.353 

4.010 

3.900 

3.528 

3.149 

2.790 

2.621 

2.375 

2.206 

2.096 

2.026 

LOG(N) 

3.982 

3.582 

3.225 

2.920 

2.759 

2.439 

2.300 

2.100 

1.936 

AUTHOR 

NAPOLITANO AND HAWKINS (1966) 

DERIVED FROM 

TABLE 1 

P=1.0ATM. 

Z = 10 0 0 0 . 0 /T (K) ( 1 /K) 7 1 1 - 1 

N 

1.16*10E 5 

7.91*10E 4 

2.25*10E 4 

1.02*10E 4 

7943.28 

3372.87 

1409.29 

616.60 

417.83 

237.14 

160.69 

124.74 

106.17 

AUTHOR 

NAPOLITANO AND HAWKINS (1966) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

9594.01 

3819.44 

1678.80 

831.76 

574.12 

274.79 

199.53 

125.89 

86.30 

(1/K) 711-2 

------------------------------------------------------------------------------

SYSTEM 

SRM 711 (BAR NO. 205) 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

899.0 8.532 

952.3 8.161 

1009.0 7.800 

1019.6 7.736 

1099.4 7.287 

1103.0 7.267 

1197.9 6.799 

1240.0 6.609 

1300.3 6.356 

1352.3 6.153 

LN(N) 

9.392 

8.540 

7.737 

7.608 

6.643 

6.602 

5.667 

5.296 

4.822 

4.432 

LOG(N) 

4.079 

3.709 

3.360 

3.304 

2.885 

2.867 

2.461 

2.300 

2.094 

1.925 

AUTHOR 

NAPOLITANO AND HAWKINS (1966) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 7 1 1-3 

N 

1.2*10E 4 

5116.82 

2290.87 

2013.72 

767.36 

736.21 

289.07 

199.53 

124.17 

84.14 

Standard Glasses 521 
SYSTEM 

SRM 711 (BAR NO. 280) 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

876.2 8.702 

907.8 8.469 

997.2 7.873 

1012.0 7.782 

1067.7 7.459 

1108.0 7.241 

1166.4 6.947 

1197.8 6.799 

1273.6 6.466 

1321.0 6.274 

1343.3 6.187 

SYSTEM 

LN(N) 

9.809 

9.233 

7.893 

7.668 

6.986 

6.528 

5.961 

5.648 

5.038 

4.651 

4.483 

SRM 711 (BAR NO. 353) 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

799.7 9.322 

847.7 8.923 

925.0 8.347 

997.7 7.870 

1051.0 7.553 

1095.3 7.308 

1164.0 6.959 

1195.0 6.812 

1237.0 6.623 

1285.3 6.417 

1325.0 6.258 

1352.5 6.152 

LN(N) 

11.409 

10.362 

8.964 

7.866 

7.191 

6.684 

5.975 

5.680 

5.301 

4.916 

4.630 

4.428 

LOG(N) 

4.260 

4.010 

3.428 

3.330 

3.034 

2.835 

2.589 

2.453 

2.188 

2.020 

1.947 

LOG(N) 

4.955 

4.500 

3.893 

3.416 

3.123 

2.903 

2.595 

2.467 

2.302 

2.135 

2.011 

1.923 

522 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

NAPOLITANO AND HAWKINS (1966) 

DERIVED FROM 

TABLE 1 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 7 11-4 

N 

1.82*10E 4 

1.02*10E 4 

2679.17 

2137.96 

1081.43 

683.91 

388.15 

283.79 

154.17 

104.71 

88.51 

AUTHOR 

NAPOLITANO AND HAWKINS (1966) 

DERIVED FROM 

TABLE 1 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

9.02*10E 4 

3.16*10E 4 

7816.28 

2606.15 

1327.39 

799.83 

393.55 

293.09 

200.45 

136.46 

102.57 

83.75 

711-5 
~ Ill! 

:I 

Cl.. 

Ill! 

a. 

"' ii:i' 

I 

"" N 

IN 

5.5 r------r---,.---------...-------,r-------------------------. 

....--... 

~ 4.5 

0 

a.. 

.__ 

>-

IQ3.5 

u 

V) 

-

> 

~ 

92.5 

LEAD SILICA GLASS 

NBS Standard Glass No. 711 (Nos. 711-1-711-5) 

NAPOLITANO and HAWKINS (1966) 

1.5 L_i__L~--L_~~~L_~~~~~~~~ 

700 800 900 1000 1100 1200 1300 1400 

TEMPERATURE (°C) 
4.5 

~ 

w 

c./) 

0 

a_ 

-

>- tQ3.5 

u 

c./) 

> 

0 

g 

2.5 

LEAD SILICA GLASS 

NBS Standard Glass No. 711 (Nos. 711-1- 711- 5) 

NAPOLITANO and HAWKINS (1966) 

1.5 ~----11.....------'-----L-----&.-----&.----'---~----' 

6 7 8 9 10 

10 000/T (KELVINS-1) 

524 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

SRM 711 

(LEAD SILICA GLASS) 

MEASUREMENT METHOD 

FIBER ELONGATION 

N ~POISES) T DEGREES C) 

T 

396.3 

411.1 

414.5 

420.7 

422.3 

431.5 

441.3 

441.9 

451.4 

456.0 

460.7 

466.2 

470.1 

475.3 

482.2 

488.2 

491.3 

495.4 

501.5 

506.5 

511.9 

516.9 

521.9 

526.7 

535.7 

SYSTEM 

SRM 711 

z 

14.941 

14.618 

14.545 

14.415 

14.382 

14.194 

14.000 

13.988 

13.805 

13.717 

13.630 

13.528 

13.457 

13.364 

13.242 

13.137 

13.084 

13.014 

12.912 

12.829 

12.740 

12.660 

12.580 

12.505 

12.366 

LN(N) 

35.278 

33.275 

32.925 

32.068 

31.935 

30.921 

29.708 

29.729 

28.646 

28.276 

27.728 

27.299 

26.781 

26.500 

25.794 

25.299 

25.015 

24.684 

24.327 

23.945 

23.496 

23.176 

22.789 

22.397 

21.888 

LEAD SILICA GLASS 

MEASUREMENT METHOD 

BEAM BENDING 

N (POISES) 

T (DEGREES C) T Z 

398.0 14.903 

408.3 14.678 

420.8 14.413 

430.2 14.221 

434.3 14.138 

441.6 13.994 

448.8 13.854 

452.9 13.776 

458.1 13.678 

475.3 13.364 

479.6 13.287 

494.9 13.023 

502.0 12.903 

502.0 12.903 

503.0 12.887 

510.4 12.765 

520.9 12.596 

LN(N) 

34.810 

33.645 

32.123 

30.997 

30.495 

29.731 

29.029 

28.805 

27.963 

26.641 

25.870 

24.824 

24.133 

24.380 

24.004 

23.737 

22.957 

LOG(N) 

15.321 

14.451 

14.299 

13.927 

13.869 

13.429 

12.902 

12.911 

12.441 

12.280 

12.042 

11.856 

11.631 

11.509 

11.202 

10.987 

10.864 

10.720 

10.565 

10.399 

10.204 

10.065 

9.897 

9.727 

9.506 

LOG(N) 

15.118 

14.612 

13.951 

13.462 

13.244 

12.912 

12.607 

12.510 

12.144 

11.570 

11.235 

10.781 

10.481 

10.588 

10.425 

10.309 

9.970 

p = 

z = 

AU1HOR 

NAPOLITANO, SIMMONS 

BLACKBURN AND CHIDESTER 

DERIVED FROM 

TABLE 3 

1.0 ATM. 

10000.0/T(K) (1/K) 

