INST- OF STAND S TECH

AlllOb 'W'lOSB

NBSIR 78-1483

NBS: Properties of Electronic

Materials

J. R. Manning, R. L. Parker

National Bureau of Standards

Washington, D.C. 20234

Phone: (301) 921-3354

June 1 978

Annua! Report

For the Period 1 April 1977 - 31 March 1978

NASA Goveroment Order H-27954B

’ QC U S. DEPARTMENT OF COMMERCE

100

. U56

78-1483

NATIONAL BUREAU OF STANDARDS

J&ttaaafl Bareaa ef Standards APR l 7 1979

NBSIR 78-1483 £pO VOO « « ¥ MBS: PROPERTIES OF ELECTRONIC

MATERIALS

J. R. Manning, R. L. Parker

National Bureau of Standards

Washington, D.C. 20234

Phone: (301) 921-3354

June 1 978

Annual Report

For the Period 1 April 1977 - 31 March 1978

NASA Government Order H-27954B

U\XE^(UvUj 1 , (U3ol^

U S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Page

Summary 1-2

Task 1 - SURFACE TENSIONS AND THEIR VARIATIONS WITH TEMPERATURE

AND IMPURITIES by

S. C. Hardy and S. R. Coriell 3-14

Task 2 - SOLUTAL CONVECTION AND LIQUID DIFFUSION COEFFICIENTS by

W. J. Boettinger, S. R. Coriell, F. S. Biancaniello and

M. R. Cordes 15-68

Task 3 - DETERMINATION OF CRYSTAL PERFECTION by

M. Kuriyama and H. E. Burdette 69-83

Task 4 - A THERMOCHEMICAL STUDY OF CORROSIVE REACTIONS IN OXIDE

MATERIALS by H. S. Parker, R. S. Roth, C. D. Olson and

E. R. Plante 84-100

Task 5 - GRAVITY EFFECTS ON FLAME INHIBITION by

J. W. Hastie 101-111

Distribution List 112-113

i

National Bureau of Standards

Properties of Electronic Materials

Summary

This report describes NBS work for NASA in support of NASA's

Materials Processing in Space Program covering the period

April 1, 1977 to March 31, 1978. The NBS program has two main

thrusts:

1) Carrying out precision measurements in space and investigating

the feasibility of improved measurements when the space environment

offers a unique opportunity for performing such measurements. These

measurements would be useful for either space processing or processes

on the ground.

2) Obtaining precision measurements on materials properties when

these properties are important to the design and interpretation of

space processing experiments . These measurements would be carried out

either in space or on the ground.

The NBS work is carried out in five tasks. These tasks have, as

two of their focal points, the role of convection effects and the role

of container effects, both of which would differ in space-based experiments from those found in ground-based experiments. The results

obtained for each task are given in detailed summaries in the body of

the report. Briefly, in Task I - Surface Tensions and their Variations

with Temperature and Impurities - surface tension measurements have

been made for gallium using the pendant drop technique and some complex
effects ascribed to impurities were observed 0 In Task 2 - Solutal

Convection and Liquid Diffusion Coefficients - the onset of convective

and interfacial instabilities during the vertical directional solidification of a binary alloy has been determined theoretically by means

of a linear stability analysis,, In Task 3 - Determination of Crystal

Perfection - a study has been performed on the improvement in resolution

of x-ray imaging systems for real-time assessment of crystal perfection.

In Task 4 - A Thermochemical Study of Corrosion Reactions in Oxide

Materials - the system RFcO^-P^O- has been examined over portions of

the subsolidus region, and the occurrence of a beta alumina structuretype at 85.2 mole percent Fe o 0„ has been observed. In Task 5 - Gravity

Effects on Flame Inhibition - a high pressure sampling mass spectrometer facility has been designed and construction on it is nearly

completed.

2
Task 1

Surface Tensions and Their Variations

with Temperature and Impurities

S. C. Hardy and S. R. Coriel

Metal Science and Standards Division

Center for Materials Science

Summary

We have measured the surface tension of gallium in ultra pure helium

atmospheres at room temperature using the pendant drop technique and have

observed a time dependence. This time dependence is more complex than

that found in previous work. We have tentatively interpreted the

observed time variation of the surface tension in terms of a bulk phase

impurity which diffuses to the surface and desorbs. These preliminary

investigations indicate the surface tension of pure gallium is near

2 800 mJ/m , a value about 10% higher than the equilibrium values previously reported.