N 

2.09*10E15 

2.82*10E14 

1.99*10E14 

8.45*10E13 

7.40*10E13 

2.69*10E13 

7.98*10E12 

8.15*10E12 

2.76*10E12 

1.91*10E12 

1.10*10E12 

7.18*10E11 

4.28*10E11 

3.23*10E11 

1.59*10E11 

9.71*10E10 

'7. 31*10E10 

5.25*10E10 

3.67*10E10 

2.51*10E10 

1.60*10E10 

1.16*10E10 

7.89*10E 9 

5.33*10E 9 

3.21*10E 9 

AU1HOR 

NAPOLITANO, SIMMONS, 

BLACKBURN AND CHIDESTER 

DERIVED FROM 

TABLE 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.31*10E15 

4.09*10E14 

8.93*10E13 

2.90*10E13 

1.75*10E13 

8.17*10E12 

4.05*10E12 

3.24*10E12 

1.39*10E12 

3.72*10E11 

1.72*10E11 

6.04*10E10 

3.03*10E10 

3.87*10E10 

2.66*10E10 

2.04*10E10 

9.33*10E 9 

(1974) 

711-6 

(1974) 

711-7 

Standard Glasses 525 
..--..... 

w 

V') 

-

0 

a... 

........ 

>- 1--

-

V') 

o. 

u 

V') 

-

> 

0 

g 

17 ~----~------~----~------~------~-----, 

15 

13 

11 

LEAD SILICA GLASS 

NBS Standard Glass No. 711 (Nos. 711-6-711-7) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974) 

9 ~----~------~----~------~------~~--~ 

300 400 500 600 

TEMPERATURE (°C) 

526 Viscosity of Synthetic and Natural Melts and Glasses 
........... 

w 

V') 

-

0 

a.. 

..__.. 

>- t-

-

V') 

0 

u 

V') 

-

> 

~ 

0 

.....J 

17~----~------------~----~------~----~ 

15 

13 

11 

LEAD SILICA GLASS 

NBS Standard Glass No.711 (Nos. 711-6-711-7) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974} 

9 ~----~----~------~----~------~----~ 

12 13 14 15 

10 000/T (KELVINS- 1

) 

Standard Glasses 527 
SYSTEM 

SRM 717 (STRIP NO. 70) 

(BOROSILICATE GLASS} 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N ~POISES) 

T tDEGREES ~) 

636.6 10.994 

643.2 10.915 

681.0 10.482 

749.8 9.777 

835.8 9.019 

893.4 8.573 

914.4 8.422 

1078.9 7.397 

1177.5 6.894 

1283.5 6.425 

1359.6 6.125 

SYSTEM 

LN(N) 

21.598 

21.168 

19.187 

16.328 

13.670 

12.243 

11.831 

8.856 

7.631 

6.562 

5.915 

SRM 717 (STRIP NO. 100) 

(BOROSILICATE GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N ~POISES) T DEGREES C) 

T z LN(N) 

599.3 11.464 23.979 

600.8 11.444 23.627 

652.0 10.811 20.758 

704.3 10.232 18.248 

725.9 10.011 17.348 

763.7 9.646 15.962 

804.5 9.281 14.631 

858.8 8.835 13.102 

909.8 8.455 11.870 

935.0 8.278 11.395 

983.2 7.961 10.440 

1051.0 7.553 9.284 

1144.2 7.056 8.089 

1250.4 6.564 6.850 

1300.3 6.356 6.477 

1333.7 6.224 6.194 

1401.2 5.973 5.653 

LOG(N) 

9.380 

9.193 

8.333 

7.091 

5.937 

5.317 

5.138 

3.846 

3.314 

2.850 

2.569 

LOG(N) 

10.414 

10.261 

9.015 

7.925 

7.534 

6.932 

6.354 

5.690 

5.155 

4.949 

4.534 

4.032 

3.513 

2.975 

2.813 

2.690 

2.455 

528 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

NAPOLITANO AND HAWKINS (1970) 

DERIVED FROM 

TABLE 1 

P = 1.0 A'IM. 

Z = 10 0 0 0 . 0 /T (K) ( 1 /K) 7 1 7 - 1 

N 

p 

2.40*10E 9 

1.56*10E 9 

2.15*10E 8 

1.23*10E 7 

8.65*10E 5 

2.07*10E 5 

1.37*10E 5 

7014.55 

2060.63 

707.95 

370.68 

AUTHOR 

NAPOLITANO AND HAWKINS 

DERIVED FROM 

TABLE 1 

= 1.0 A'IM. 

z = 10000.0/T(K) (1/K) 

N 

2.59*10E10 

1.82*10E10 

1.04*10E 9 

8.41*10E 7 

3.42*10E 7 

8.55*10E 6 

2.26*10E 6 

4.90*10E 5 

1.43*10E 5 

8.89*10E 4 

3.42*10E 4 

1.08*10E 4 

3258.37 

944.06 

650.13 

489.78 

285.10 

(1970) 

717-2 
SYSTEM 

SRM 717 (STRIP NO. 125) 

(BOROSILICATE GLASS) 

MEASUREMENT METHOD 

FIBER ELONGATION 

N (POISES) 

T (DEGREES C) T Z 

607.0 11.364 

619.5 11.204 

709.3 10.180 

781.7 9.481 

810.9 9.226 

908.2 8.466 

929.9 8.313 

996.2 7.879 

1027.0 7.692 

1095.0 7.310 

1129.6 7.130 

1195.3 6.811 

1227.7 6.664 

1294.7 6.379 

1320.7 6.275 

1377.0 6.061 

1408.9 5.946 

SYSTEM 

LN(N) 

23.367 

22.561 

18.006 

15.347 

14.442 

11.934 

11.492 

10.237 

9.703 

8.688 

8.266 

7.467 

7.143 

6.489 

6.279 

5.823 

5.591 

SRM 717 (STRIP NO. 85) 

(BOROSILICATE GLASS) 

MEASUREMENT METHOD 

ROTATING CYLINDER 

N (POISES) 

T (DEGREES C) T Z 

613.4 11.282 

710.9 10.164 

798.6 9.332 

901.8 8.512 

1010.7 7.790 

1104.3 7.261 

1196.0 6.807 

1302.6 6.347 

1400.1 5.977 

LN(N) 

23.014 

17.988 

14.833 

12.098 

9.975 

8.602 

7.483 

6.436 

5.664 

LOG(N) 

10.148 

9.798 

7.820 

6.665 

6.272 

5.183 

4.991 

4.446 

4.214 

3.773 

3.590 

3.243 

3.102 

2.818 

2.727 

2.529 

2.428 

LOG(N) 

9.995 

7.812 

6.442 

5.254 

4.332 

3.736 

3.250 

2.795 

2.460 

AUTHOR 

NAPOLITANO AND HAWKINS (1970) 

DERIVED FROM 

TABLE 1 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.41*10E10 

6.28*10E 9 

6.61*10E 7 

4.62*10E 6 

1.87*10E 6 

1.52*10E 5 

9.79*10E 4 

2.79*10E 4 

1.64*10E 4 

5929.25 

3890.45 

1749.85 

1264.74 

657.66 

533.33 

338.06 

267.92 

AUTHOR 

NAPOLITANO AND HAWKINS (1970) 

DERIVED FROM 

TABLE 1 

717- 3 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 7 17-4 

N 

9.89*10E 9 

6.49*10E 7 

2.77*10E 6 

1.79*10E 5 

2.15*10E 4 

5445 0 \)3 

1778.L.8 

623.7J 

-288.40 

Standard Glasses 529 
(oil 

w 

0 

< §" 

~ 

9. 

~ 

a !" 10.5 

;:;· 

Dl 

5. 

z 

~ !!. 

3': 

tD 

= Dl 

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[ 

-w 

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0 

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BOROSILICATE GLASS 

NBS Standard Glass No. 717 (Nos. 717-1-717-4) 

NAPOLITANO and HAWKINS (1970) 

2.5 ....____-.L--.L..--~-~---~--------.L...-~-...1....---L-~-~---------~---L-...........-:=--.,.a.------J 

550 650 750 850 950 1050 1150 1250 1350 1450 

TEMPERATURE (°C) 
[ 

I» 

a 

~ 

r 

!i 

~ 

~ 

""" 

BOROSILICATE GLASS 

95 NBS Standard Glass No. 717 (Nos. 717-1-717-4) 

NAPOLITANO and HAWKINS {1970/ 

-

~ 75 

0 

a.. 

-

>-

...... 

c.l) 

0 

u 

c.l) 5.5 

> 

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g 

3.5 

1.5 L__L __ ~ __ L__L __ i_~L_~--~~~~~~~ 

5.5 6.5 Z5 &5 95 10.5 11.5 

10 000/T (KELVINS-1) 
SYSTEM 

SRM 717 

BOROSILICATE GLASS 

MEASUREMENT METHOD 

FIBER ELONGATION 

N (POISES) T (DEGREES C) T Z 

470.9 13.443 

485.5 13.184 

501.1 12.918 

515.0 12.690 

528.7 12.473 

539.5 12.308 

549.0 12.165 

555.2 12.074 

556.0 12.063 

560.0 12.005 

564.0 11.947 

564.4 11.942 

568.6 11.882 

574.4 11.801 

577.6 11.756 

580.8 11.712 

580.9 11.711 

585.5 11.648 

590.4 11.582 

596.0 11.507 

600.2 11.452 

600.4 11.450 

LN(N) 

35.082 

33.625 

32.045 

30.797 

29.445 

28.460 

27.689 

27.069 

27.161 

26.793 

26.533 

26.519 

26.259 

25.715 

25.501 

25.287 

25.259 

24.856 

24.546 

24.039 

23.737 

23.758 

605.0 11.390 23.507 

610.8 11.315 23.090 

614.9 11.263 22.869 

620.7 11.189 22.547 

LOG(N) 

15.236 

14.603 

13.917 

13.375 

12.788 

12.360 

12.025 

11.756 

11.796 

11.636 

11.523 

11.517 

11.404 

11.168 

11.075 

10.982 

10.970 

10.795 

10.660 

10.440 

10.309 

10.318 

10.209 

10.028 

9.932 

9.792 

532 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

NAPOLITANO, SIMMONS, 

BLACKBURN, AND CHIDESTER 

DERIVED FROM 

TABLE 5 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

1.72*10E15 

4.01*10E14 

8.26*10E13 

2.37*10E13 

6.14*10E12 

2.29*10E12 

1.06*10E12 

5.70*10E11 

6.25*10E11 

4.33*10E11 

3.33*10E11 

3.29*10E11 

2.54*10E11 

1.47*10E11 

1.19*10E11 

9.59*10E10 

9.33*10E10 

6.24*10E10 

4.57*10E10 

2.75*10E10 

2.04*10E10 

2.08*10E10 

1.62*10E10 

1.07*10E10 

8.55*10E 9 

6.19*10E 9 

(1974) 

717-5 
SYSTEM 

SRM 717 

BOROSILICATE GLASS 

MEASUREMENT METI-IOD 

BEAM-BENDING 

N (POISES) T (DEGREES C) 

T Z 

460.0 13.643 

482.6 13.235 

490.8 13.092 

501.7 12.908 

508.0 12.804 

517.7 12.647 

526.6 12.506 

542.0 12.270 

544.3 12.235 

550.7 12.140 

555 .. 2 12.074 

563.1 11.960 

573.4 11.815 

575.0 11.792 

585.1 11.654 

591.0 11.574 

594.3 11.530 

613.3 11.283 

615.3 11.257 

616.5 11.242 

618.1 11.222 

LN(N) 

36.270 

33.924 

33.084 

32.220 

31.329 

30.307 

29.586 

28.340 

28.140 

27.495 

27.099 

26.544 

25.992 

25.741 

24.919 

24.596 

24.419 

23.268 

22.895 

22.786 

22.722 

LOG(N) 

15.752 

14.733 

14.368 

13.993 

13.606 

13.162 

12.849 

12.308 

12.221 

11.941 

11.769 

11.528 

11.288 

11.179 

10.822 

10.682 

10.605 

10.105 

9.943 

9.896 

9.868 

AUTHOR 

NAPOLITANO, SIMMONS, 

BLACKBURN, AND CHIDESTER 

DERIVED FROM 

TABLE 6 

P = 1. 0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

5.65*10E15 

5.41*10E14 

2.33*10E14 

9.84*10E13 

4.04*10E13 

1.45*10E13 

7.06*10E12 

2.03*10E12 

1.66*10E12 

8.73*10E11 

5.87*10E11 

3.37*10E11 

1.94*10E11 

1.51*10E11 

6.64*10E10 

4.81*10E10 

4.03*10E10 

1.27*10E10 

8.77*10E 9 

7.87*10E 9 

7.38*10E 9 

(1974) 

717-6 

Standard Glasses 533 
.......... 

lU 

(./) 

0 

a.. 

___.. 

>- 1-

-(./) 

0 

u 

(./) 

-

> 

0 

g 

17 ~----~------~----~------~------~----~ 

15 

13 

11 

BOROSILICATE GLASS 

NBS Standard Glass No. 717 (Nos. 717-5, 717-6) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974) 

9 ------~------~----~------~------~------

400 500 600 700 

TEMPERATURE {°C) 

534 Viscosity of Synthetic and Natural Melts and Glasses 
.....--

UJ 

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-

0 

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11 

BOROSILICATE GLASS 

NBS Standard Glass No. 717 (Nos. 717-5, 717-6) 

NAPOLITANO, SIMMONS, BLACKBURN and CHIDESTER (1974} 

9 ~----~------~----~----~------~----~ 

11 12 13 14 

10 000/T (KELVINS- 1

) 

Standard Glasses 535 

Commercial Glasses 

Commercial Glasses 537 
SYSTEM 

GLASS NO. 1 

R20(14.22) ,R0(10.68),R203(0.66), 

SI02 (74. 59) (%) 

MEASUREMENT METHOD 

CONCEN'IRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1000.00 7.855 9.662 4.196 

1100.00 7.283 8.015 3.481 

1300.00 6.357 5.724 2.486 

SYSTEM 

GLASS NO. 2 

R20(13.54) ,R0(9.83),R203(0.5), 

SI02 (74 .13) (%) 

MEASUREMENT METHOD 

CONc;ENIRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1000.00 7.855 9.800 4.256 

1100.00 7.283 8.170 3.548 

1300.00 6.357 5.902 2.563 

SYSTEM 

GLASS NO. 3 

R20(13.54) ,R0(9.83),R203(1.5), 

SI02 (74 .13) (%) 

MEASUREMENT METHOD 

CONCEN'IRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1000.00 7.855 9.961 4.326 

1100.00 7.283 8.404 3.650 

1300.00 6.357 6.132 2.663 

SYSTEM 

GLASS NO. 10 

R20(14.22) ,R0(10.68),R203(0.66), 

SI02 (74. 59) (%) 

MEASUREMENT METHOD 

CONCEN'IRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 

1000.00 7.855 9.510 4.130 

1100.00 7.283 8.006 3.477 

1300.00 6.357 5.941 2.580 

538 Viscosity of Synthetic and Natural Melts and Glasses 

AUI'f.IOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 4 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