3
I. INTRODUCTION

We have started an experimental and theoretical program to accurately measure the liquid-vapor surface tensions of metals and

semiconductors. Accurate measurements of surface tension as a function

of temperature and concentration would be of value in many industrial

applications on earth and are essential in developing experiments and

manufacturing processes for space which involve free liquid surfaces.

The importance of surface tension related phenomena in microgravity is

attested by a number of unpredicted and essentially not understood

phenomena which have occurred in space experiments involving solidification.

Although technologically significant, the surface tensions of many

metals and semiconductors are not well known and the temperature and

concentration variations are uncertain. Indeed, even the qualitative

variation of surface tension with temperature is in doubt with contradictory measurements showing surface tension both increasing and

decreasing with temperature in some cases. Although fluid flow can be

calculated from the relevant differential equations, such calculations

require knowledge of the temperature and concentration dependence of

the surface tension in order to be predictive.

Gallium was selected for the first measurements in this program because it has been suggested as a model material for ground based fluid

flow studies in the NASA program, it is an intrinsically interesting

metal, and its surface tension is known only approximately. In

4
addition, it has a boiling point near 2200 °C and it can be supercooled

by more than 100 °C below its 30 °C melting point. Thus a very large

temperature range is available for surface tension measurements.

There have been four previous studies of the surface tension of

gallium. An early measurement by Richards and Boyer

^

found a value

2 of 358.2 mJ/m in an atmosphere of carbon dioxide. This result is

certainly very much lower than the value for pure gallium. Later

measurements by Mack et al

^

and Timofeevicheva and Pubachevich

^

2 2 found surface tensions in the 700 mJ/m to 750 mJ/m range at temperatures near the melting point and under atmospheres of hydrogen and

[41 carbon dioxide. The most recent measurements by Abbaschian 1- J also

found values in this range with nitrogen atmospheres. However, he also

observed a time dependence of the surface tension; the surface tensions

2 of the pendant drops declined from over 800 mJ/m initially to a constant

value of about 725 mJ/m in fifteen minutes. This terminal value is

thus in agreement with earlier measurements. However, the time dependence of his observations suggests impurity adsorption with a

consequent surface tension lowering. Thus it seems probable that all

previous measurements of the gallium surface tension were strongly

influenced by surface adsorption with the clean gallium value being

over 800 mJ/rn^. The temperature variation of the surface tension derived from these measurements must be regarded as highly uncertain.

5
II. EXPERIMENTAL PROCEDURES

The initial phase of this work has attempted to develop techniques

for handling gallium which, by generating a clean surface, will produce an

accurate surface tension value. Since the temperature variation of the

surface tension can not profitably be studied until such a clean surface is obtained, all the measurements have been made at ambient

temperature, i.e., 23 °C. Thus the gallium is undercooled by about 7

°C. Variations of several degrees in the ambient temperature will

result in only very small surface tension variations since the temper2 ature coefficients for metals are of the order of 0.1 mJ/m K.

The pendant drop technique was used for the measurements, the

gallium drops being formed at the end of a micrometer syringe with a

pyrex-glass tip of about 1.25 mm i.d. The teflon plunger of

syringe passed through an 0-ring which formed an air tight seal and the

syringe was inserted through a vacuum coupling into a glass cell with

flat faces. The cell-syringe assembly was checked for leaks by

pressurizing to several psi and immersing in water to detect bubbles.

The gallium was obtained in 1 gm units in plastic ampoules and was

nominally 99.9999% pure. The ampoules were filled with alcohol containing a little hydrochloric acid and slightly warmed on a hot plate

to melt the solid gallium and to form a compact drop at the bottom of the

ampoule. The contents of several ampoules were then drawn into the

micrometer syringe which had been previously filled with alcohol. The

gallium was rinsed at least six times with absolute ethyl alcohol

6
within the syringe to eliminate all acid. The alcohol during this

procedure was kept vigorously boiling to minimize dissolved gases.

The cell prior to and during the measurements was continuously

flushed with helium gas purified by an instrument which uses titanium

metal at 800 °C to remove impurities. The manufacturer of this device

-72

claims titanium getter ing reduces oxygen pressures to about 10

atmospheres with similar levels for carbon and nitrogen. These are

impurity levels lower than those found in ultra high vacuum, i.e.,

10 ^ atmosphere. However, gases desorbed from the tubulation to this

device and from the cell are probably far above this level.