15703.63 

3026.91 

306.20 

AUTHOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 4 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

18030.18 

3531.83 

365.59 

AUTHOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

21183.61 

4466.84 

460.26 

AUTHOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

13489.63 

2999.16 

380.19 

CG-1 

CG-2 

CG- 3 

CG-4 
SYSTEM 

GLASS NO. 460 

R20(13.54) ,R0(9.83) ,R203(2.76), 

SI02 (.74 .13) (%) 

MEASUREMENT METHOD 

CONCENTRIC CYLINDER 

N (POISES) 

T (DEGREES C) 

T Z LN(N) LOG(N) 1000.00 7.855 9.210 4.000 

1100.00 7.283 8.130 3.531 

1300.00 6.357 6.537 2.839 

AUTHOR 

LILLIE (1929) 

DERIVED FROM 

FIG. 4 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10000.0 

3396.25 

690.24 

CG-5 

Commercial Glasses 539 
~ 

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0 

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6 

5 

4 

3 

COMMERCIAL GLASSES 

LILLIE (1929) 

2 ~----~------~------~----~------~----~ 

1000 1100 1200 1300 

TEMPERATURE (°C) 

540 Viscosity of Synthetic and Natural Melts and Glasses 
......--. 

w 

(./') 

-

0 

a... 

__.... 

>- 1-

-

(./') 

0 

u 

(./') 

-

> 

l? 

0 

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6 ~----~----~------~----~------~----~ 

5 

4 

3 

COMMERCIAL GLASSES 

LILLIE (1929) 

CG-3 

CG-2 

CG-1 

CG-4 

CG-5 

2 ~----~----~------~----~------~----~ 

6 7 8 9 

10 000/T (KELVINS- 1

) 

Commercial Glasses 541 
SYSTEM 

GLASS I 

MEASUREMENT METHOD 

FIBER ELONGATION 

(ANNEALING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

509.00 12.788 30.855 

519.00 12.626 29.934 

545.00 12.225 27.631 

570.00 11.862 25.328 

596.00 11.507 23.026 

624.00 11.148 20.723 

658.00 10.741 18.421 

SYSTEM 

GLASS II 

MEASUREMENT METHOD 

FIBER ELONGATION 

(ANNEALING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

515.00 12.690 30.855 

525.00 12.531 29.934 

551.00 12.136 27.631 

577.00 11.765 25.328 

604.00 11.403 23.026 

633.00 11.038 20.723 

668.00 10.627 18.421 

SYSTEM 

GLASS III 

MEASUREMENT METHOD 

FIBER ELONGATION 

(ANNEALING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

501.00 12.920 30.855 

511.00 12.755 29.934 

537.00 12.346 27.631 

563.00 11.962 25.328 

589.00 11.601 23.026 

619.00 11.211 20.723 

652.00 10.811 18.421 

LOG(N) 

13.4 

13.0 

12.0 

11.0 

10.0 

9.0 

8.0 

LOG (N) 

13.4 

13.0 

12.0 

11.0 

10.0 

9.0 

8.0 

LOG(N) 

13.4 

13.0 

12.0 

11.0 

10.0 

9.0 

8.0 

542 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.51*10E13 

1.0*10E13 

1.0*10E12 

1.0*10E11 

1.0*10E10 

1.0*10E 9 

1.0*10E 8 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

-2 .51*10E13 

1.0*10E13 

1.0*10E12 

1.0*10E11 

1.0*10E10 

1.0*10E 9 

1.0*10E 8 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

2.51*10E13 

1.0*10E13 

1.0*10E12 

1.0*10E11 

1.0*10E10 

1.0*10E 9 

l.O*lOE 8 

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CG-7 a 

CG-8a 
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tCommercial Glasses 543 
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(3SIOd) AliSO)SIA 901 

544 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

GLASS I 

MEASUREMENT METHOD 

FIBER ELONGATION 

(SOFTENING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

670.00 10.604 17.615 

702.00 10.256 16.118 

759.00 9.690 13.816 

793.00 9.381 12.664 

833.00 9.042 11.513 

888.00 8.613 10.362 

936.00 8.271 9.210 

1004.00 7.831 8.059 

1087.00 7.353 6.908 

1194.00 6.817 5.756 

1325.00 6.258 4.605 

LOG(N) 

7.65 

7.00 

6.00 

5.50 

5.00 

4.50 

4.00 

3.50 

3.00 

2.50 

2.00 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000.0/T(K) (1/K) 

N 

4.47*10E 7 

1.00*10E 7 

1.00*10E 6 

3.16*10E 5 

1.00*10E 5 

3.16*10E 4 

1.00*10E 4 

3162.28 

1000.00 

316.23 

100.00 

CG-6b 

-------------------------------------------------------------------------~----

SYSTEM 

GLASS II 

MEASUREMENT METHOD 

FIBER ELONGATION 

(SOFTENING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

679.00 10.504 17.615 

709.00 10.183 16.118 

768.00 9.606 13.816 

803.00 9.294 12.664 

845.00 8.945 11.513 

903.00 8.503 10.362 

953.00 8.157 9.210 

1024.00 7.710 8.059 

1109.00 

1206.00 

1352.00 

SYSTEM 

7.236 

6.761 

6.154 

6.908 

5.756 

4.605 

GLASS III 

MEASUREMENT METHOD 

FIBER ELONGATION 

(SOFTENING POINT) 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

665.00 10.661 17.615 

696.00 10.320 16.118 

752.00 9.756 13.816 

798.00 9.337 12.664 

832.00 9.050 11.513 

891.00 8.591 10.362 

940.00 8.244 9.210 

1012.00 7.782 8.059 

1102.00 7.273 6.908 

1200.00 6.789 5.756 

1346.00 6.177 4.605 

LOG(N) 

7.65 

7.00 

6.00 

5.50 

5.00 

4.50 

4.00 

3.50 

3.00 

2.50 

2.00 

LOG(N) 

7.65 

7.00 

6.00 

5.50 

5.00 

4.50 

4.00 

3.50 

3.00 

2.50 

2.00 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.47*10E 7 

1.00*10E 7 

1.00*10E 6 

3.16*10E 5 

1.00*10E 5 

3.16*10E 4 

1.00*10E 4 

3162.28 

1000.00 

361.23 

100.00 

AUTHOR 

LILLIE (1931) 

DERIVED FROM 

FIG. 3 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

4.47*10E7 

1.00*10E7 

1.00*10E6 

3.16*10E5 

1.00*10E5 

3.16*10E4 

1.00*10E4 

3162.28 

1000.0 

316.23 

100.00 

CG-7b 

CG-8b 

Commercial Glasses 545 
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(3SIOd) AliSOJSIA 901 

546 Viscosity of Synthetic and Natural Melts and Glasses 

0 

0 

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COMMERCIAL SILICA GLASSES 

LILLIE (1931) 

~ CG-8b 

7 8 9 10 

10 000/T (KELVINS-1

) 

CG-6a --/ 

11 12 13 
1.11 

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500 600 700 800 900 1000 1100 1200 1300 1400 

TEMPERATURE (°C) 
SYSTEM 

RENNANLAGE LARYMNA 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

"'9.903 

8.795 

7.832 

7.048 

6.446 

RENNANLAGE AVILES 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

LOG(N) N 

"'4.301 "'20000. 

3.820 6600. 

3.401 2520. 

3.061 1150. 

2.799 630. 

AUTHOR 

JOHANNSEN AND BRUNION (1959) 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

CG-9 

N (POISES) 

T (DEGREES C) 

T Z LN(N) 

z = 10 0 0 0 . 0 /T (K) ( 1/K) c G - 1 0 

LOG(N) N 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

"'9.741 

9.197 

8.343 

7.550 

6.908 

6.354 

RENNANAGE WATENSTEDT 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

9.259 

8.357 

7.467 

6.709 

6.087 

5.521 

"'4.230 "'17000. 

3.994 9870. 

3.623 4200. 

3.279 1900. 

3.000 1000. 

2.760 575. 

LOG(N) 

4.021 

3.629 

3.243 

2.914 

2.643 

2.398 

AUTHOR 

JOHANNSEN AND BRUNION 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

10500. 

4260. 

1750. 

820. 

440. 

250. 

AUTHOR 

RENN-WAELZANLAGE STUERZELBERG 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

JOHANNSEN AND BRUNION 

DERIVED FROM 

TABLE 2 

N (POISES) 

T (DEGREES C) T Z 

1150.06 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

9.413 

8.487 

7.682 

6.947 

6.328 

5.799 

LOG(N) 

4.088 

3.686 

3.336 

3.017 

2.748 

2.519 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

12300. 

4850. 

2170. 

1040. 

560. 

330. 

(1959) 

CG -11 

(1959) 

CG-12 

Commercial Glasses 549 
SYSTEM 

RENN -WAELZANLAGE NORDENHAM 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

8.802 

7.941 

7.139 

6.461 

5.814 

5.193 

RENN-WAELZANLAGE BERZELIUS 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

SYSTEM 

LN(N) 

7.307 

6.646 

5.966 

5.247 

4.700 

3.912 

SCHACHTOFEN MANSFELD 

MEASUREMENT METHOD 

ROTATIONAL VISCOMETER 

N (POISES) 

T (DEGREES C) 

T Z 

1150.00 7.027 

1200.00 6.789 

1250.00 6.566 

1300.00 6.357 

1350.00 6.161 

1400.00 5.977 

LN(N) 

6.551 

5.635 

5.011 

4.500 

4.007 

3.401 

LOG(N) 

3.823 

3.449 

3.100 

2.806 

2.525 

2.255 

LOG(N) 

3.173 

2.886 

2.591 

2.279 

2.041 

1.699 

LOG(N) 

2.845 

2.447 

2.176 

1.954 

1.740 

1.477 

550 Viscosity of Synthetic and Natural Melts and Glasses 

AUTHOR 

JOHANNSEN AND BRUNION (1959) i 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000.0/T(K) 

N 

6650. 

2810. 

1260. 

640. 

335. 

180. 

AUTHOR 

(1/K) 

JOHANNSEN AND BRUNION 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000-.0/T(K) (1/K) 

N 

1490. 

770. 

390. 

190. 

110. 

50. 

AUTHOR 

JOHANNSEN AND BRUNION 

DERIVED FROM 

TABLE 2 

P = 1.0 ATM. 

Z = 10000. 0/T (K) (1/K) 

N 

700. 

280. 

150. 

90. 

55. 

30. 

(1959) 

(1959) 

CG-13 

CG-14 

CG-15 
.......... 

UJ 

V") 

0 

0.. 

.........,_ 

>-

~ 

-

V") 

0 

u 

V") 

-

> 

l? 

0 

__. 

5 ~----~--------------------~------~----~ 

4 

3 

2 

1 

1100 

CG-10 

CG-12 

CG-11 

CG-13 

CG-14 

CG-15 

COMMERCIAL SILICA GLASSES 

.JOHANNSEN and BRUNtON (1959/ 

1200 1300 1400 

TEMPERATURE (°C) 

Commercial Glasses 551 
5 ~----~------~------~------~------~----~ 

COMMERCIAL SILICA GLASSES 

JOHANNSEN and BRUNtON (19.59) 

CG-10 

CG-12 

4 CG-11 

CG-13 

---- LU 

(./") 

-

0 

0... 

-......... 

>- CG-14 

.._ 

-(./") 3 0 

u CG-15 

(./") 

-

> 

0 

0 

__, 

2 

1 

5 6 7 8 

10 000/T (KELVINS- 1

) 

552 Viscosity of Synthetic and Natural Melts and Glasses 
SYSTEM 

SODA-POTASH-LIME-SILICA GLASS 

MEASUREMENT METHOD 

ROTATING-CYC. VISCOMETER 

N (POISES) 

T (DEGREES C) T Z 

700.00 10.277 

800.00 9.320 

900.00 8.525 

1000.00 7.855 

1100.00 7.283 

1200.00 6.789 

1300.00 6.357 

LN(N) 

17.217 

13.661 

11.402 

9.642 

8.304 

7.352 

6.234 

LOG(N) 

7.477 

5.933 

4.952 

4.188 

3.606 

3.193 

2.708 

AUTHOR 

VOLAROVICH AND TOLSTOI 

DERIVED FROM 

TABLE II 

P = 1.0 A'IM. 

Z = 10000. 0/T (K) (1/K) 

N 

3.0*10E7 

8.57*10E5 

89500. 

15400. 

4040. 

1560. 

510. 

(1936) 

CG- 16 

Commercial Glasses 553 
Ul 

Ul 

... 

< w;· 

n 

Q 

8 (II 

~-

s. 

II) 

-< 

~ No- K- Co- Si02 GLASS :I 

:;. 

!!. 

;:::;· 

:I 

Dol VALAROVICH and TOLSTOI /19.16) Cl.. 

z ..-- ~ UJ 6 c: 

.. 

~ (./') 

tD 

~ - ~ 0 

! a.. Cl.. 

~ -

>- i» 

(II 

(II 

m 1--

-(./') 4 0 

u 

(./') 

> 

t? 

0 

__. 2 

0 ~~--~--~--~--~--~--~~~~--~--~--~--~~ 

700 800 900 1000 1100 1200 1300 1400 

TEMPERATURE {°C) 
.......... 

L.U 

V') 

0 

CL 

-

>- 1-

-

8 ~----~--------------~----~~----~------~ 

6 

Na- K- Co- Si02 GLASS 

VOLAROVICH and TOLSTOI (19.36) 

M T. VESUVIUS LAVA 

No-K-Co-Si02 GLASS 

V') 4 

0 

u 

V') 

> 

0 

0 

.....J 

2 

0 ~----~------~------~----~~----~------~ 

5 7 9 1 1 

10 000/T (KELVI NS-1

) 

Commercial Glasses 555 

Indexes 

Indexes 557 
INDEXES 

Two-Component Systems 

Ba0-Si02: 

Bockris and others ( 1955) 32 

Ca0-Si02: 

Bockris and Lowe ( 1954) 36 

Machin and others ( 1952) 43 

Machin and Y ee (1954) 43 

FeO-SiOi: 

Roentgen and others (1956) 44 

K20-Si02: 

Bockris and others (1955) 55 

Li20-Si02: 

Bockris and others (1955) 59 

Shartsis and others (1952) 64 

Mg0-Si02: 

Bockris and others ( 1955) 66 

Riebling ( 1964) 70 

Na20-Si02: 

Bockris and others (1955) 71 

Lillie ( 1939) 76 

Sr0-Si02: 

Bockris and others (1955) 87 

Three-Component Systems 

Al20rCaO-Si02: 

Bills (1963) 92 

Johannsen and Brunion ( 1959) 92 

Kozakevitch ( 1960) 98 

Kushiro (1981) 512 

Machin and Hanna (1945) 129 

Machin and Yee (1948) 133 

Machin and Y ee ( 1954) 159 

Machin and others (1952) 161 

Rossin and others ( 1964) 166 

Al20 3-Mg0-Si02: 

Machin and Y ee (1954) 170 

Riebling (1964) 171 

Al20rK20-Si02: 

N'Dala and others (1984) 169 

Al20rNa20-Si02: 

N'Dala and others (1984) 175 

Mg0-Ca0-Si02: 