Several drops of gallium were formed and discarded before retaining

one for measurement in order to clean the bore and tip of the syringe.

The drops were observed and photographed on Polaroid film through a low

power microscope and the photographs were analyzed on an X-Y measuring

microscope. The pendant drop technique requires the measurement of d

g

,

the equatorial diameter and d^ , the diameter measured at a height d^

from the bottom of the drop. These dimensions are used to calculate a

shape determining variable S = d

e /d

s

. Solutions to the Young-Laplace

equation for the pendant drop characterize the drop profile in terms of

a shape dependent quantity H which is a function of S. Tables of H as

a function of S permit the calculation of the surface tension from the

Pgd

0

2 relationship y

= “p~ , where p is the density and g is the gravitational acceleration. The magnification of each picture is determined

precisely by measurement of the diameter of the syringe tip at a

7
specific cross section marked by a notch. A typical drop is shown in

Figure 1.

III. EXPERIMENTAL RESULTS

We have found a time dependence of the gallium surface tension

which is complex and qualitatively different from that observed by

Abbaschian. The changes in surface tension with time we observe appear

to be dependent on the helium flow rate. Figure 2 shows the surface

tension as a function of time for a low flow rate, e.g., 4 bubbles/sec.

2 2 The surface tension declines from about 710 mJ/m“ to about 629 mJ/m in

2 hours. This differs from Abbaschian's observations in several re2 spects: the surface tension values here are about 100 mJ/m lower than

Abbaschian's and the decay to a constant value takes much longer than

in his experiments.

A quite different result is obtained with a high helium flow rate,

e.g., 2 liters/min. As seen in Figure 3, the surface tension declines

initially but rises sharply after about fifty minutes to a value near

2 780 mJ/m . The rise is not monotonic; reanalysis of the pictures confirms the several local minima seen in the data. Note also the large

decrease in surface tension after the titanium getter was turned off at

420 minutes. These two curves represent the extremes of the observed

time dependences we have observed. Other data lie between the results

shown here.
Conclusions and Discussions

The complex time dependent surface tensions we observe are probably

the result of several coupled dynamic processes. Although we do not

understand the curves we think they reflect the diffusion of a bulk

phase species to the surface with a subsequent desorption. Initially

the flux of this species to the surface from the bulk is much faster

than the desorption so the surface concentration increases and the

surface tension falls. As this concentration builds up, however, the

diffusion flux decreases and the desorption rate increases. If the

bulk concentration of the impurity is decreased sufficiently, the

diffusion flux will become smaller than the desorption flux and the

surface concentration will decline leading to an increase in surface

tension as seen in Figure 3. Eventually an equilibrium concentration

is established on the surface which gives a constant surface tension.

The gas phase impurities which come primarily from the cell walls and

tubulation play a critical role in this equilibration as shown by the

dependence on flow rate and on the use of the titanium getter.

The time dependent behavior described above postulates a bulk phase

impurity which diffuses to the gallium surface and desorbs at room

temperature. We can not identify the impurity at this point. It may

be significant that the initial surface tensions of Abbaschian are much

higher than those we observe. We believe this indicates his gallium is

cleaner than ours. Although nominally six nines pure, our gallium

comes in one gram ampoules whereas Abbaschian' s gallium was in ingot

9
form. The subdivision of the zone refined gallium for packaging in the

ampoules may have introduced impurities. It is also possible the

impurity is introduced from the alcohol and hydrochloric acid used in

the handling procedure discussed earlier.

To resolve this complex picture it will probably be necessary to

measure the gallium surface tension in ultra high vacuum. A system to

do this is being assembled.

We note that two articles, based on previous work on this task,

have been published during the past year, viz. "Stability of Liquid

Zones", S. R. Coriell, S. C. Hardy, and M. R. Cordes, J. Colloid and

Interface Science 6(3, 126 (1977) and "Theory of Molten Zone Shape and

Stability", S. R. Coriell and M. R. Cordes, J. Crystal Growth, 42 ,

466 (1977). An article "The Motion of Bubbles in a Vertical Temperature Gradient" by S. C. Hardy is in preparation.

10
References

[1] T. W. Richards and S. Boyer, J. Amer. Chem. Soc. 43 , 283 (1931).