Machin and Y ee ( 1954) 176 

Machin and others (1952) 180 

558 Viscosity of Synthetic and Natural Melts and Glasses 

Na20-Ca0-Si02: 

Mackenzie (1957) 183 

NazO-KzO-SiOz: 

Mackenzie ( 1957) 186 

Na20-Li20-Si0z 

Mackenzie ( 1957) 189 

Four-Component Systems 

AI20 3-CaO-CaF2-Si02: 

Bills (1963) 194 

Al20 3-Ca0-Fe0-Si02: 

Johannsen and Brunion (1959) 197 

Al20rCaO-K20-Si02: 

N'Dala and others (1984) 203 

Al20 3-Ca0-Mn0-Si02: 

Johannsen and Brunion (1959) 204 

Al20rCa0-Na20-Si02: 

N' Dala and others (1984) 207 

AI20 3-Ca0-Ti02-Si02: 

Johannsen and Brunion (1959) 208 

Al~OrK 0-Na 0-Si02 

N'Dala and others (1984) 332 

Al20 3-Mg0-Ca0-Si02: 

Hofmann (1959) 212 

Johannsen and Brunion ( 1959) 230 

Machin and Hanna (1945) 235 

Machin and Y ee ( 1954) 253 

Machin and others (1952) 281 

Na20-K20-Ca0-Si02: 

Volarovich and Tolstoi (1936) 554 

Five-Component Systems 

Al20rCa0-BaO-MgO-Si02: 

Hofmann ( 1959) 334 

Al20rCaO-K20-Na20-Si02: 

N'Dala and others (1984) 375 

Six-Component Systems 

Al20 3-Ca0-Mg0-Ba0-Sr0-Si02: 

Hofmaier ( 1968) 378 

Al20 3-Mg0-Ca0-Fe0-Fe20 3-Si02: 

Bills (1963) 381 
Seven-Component Systems 

AI203-CaO-MgO-MnO-~Fe-~S-Si0 : 

H9fmaier (1968) 390 

Al203-Fe20rCaO-MgO-Na20-K20-Si02: 

Lillie ( 1929) 391 

Oxide Systems 

THREE-COMPONENT SYSTEMS 

Al20rCaO-Si02 (Bills, 1963) 92 

Al203-CaO-Si02 (Johannsen and Brunion, 1959) 92 

Al20rCaO-Si02 (Kozakevitch, 1960) 98 

Al20rCaO-Si02 (Machin and Hanna, 1 945) 129 

Al203-CaO-Si02 (Machin and Yee, 1948) 133 

Al203-CaO-Si02 (Machin and Yee, 1954) 159 

Al203-CaO-Si02 (Machin and others, 1952) 161 

Al20rCaO-Si02 (Rossin and others, 1964) 166 

Al20rK20-Si02 (N'Dala and others, 1984) 169 

Al20rMgO-Si02 (Machin and Yee, 1954) 170 

Al203-MgO-Si02 (Riebling, 1964) 171 

Al203-Na20-Si02 (N'Dala and others, 1984) 175 

FOUR-COMPONENT SYSTEMS 

Al20rCaO-CaFrSi02 (Bills, 1963) 194 

Al20rCaO-K20-Si02 (N'Dala and others, 1984) 203 

Al20rCaO-Na20-Si02 (N'Dala and others, 1984) 207 

Al20rK20-Na20-Si02 (N'Dala and others, 1984) 332 

AI20rMgO-CaO-Si02 (Hofmann, 1959) 212 

Al203-MgO-CaO-Si02 (Johannsen and Brunion, 1959) 230 

Al20rMgO-CaO-Si02 (Machin and Hanna, 1945) 235 

Al20rMgO-CaO-Si02 (Machin and Yee, 1954) 253 

AI20rMgO-CaO-Si02 (Machin and others, 1952) 281 

Al20rCaO-FeO-Si02 (Johannsen and Brunion, 1959) 197 

Al20rCaO-MnO-Si02 (Johannsen and Brunion, 1959) 204 

AI20rCaO-Ti02-Si02 (Johannsen and Brunion, 1959) 208 

FIVE-COMPONENT SYSTEM 

Al20rCaO-BaO-MgO-Si02 (Hofmann, 1959) 334 

SIX-COMPONENT SYSTEM 

Al203-MgO-CaO-FeO-Fe20rSi02 (Bills, 1963) 381 

BaO: 

TWO-COMPONENT SYSTEM 

Ba0-Si02 (Bockris and others, 1955) 32 

FIVE-COMPONENT SYSTEM 

Al203-CaO-BaO-MgO-Si02 (Hofmann, 1959) 334 

SIX-COMPONENT SYSTEM 

Al203-CaO-MgO-BaO-SrO-Si02 (Hofmaier, 1968) 378 

CaO: 

TWO-COMPONENT SYSTEMS 

Ca0-Si02 (Bockris and Lowe, 1954) 36 

Ca0-Si02 (Machin and Yee, 1954) 43 

Ca0-Si02 (Machin and others, 1952) 43 

THREE-COMPONENT SYSTEMS 

Al203-CaO-Si02 (Bills, 1963) 92 

Al203-CaO-Si02 (Kozakevitch, 1960) 98 

Al203-CaO-Si02 (Johannsen and Brunion, 1959) 92 

Al203-CaO-Si02 (Machin and Hanna, 1945) 129 

Al203-CaO-Si02 (Machin and Yee, 1948) 133 

Al203-CaO-Si02 (Machin and Yee, 1954) 159 

Al20rCaO-Si02 (Machin and others, 1952) 161 

Al20rCaO-Si02 (Rossin and others, 1964) 166 

Na20-CaO-Si02 (Mackenzie, 1957) 183 

Mg0-Ca0-Si02 (Machin and others, 1954) 180 

Mg0-Ca0-Si02 (Machin and Yee, 1954) 176 

FOUR-COMPONEJ\IT SYSTEMS 

Al203-CaO-CaF2-Si02 (Bills, 1963) 194 

Al203-CaO-K20-Si02 (N'Dala and others, 1984) 203 

Al203-CaO-MnO-Si02 (Johannsen and Brunion, 1959) 204 

Al203-CaO-Na20-Si02 (N'Dala and others, 1984) 207 

Al203-CaO-Ti02-Si02 (Johannsen and Brunion, 1959) 208 

Al203-MgO-CaO-Si02 (Hofmann, 1959) 212 

Al203-MgO-CaO-Si02 (Johannsen and Brunion, 1959) 230 

Al203-MgO-CaO-Si02 (Machin and Hanna, 1945) 235 

Al203-MgO-CaO-Si02 (Machin and Yee, 1954) 253 

Al20rMgO-CaO-Si02 (Machin and others, 1952) 281 

Al203-CaO-FeO-Si02 (Johannsen and Brunion, 1959) 197 

Na20-K20-CaO-Si02 (Volarovich and Tolstoi, 1936) 554 

FIVE-COMPONENT SYSTEMS 

Al203-CaO-BaO-MgO-Si02 (Hofmann, 1959) 334 

Al203-CaO-K20-Na20-Si02 (N'Dala and others, 1984) 375 

SIX-COMPONENT SYSTEMS 

Al203-CaO-MgO-BaO-SrO-Si02 (Hofmaier, 1968) 378 

AI203-MgO-CaO-FeO-Fe20 3-Si02 (Bills, 1963) 381 

SEVEN-COMPONENT SYSTEMS 

Al20rCaO-MgO-MnO-Fe-~S-Si02 (Hofmaier, 1968) 390 

AI203-Fe203-CaO-MgO-Na20-K20-Si02 (Lillie, 1929) 391 

Indexes 559 
FeO: 

TWO-COMPONENT SYSTEM 

Feo...:..si02 (Roentgen and others, 1956) 44 

FOUR-COMPONENT SYSTEM 

Al20 3-Ca0-Fe0-Si02 (Johannsen and Brunion, 1959) 197 

SIX-COMPONENT SYSTEM 

Al20rMgO-CaO-FeO-Fe20rSi02 (Bills, 1963) 381 

SIX-COMPONENT SYSTEM 

SEVEN-COMPONENT SYSTEM 

TWO-COMPONENT SYSTEM 

K20-Si02 (Bockris and others, 1955) 55 

THREE-COMPONENT SYSTEMS 

Al20rK20-Si02 (N'Dala and others, 1984) 169 

Na20-K20-Si02 (Mackenzie, 1957) 186 

FOUR-COMPONENT SYSTEMS 

Al20rCaO-K20-Si02 (N'Dala and others, 1984) 203 

Na20-K20-Ca0-Si02 (Volarovich and Tolstoi, 1936) 554 

Al20rK20-Na20-Si02 (N'Dala and others, 1984) 332 

SEVEN-COMPONENT SYSTEM 

TWO-COMPONENT SYSTEMS 

Li20-Si02 (Bockris and others, 1955) 59 

Li20-Si02 (Shartsis and others, 1952) 64 

THREE-COMPONENT SYSTEM 

MgO: 

TWO-COMPONENT SYSTEMS 

Mg0-Si02 (Bockris and others, 1955) 66 

Mg0-Si02 (Riebling, 1964) 70 

560 Viscosity of Synthetic and Natural Melts and Glasses 

THREE-COMPONENT SYSTEMS 

Al20 3-MgO-Si02 (Machin and Yee, 1954) 170 

Al20 3-Mg0-Si02 (Riebling, 1964) 171 

Mg0-Ca0-Si02 (Machin and others, 1952) 180 

Mg0-Ca0-Si02 (Machin and Yee, 1954) 176 

FOUR-COMPONENT SYSTEMS 

Al20rMgO-CaO-Si02 (Hofmann, 1959) 212 

Al20rMgO-CaO-Si02 (Johannsen and Brunion, 1959) 230 

Al20 3-Mg0-Ca0-Si02 (Machin and Hanna, 1945) 235 

Al20 3-Mg0-Ca0-Si02 (Machin and Yee, 1954) 253 

Al20 3-Mg0-Ca0-Si02 (Machin and others, 1952) 281 

FIVE-COMPONENT SYSTEM 

Al20 3-Ca0-Ba0-Mg0-Si02 (Hofmann, 1959) 334 

SIX-COMPONENT SYSTEMS 

Al20 3-Ca0-Mg0-Ba0-Sr0-Si02 (Hofmaier, 1968) 378 

Al20 3-Mg0-CaO-FeO-Fe20rSi02 (Bills, 1963) 381 

SEVEN-COMPONENT SYSTEMS 

Al 0rCaO-Mg0-Mn0-LFe-~S-Si02 (Hofmaier, 1968) 390 

Al20 3-Fe20rCa0-MgO-Na20-K20-Si02 (Lillie, 1929) 391 

MnO: 

FOUR-COMPONENT SYSTEM 

Al20rCa0-MnO-Si02 (Johannsen and Brunion, 1959) 204 

SEVEN-COMPONENT SYSTEM 

TWO-COMPONENT SYSTEMS 

Na20-Si02 (Bockris and others, 1955) 71 

Na20-Si02 (Lillie, 1939) 76 

THREE-COMPONENT SYSTEMS 

Al20rNa20-Si02 (N'Dala and others, 1984) 175 

Na20-Ca0-Si02 (Mackenzie, 1957) 183 

Na20-K20-Si02 (Mackenzie, 1957) 186 

Na20-Li20-Si02 (Mackenzie, 1957) 189 

FOUR-COMPONENT SYSTEMS 

Al20 3-Ca0-Na20-Si02 (N'Dala and others, 1984) 207 

Na20-K20-Ca0-Si02 (Volarovich and Tolstoi, 1936) 554 

Al20rK20-Na20-Si02 (N'Dala and others, 1984) 332 

SEVEN-COMPONENT SYSTEM 
SrO: 

TWO-COMPONENT SYSTEM 

Sr0-Si02 (Bockris and others, 1955) 87 

SIX-COMPONENT SYSTEM 

Al20rCaO-MgO-BaO-SrO-Si02 (Hofmaier, 1968) 378 

FOUR-COMPONENT SYSTEM 

Al20rCa0-Ti02-Si02 (Johannsen and Brunion, 1959) 208 

Oxides by Author 

[In addition to Si02] 

Al20 3: 

Bills (1963) 92, 194, 381 

Hofmaier ( 1968) 378, 390 

Hofmann ( 1959) 212, 334 

Johannsen and Bruni on ( 1959) 92, 197, 204, 208, 230 

Kozakevitch ( 1960) 98 

Lillie (1929) 391 

Machin and Hanna (1945) 129, 235 

Machin and Y ee (1948) 133 

Machin and Yee (1954) 159, 170, 253 

Machin and others (1952) 161, 281 

N'Dala and others (1984) 169, 175, 203, 207, 332, 375 

Riebling (1964) 171 

Rossin and others (1964) 166 

BaO: 

Bockris and others (1955) 32 

Hofmaier ( 1968) 378 

Hofmann (1959) 334 

CaO: 

FeO: 

Bills (1963) 92, 194, 381 

Bockris and Lowe ( 1954) 36 

Hofmaier (1968) 378, 390 

Hofmann (1959) 212, 334 

Johannsen and Brunion ( 1959) 92, 197, 204, 208, 230 

Kozakevitch ( 1960) 98 

Lillie ( 1929) 391 

Machin and Hanna (1945) 129, 235 

Machin and Yee (1948) 133 

Machin and Yee (1954) 43, 159, 176, 253 

Machin and others (1952) 161, 180, 281 

Mackenzie ( 1957) 183, 186, 189 

N'Dala and others (1984) 203, 207, 375 

Rossin and others (1964) 166 

Volarovich and Tolstoi (1936) 554 

Bills (1963) 381 

Johannsen and Brunion (1959) 197 

Roentgen and others (1956) 44 

Fe20 3: 

K20: 

Bills (1963) 381 

Lillie ( 1929) 391 

Bockris and others ( 1955) 55 

Lillie ( 1929) 391 

Mackenzie ( 1957) 186, 189 

N'Dala and others (1984) 169, 203, 332, 375 

Volarovich and Tolstoi (1936) 554 

MgO: 

Bills (1963) 381 

Bockris and others ( 1955) 66 

Hofmaier ( 1968) 378, 390 

Hofmann (1959) 212, 334 

Johannsen and Brunion ( 1959) 230 

Lillie ( 1929) 391 

Machin and Hanna (1945) 235 

Machin and Yee (1954) 170, 176, 253 

Machin and others ( 1952) 180, 281 

Riebling (1964) 171 

MoO: 

Hofmaier ( 1968) 390 

Johannsen and Brunion ( 1959) 204 

Na20: 

Bockris and others (1955) 71 

Lillie ( 1929) 391 

Lillie (1939) 76 

Mackenzie ( 1957) 183, 186, 189 

N'Dala and others (1984) 175, 207., 322, 375 

Volarovich and Tolstoi (1936) 554 

SrO: 

Bockris and others (1955) 87 

Hofmaier ( 1968) 378 

Ti02: 

Johannsen and Bi-union (1959) 208 

Minerals 

Quartz (Si02) 

Wollastonite (CaSi03) 

Diopside (CaMg(Si03h) 

Anorthite (CaAl2Si30g) 

Diopside (CaMg(Si03h-anorthite 

(CaAl2Si20g). 