[2] G. L. Mack, J. K. Davis and F. E. Bartell, J. Phys. Chem. 45_,

846 (1941).

[3] 0. A. Timofeevicheva and P. P. Pugachevich, Handbook of the Rare

Elements . Vol. 1, Eds. M. A. Filyand and E. I. Semenova, M. E.

Alferieff (Transl.) (MacDonald Technical and Scientific, London

1968) p. 13.

[4] G. J. Abbaschian, Journal of Less-Common Metals 4C , 329 (1975).

1 1
Fig. 1. Photograph of a pendant drop of gallium

showing the dimensions which are used to

calculate surface tension. For this drop

^ the calculated surface tension was 790 mJ/m .

1 2
710

700

690

680

670

660

650

640

630

620

610

TIME (min.)

Fig. 2. The variation of surface tension with time for a low

helium flow rate.

13
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14

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Task 2

Solutal Convection and Liquid Diffusion Coefficients

W. J. Boettinger, S. R. Coriell, and F. S. Biancaniello

Metal Science and Standards Division

Center for Materials Science

and

M. R. Cordes

Mathematical Analysis Division

Center for Applied Mathematics

Summary

This research is directed towards an understanding of solutal convection caused by the simultaneous concentration and temperature gradients

present during the directional solidification of alloys. Included in

this study is investigation of the effects of convection on the microstructure and chemical homogeneity of directionally solidified alloys

and of the conditions under which undesirable effects can be eliminated.

The onset of convective and interfacial instabilities during the

vertical directional solidification of a binary alloy is determined

theoretically by means of a linear stability analysis. For values of

the physical constants appropriate to the solidification of lead containing tin, the critical bulk solute concentration delineating the

demarcation between stability and instability is numerically calculated

as a function of growth velocity. For concentrations less than the

critical concentration, the system is stable. For growth velocities

15
between 1 and 40 ym/s, the critical concentration increases with increasing velocity; for velocities greater than approximately 40 ym/s, it

decreases with velocity.

The occurrence of solutal convection and its effects on the microstructure and macrosegregation of directionally solidified alloys,

particularly off-eutectics, is investigated using lead-tin alloys.

Lead-rich lead-tin alloys have been directionally solidified vertically

upwards. During plane front solidification the concentration of less

dense solute is increased in the liquid near the solid-liquid interface

and there is the possibility of solutal convection. In this year's

research, procedures for careful directional solidification and sample

characterization have been developed and preliminary microstructural

information on lead-rich lead-tin off-eutectics has been obtained.

16
I. INTRODUCTION

In recent years there has been extensive research and development

efforts on the effect of fluid flow on solidification and on the propf 1-21

erties of the resulting solids . In general, one attempts to

control fluid flow in such a way as to obtain optimum materials properties. To minimize fluid flow, it is well known that horizontal

temperature and concentration gradients must be avoided. If the fluid

density gradient is parallel to the gravitational field, a motionless

solution of the fluid flow equations is possible; in the remaining

discussion we will assume that this is the case, i.e., there are no

horizontal density gradients.

In the plane front constant velocity directional solidification of

all alloys other than congruent melting compounds and invariant

eutectics, there exists in the liquid an exponential concentration

gradient which extends ahead of the liquid-solid interface with a decay

distance of D/V where D is the liquid interdiffusion coefficient and V

is the interface velocity. There also exists a temperature gradient

which is essentially linear in the region in which the concentration

gradient is exponential . The density, being a function of temperature

and concentration, can have various profiles depending on the solidification conditions and the properties of the fluid. The simplest

criterion of whether convection occurs might be based on whether the

[31 density decreases or increases with height in the fluid 1

. However,

this criterion will be shown to be incorrect. The complex interaction

17
of the solute gradient and temperature gradient on the presence or

absence of fluid flow and its effect on the freezing solid is the

subject of this researcho We will call convection caused by simultaneous concentration and temperature gradients, solutal convection .