Albite (NaA1Si30 8) 

Orthoclase (KAlSi30g) 

Jadeite (NaA1Si206) 

Birch and Dane (1942) 396 

Birch and Dane (1942) 396 

Birch and Dane (1942) 398 

Birch and Dane (1942) 398 

Kushiro (1981) 404 

Scarfe and others (1983) 422 

Birch and Dane ( 1942) 403 

Birch and Dane (1942) 403 

Kushiro ( 1976a) 396 

Two-~omponent Mineral Systems 

Diopside-albite 

Diops.ide-anorthite 

Albite-anorthite 

Anorthite-diopside 

Orthoclase-albite 

Kozu and Kani (1934) 408 

Scarfe and others (1983) 422 

Kozu and Kani (1934) 412 

Kozu and Kani (1934) 416 

Birch and Dane (1942) 420 

Three-Component Mineral Systems 

Diops.ide-albite-anorthite Kozu and Kani (1934) 430 

Indexes 561 
Lithologic 

BASALTS 

Columbia River Basalt (U.S.A.) 

Olivine tholeiite: 

Abyssal 

Makaopuhi lava lake, Hawaii 

1921 flow, Kilauea, Hawaii 

1961 Halemaumau 

eruption, Kilauea, Hawaii. 

Olivine basalt: 

Konoura, Japan 

Gembudo, Japan 

Vogelsburg, Germany 

Ayreshire, Scotland 

Nepheline basalt (Nagahama, 

Japan). 

Andesitic basalt (Motomura, Japan) 

Alkali olivine basalt 

Basalt (Schonen, Sweden) 

Olivine-andesitic basalt 

(Gottenburg, Germany). 

Olivine nephelinite 

Soda melilite 

Murase and McBirney (1973) 452 

Fujii and Kushiro (l977b) 463 

Shaw (1969) 458 

Kushiro and others (l976a) 461 

Fujii and Kushiro (l977a) 462 

(This report) 455 

Kani (1934b) 448 

Kani (1934b) 448 

Euler and Winkler ( 1957) 436 

Euler and Winkler ( 1957) 436 

Kani (1934b) 448 

Kani (1934b) 448 

Scarfe ( 1981) 464 

Euler and Winkler (1957) 441 

Euler and Winkler (1957) 441 

Scarfe ( 1981) 464, 465 

Scarfe ( 1981) 464, 465 

ANDESITES 

Hypersthene andesite (Old Red 

Sandstone Lava, Edinburgh. 

Scotland). 

Andesite (Crater Lake, 

Oreg .. U.S.A.). 

Mount Hood andesite 

Euler and Winkler ( 1957) 468 

Kushiro and others 

(1976a, b) 473, 477 

Murase and McBirney (1973) 475 

RHYOLITIC OBSIDIANS 

Rhyolite glass (Jemez Mountains, Friedman and others (1963) 480 

N.Mex., U.S.A.). 

Rhyolitic obsidian: 

Jemez Mountains, 

N.Mex., U.S.A. 

Newberry, Oreg., U.S.A. 

Additional Igneous Melts 

Skaergaard intrusion (Greenland) 

(35 percent crystalline). 

Mount Vesuvius lava (Vesuvius, 

Italy). 

Synthetic lunar sample(s) 

Olivine dolerite 

Nepheline-leucite-tephrite (Eifel, 

Germany). 

Kersantite (Schwartzwald, 

Germany). 

Pegmatite (Spruce Pine, 

N.C.). 

Shaw (1963) 489 

Murase and McBirney (1973) 486 

Murase and McBirney (1973) 505 

Volarovich and Tolstoi (1936) 554 

Murase and McBirney ( 1970) 508 

Euler and Winkler (1957) 498 

Euler and Winkler ( 1957) 498 

Euler and Winkler (1957) 498 

Burnham (1963) 511 

Potassium-magnesium-silicate melt Kushiro ( 1976a) 405 

and sodium-silicate melt. 

Calcium-aluminum melt Kushiro (1981) 512 

562 Viscosity of Synthetic and Natural Melts and Glasses 

Standard Glasses 

National Bureau of Standards 

Standard Glass No.: 

710 (soda-lime-silica glass) 

711 (lead-silica glass) 

717 (borosilicate glass) 

Commercial Glasses 

Commercial glasses 

Silica glass 

Na-K-Ca-Si02 glass 

Authors 

Bersan, J. 166-168 

Napolitano and Hawkins (1964) 514 

Napolitano and others (1974) 518 

Napolitano and Hawkins ( 1966) 521 

Napolitano and others (1974) 525 

Napolitano and Hawkins (1970) 528 

Napolitano and others (1974) 532 . 

Lillie ( 1929) 538 

Johannsen and Brunion (1959) 549 

Lillie ( 1931) 542 

Volarovich and Tolstoi (1936) 553 

Bills, P.M. 92, 194-196, 381-388 

Birch, F. 396-403, 420, 421 

Blackburn, D. 518-520, 525-527, 532-535 

Bockris, J.O. 32-35, 36-42, 55-58, 59-63, 66-69, 71-75, 87-90 

Brunion, H. 92-97, 197-202, 204-206, 208-211, 230-234, 549-552 

Burnham, C.W. 511 

Capps, W. 64, 65 

Chidester, R.E. 518-520, 525-527, 532-535 

Dane, E.B. 396-403, 420, 421 

Euler, R. 436-447, 466, 468-472, 498-504 

Friedman, I. 480-485 

Fujii, T. 462, 463 

Hanna, D.L. 129-132, 162-166, 180-182, 235-252, 281-331 

Hawkins, E.G. 514-517, 521-524, 528-531 

Hofmaier, G. 378-380, 390 

Hofmann, E.E. 212-230, 334-374 

Johannsen, F. 92-97, 197-202,204-206, 208-211,230-234,549-552 

Kammel, R. 44-54 

Kani, K. 408-419, 430-433, 448-450, 466 

Kitchener, J.A. 32, 33, 55-63, 66-69, 71-75, 87-90 

Kozakavitch, P. 98-128 

Kozu, S. 408-419, 430-433 

Kushiro, I. 396, 397, 404, 405, 451, 461-463, 473, 474, 477, 512 

Lillie, H.R. 76-86, 391-393, 538-548 

Long, W. 480-485 

Lowe, D.C. 36-42 

Machin, J.S. 43, 129-166, 170, 171, 176-182, 235-331 

Mackenzie, J.D. 32, 33, 55-63, 66-69, 71-75, 87-90, 183-191 

McBirney, A.R. 452-454, 466, 475, 476, 486-488, 505-510 

Murase, T. 452-454, 466, 475, 476, 486-488, 505-510 

Mysen, B.O. 473, 474, 477 

Napolitano, A. 514-535 
N'Dala, I. 169, 175, 203, 207, 332, 375 

Riebling, E.F. 70, 171-174 

Roentgen, R. 44-54 

Rossin •. R. 166-168 

Ryan, M.P. 455-457, 466 

Scarfe, C.M. 422-428, 464, 465 

Shartsis, L. 64, 65 

Shaw, H.R. 458-460, 466, 489-495 

Simmons, J.H. 518-520, 525-527, 532-535 

-t>U.S. G.P.O. 1987-181-407:60002 

Smith, R.L. 480-485 

Spinner, S. 64, 65 

Tolstoi, D.M. 553-555 

Urbain, G. 166-168 

Volarovich, M.P. 553-555 

Winkler, H.G.F. 436-447, 466, 468-472, 498-504 

Winterhager, H. 44-54 

Yee, T.B. 43, 133-166, 170, 171, 176-182, 253-331 

Yoder, H.S. 473, 474, 477 

Indexes 563