Solidification

Previous metallurgical work on solutal convection during solidification has mostly been directed towards off-eutectic and dendritic

[41 solidification. In 1967, Moilard and Flemings'- J showed that fully

lamellar structures could be solidified vertically upward from

compositions on the Sn-rich side of the Pb-Sn eutectic. In this regime

the temperature gradient and the concentration gradient in the liquid

are such that no convection is expected. Their paper claimed that on

the Pb-rich side, however, convection would be present because the

density increases with height due to the concentration gradient and

that growth of composites was impossible. However, Holder and

Oliver

^

succeeded in growing composites on the Pb-rich side up to 8

w/o from the eutectic and reported no macro segregation. Hogan and

Davis L showed data for the dendrite to composite transition in

Pb-rich Sn-Pb alloys implying that no unusual problems were enr 7 l countered. Verhoeven, Kingery, and Hofer L J in very careful

experiments, reported extensive macro segregation in Pb-rich alloys only

1 w/o from the Pb-Sn eutectic. Fitting their macrosegregation by a

rg| rg]

Burton-Prim-Slichter L J type analysis modified for thermo transport L

,

they obtained 6 parameters (width of unmixed zone at the liquid-solid

18
interface) of as small as 60 ym, which for these experiments indicates

rather strong convection. Vandenbulcke and Vuillard solidified

Sn-rich Pb-Sn off-eutectics vertically downward. Here both temperature

gradient and solute gradient contribute to a density which increases

with height. (As will be pointed out in the next section, this may or

may not cause convection.) Their work indicates macrosegregation is

present. Thus, the effect that solutal convection can have on

directional solidification is thought by these authors to fall into

three areas: 1) it prevents the growth of the composite (or perhaps

increases the fault density); 2) it causes macrosegregation in the

composite; 3) it has no effect. It appears at this time that 2) is the

most likely effect. However, the conditions under which solute convection occur and its effects on microstructure or macrosegregation are

not fully known.

Macrosegregation in off-eutectics would be deleterious to the performance of these composites for practical purposes, e.g., turbine

blades. It is important to know the extent of restrictions on composite growth because designers of these materials need flexibility in

adjusting the volume fraction of the reinforcing phase and in adding

alloying components to control high temperature microstructural

stability and to improve strength and corrosion resistance. These

alloying additions will make eutectics freeze over a range of temperature. These noninvariant eutectics in multicomponent systems behave

just like off-eutectics in binary alloys as far as solutal convection

is concerned. Hence the study of simple off- eutectics has wider
applicability.

Other work has been performed on solutal convection during dendritic and cellular solidification^^. Macrosegregation down the

length of ingots and certain casting defects (A-segregates and

freckles) have been attributed to this flow. In these situations,

horizontal solute and temperature gradients exist making this a much

more complex problem than is presently being considered here.

Convection

A classic problem is that of the onset of convection when a pure

liquid, whose density decreases with increasing temperature, is heated

from below. For sufficiently small temperature gradients, there is no

fluid flow. Convection occurs when the temperature gradient exceeds a

certain critical value. Therefore convection can occur when more dqnse

liquid is on top of less dense liquid. We shall refer to a non-increasing

density with height as a statically stable density profile; if this is

not the case we refer to it as statically unstable. For the case of a

pure liquid heated from below, a statically unstable density profile

does not necessarily cause convection; convection occurs when the

density gradient exceeds a critical value. Extensive research has been

carried out on the onset of convection .

More recently there has been research on the phenomena of solutal

convection (also called double-diffusive, thermohaline or thermosolutal

[ 13- 27 ] convection) J

. This phenomena occurs when the fluid density

depends on two variables such as temperature and solute concentration,

which have different diffusivities . An interesting aspect of solutal

20
convection is the occurrence of convection even when the density profile

is statically stable. For this example, we assume that the solute is

more dense than the solvent. Consider a fluid with a statically stable

density profile which is heated from above (positive temperature

gradient) and has a greater concentration of solute at the top (positive solute gradient) . The positive temperature gradient alone would

cause a negative density gradient and the positive solute gradient

alone would cause a positive density gradient; we assume that the

temperature gradient is sufficiently large that the net fluid density

gradient is negative, i.e., the fluid is statically stable. Consider

an element of fluid near the bottom of the container; it is cold and

dilute in solute concentration. Imagine a disturbance in which this

fluid element rises. Since the thermal diffusivity is greater than the

solute diffusivity, the fluid element increases in temperature but does

not change in solute concentration. At its new position it has nearly

the same temperature but less solute than the surrounding fluid; it is

thus less dense than the surrounding fluid and hence continues to rise,

leading to convection. Thus convection occurs even though the density

profile is statically stable. Clearly the static density profile is

not useful in predicting convection, since one can have a statically

unstable density profile without convection and a statically stable

density profile with convection.

Research Plan

In this task, the problem will be approached theoretically and experimentally. The question of when convection occurs during

21
directional solidification is being investigated theoretically using a

linear hydrodynamic stability analysis. This analysis of solutal convection is being performed for the solidification of a single phase

material. Single phase materials are being investigated because of

their intrinsic importance and because the problem is tractable.

Results obtained here will be applicable to off-eutectics to describe

the macroscopic features of their solidification. In the first year’s

work, the problem has been formulated, computer algorithms developed

and initial results obtained for a limited number of cases.

The questions of whether solutal convection occurs and of what

effects it has on the microstructure and possible macrosegregation of

directionally solidified alloys, particularly off-eutectics, is being

investigated experimentally using Pb-Sn alloys. This alloy system is

chosen because more data exists for this alloy system than others and

because it is a low temperature alloy. Results will be generalized to

other alloy systems. Pb-rich Pb-Sn alloys have been directionally

solidified vertically upwards where a less dense solute is built up in

the liquid at the liquid- solid interface. Evidence for fluid flow is

being sought. The presence of fluid flow can be detected by measuring

variations in composition and/or microstructure along the growth

direction in the solidified sample and changes in these observables

when a magnetic field is applied. Such fields are known to increase

the effective viscosity of liquid metals and retard convection. Also

it will be determined whether a high temperature gradient can suppress

22
solutal convection. In the first year’s work, procedures for careful

directional solidification and sample characterization have been

developed and preliminary microstructural information on Pb-rich, Pb-Sn

off-eutectics have been obtained.

II. THEORETICAL INVESTIGATION

In studying the onset of convection, one uses a linear stability

analysis. One considers an unperturbed state in which the temperature,

concentration, density, pressure, and fluid flow velocities are functions of height alone, and satisfy the relevant differential equations.

One then considers small disturbances in these quantities and retains

only linear terms in the disturbances in the differential equations.

In this linear theory, the time dependence of the disturbances is of

the form exp (at), where t is the time. Upon carrying out the calculation for a particular set of physical variables, e.g. temperature

gradient, solute gradient, viscosity, etc., one determines a. If the

real part of a is positive, then the disturbances increase exponentially with time; the unperturbed state is unstable and convection

occurs. If the real part of a is negative for all possible disturbances, the system is stable. The onset of convection corresponds to

the set of physical variables for which the real part of a vanishes for

some particular disturbance and is negative for all other disturbances.

For example, we might fix all physical variables except the temperature

gradient, and determine the critical value of the temperature gradient

at the onset of convection. This critical temperature gradient is then

the demarcation between stable (no convection) and unstable (convection)

23
behavior. The onset of convection can occur in two different ways

depending on whether or not the imaginary part of sigma vanishes when

the real part of sigma vanishes. Writing a = + ia^, if cm = 0 when

= 0, the principle of the exchange of stabilities holds and the

onset of convection corresponds to a monotonic (exponential) increase

in the size of the disturbances. If a. / 0 when a =0, there is

overstability and the disturbances oscillate in time with exponentially

increasing amplitude at the onset of convection.

Linear hydrodynamic stability theory for solutal convection with

rigid and/or free boundary conditions and constant temperature and

r 1 3-22

1

solute gradients has been developed by numerous scientists 1- J

.

Some research has been carried out on non-linear theories of solutal

[23-271 convection J

. However, the onset of convection during the

vertical directional solidification of a binary alloy differs in

several ways from previous treatments of solutal convection. Since the

solid-liquid interface is moving at constant velocity V, the concentration gradient is not constant, but decreases exponentially with

distance z from the interface, i.e. the concentration gradient

decreases as exp (-Vz/D), where D is the diffusion coefficient in the

liquid. The temperature gradient is also of this form with D replaced

by k

,

the thermal diffusivity in the liquid. However, the quantity

(Vz/k) is usually sufficiently small that the thermal gradient is

approximately constant. The boundary conditions at the solid-liquid

interface are different from those used in treatments of double24
diffusive convection. The sol id- liquid interface can change shape as a

result of fluctuations, and the solidification boundary conditions are

applied at the actual solid- liquid interface.

In the absence of convection the stability of the shape of a solidliquid interface during solidification has been treated extensively in

T28-29 1 the last fifteen years by morphological stability theory 1 J

.

During directional solidification a non-planar interface will give rise

to a non-uniform solute distribution in the solidified material. A

non-planar interface can occur without convection through the usual

morphological instability mechanism. Clearly, convection can also

cause a non-planar solid-liquid interface. Of course these are not

distinct problems; both are governed by the same differential equations

and boundary conditions. Previous morphological stability theory has

assumed that the liquid density is independent of temperature and

solute concentration. In this report we will generalize morphological

stability theory and remove this assumption. We will also take account

of the density change on solidification. Thus, one may look on the

present calculations as double diffusive convection with solidification

occurring or as morphological stability theory with fluid flow. They

are simply different vantage points for the same physical problem.

We will present a few results for the case of directional solidification upwards of a binary alloy, which is rejecting solute which is

less dense than the solvent, e.g., a small concentration of tin in

leado The temperature gradients are positive; i.e., the temperature

25
increases with height. The temperature gradient contributes to a

negative liquid density gradient, i.e., a statically stable density

gradient. The concentration gradient contributes to a positive liquid

density gradient. However, the concentration gradient exponentially

decreases with distance from the solid-liquid interface with decay

distance D/V; typically D/V is of the order of 0. 1-1.0 mm. Thus, near

the solid-liquid interface the density gradient may be statically

stable or unstable depending on the relative magnitudes of the temperature and concentration gradients. Far from the interface the

concentration gradient vanishes and the density gradient is statically

stable. Our calculations will determine the conditions for the onset

of convection and interface instability in such a system.

26
Theory

We consider unidirectional vertical solidification of a binary alloy

at constant velocity. We choose an (x' ,y' ,z') laboratory coordinate system

such that the z' axis is perpendicular to the planar solid-liquid interface.

The gravitational field is of the form g =(0,0,-g), i.e., positive g

implies a field anti-parallel to the z' axis. The following differential

equations govern the fluid velocity u =(u^^,u^.,u^J , temperature T,

and concentration c^^

div u = 0

(3 u/3 t') + (uV^)u = - ( Vp/ p q) + vV"“u - g[a(T-T) + a

c (c-c)]

( 3 T/ St") + uV'T = kV " T, _ ?

( 3 c/ 3 t') + uV'c = DV" c.

CD

( 2 )

(3)

(4)

where t' is the time, p is a pressure, v is the kinematic viscosity, k

is the liquid thermal diffusivity, and D is the liquid diffusion coefficient. The prime on the operator V indicates that it is with respect

to the (x' ,y' , z') coordinate system. We have assumed that the fluid

density p is given by p = [l-a(T-T) - a

c (c-c)], where p^ is the

density at T = ? and c = c. The above equations are based on the

Oberbeck -Boussinesq approximation^^ ^ ^ and the coefficients v, k, and

D are assumed constant.

We transform to a moving coordinate system (x,y,z) attached to the

unperturbed planar solid-liquid interface which is moving with constant

velocity V = (0,0, V) in the z - direction, i.e., x = x", y = y' , z =

z'-Vt, and t = t'

.

27
We obtain

div u = 0

( 5 ) (3u/3 t) - (VV)u + (uV)u = - (Vp/p

Q

) + vV

2 u-g[a(T-T) + a

c (c-c)](6)

( 3 T/ 3 t) - VVT + uVT = kV T

2

(7)

(8 c/ 3 t) - Vvc + uVc = DV“c ^

Note that u is still measured in the laboratory coordinate system

•k The boundary conditions at the solid-liquid interface are that the

tangential components of the fluid velocity vanish (no slip condition)

and that the normal component satisfy

vn(p

L -p ) = ( u *n) p L

, (9)

where v is the solidification velocity, n is the unit normal to the

solid-liquid interface, and p and p are liquid and solid densities,

s respectively, at the solid-liquid interface. The temperature and concentration satisfy

( 10 )

( 11 )

(v*n)L = f-k T VT + k VT )*n, v L s s (v-n) (c sl -c

J

) = ( p L

/ p

s )D Vc-n,

where L is the latent heat of fusion per unit volume of solid, k and

k^ are thermal conductivities of liquid and solid, respectively, c

^ and Cj are solid and liquid concentrations at the solid-liquid interface,

and all quantities are evaluated at the interface. The temperature

T^ in the solid satisfies the differential equation

( 3T/3t) - (VV) T = k V T , s s s s

( 12 )

The authors are indebted to R. F. Sekerka for detailed discussions and

derivations of the boundary conditions at the solid-liquid interface.

28
where is the thermal diffusivity of the solid. Diffusion in the solid

has been neglected. In addition, we have

T T = T t si I (13)

c T = k c T si I (14)

(v*n) = y{T - T } v e i (15)

T = TM + rac - T.TK . e M I M

(16)

Here, we have used a subscript I to denote evaluation of the quantity at

the solid-liquid interface; k is the partition coefficient, p is a linear

kinetic coefficient, is the equilibrium temperature of a curved interface in the presence of solute, T is the melting point of the pure

substance with a planar interface, m is the slope of the liquidus line,

f is the capillary constant, i.e., the solid-liquid surface tension

Y

= L T, and K is the interface curvature,

vWe now solve the equations for a planar solid-liquid interface

located at z = 0; all quantities are functions of z alone. We assume

that in the moving frame there is no dependence on time. The fluid

velocity, temperature, and concentration fields are

u

Q = (0,0, - eV) (17)

T

0

= d

i

“ (kG

l

/V*) exp (-V*z/k) (18)

T

s0

= d

2

‘ 6Xp (_Vz/k

s

) (19)

c

0

= c

oo • (c

oo/k)(k-l) exp (-V*z/D), (20)

where e = (p /p ) -1, d and d are constants, V* = V(p /p ) , G and G

S L 1 Z SJ-ji-jS

are temperature gradients in the liquid and solid, respectively, at the

solid-liquid interface, c is the solute concentration far from the

29
interface, and the subscript 0 indicates that the solutions are for an

unperturbed planar interface. From the boundary conditions we also have

the relationships

VL = k G - k T G T v s s L L V* (c^/k) (k-1) = DG

c

d

x - (kG

l

/V*) = d

2

- C«

s Gs /V)

c T = c si 00 V = y{T + (mc^/k) - d.^ + (kG^/V*)

}

( 21 )

( 22 )

(23)

(24)

(25)

where G

c is the concentration gradient in the liquid at the solid-liquid

interface. These relationships may be used to find explicit expressions

for the constants d^ and d 0

.

We now consider whether the above solutions, for which there is only

a trivial fluid flow corresponding to the density change on solidification, are stable with respect to small fluctuations. We write

“ = “0 * W(x,y,z,t) (26)

T = T

o

+ T (x,y,z,t) (27)

T

s ' T

s0

+ T.(x,y, z,t) (28)

O

II O

O

+ c (x,y,z,t) (29)

"d 11 id 0

+ P 2 (x,y,z,t) (30)

Z = 2sL

(x ’ y - t) (31)

and will retain only linear terms in the perturbation quantities, W,

T, T , C, p and z . The function z (x,y,t) represents the shape of

S -L S S J-j the solid- liquid interface which in general is not planar and the

function p^(z) satisfies the unperturbed equations. We obtain the

following differential equations for the fluctuations
div W = 0 C32)

(3W/3t) - V* ( 3 W/ 3 z) = - (VPi /p 0

)h- vV y; - g(aT+a

c C), (33)

( 3 T/ 3 t) - V * ( 3 7/ 3 z) + W^(3 Tq/ 3z) - kV T ,

( 3 C/3 t) - V*(

3

C/

3

z) + W (

3

c

Q

/ 3 z) = DV

2 C,

(3 T

s /3 t) - V(3 7/3 z) = k

s V

2 T

s

.

(34)

(35)

(36)

Since equation (33) is a vector equation, we have seven equations for

the seven functions W , W , W , p , T, C, and T . By appropriate rex y Zi j. s arrangement of these equations, we can eliminate W , W , and p, , and

x y i obtain a higher order equation for W . Briefly, we apply the operator

2 2 (3 / 3 z 3 x) to the W equation, the operator (3 / 3 z3 y) to the

2 2 2 2 2

W equation, and the operator V =(3 / 3 x ) + ( 3 / 3 y ) to the W

7 y l z equation. Noting that from the continuity equation

( 3 2 W

x

/ 3 x 3 z) + (3

2W / 3 y 3 z) + ( 3 2

|f / 3 z 2

) =0, (37)

y z we obtain after algebraic manipulation

(3V2 W

z /3t) - V*(3V2 W

z /3z) - vV

4

W

z = gV

1

2 (aT+c^C) , (38)

which is equivalent to equations (32) and (33).

The boundary conditions on the perturbed quantities at z = 0 follow

from the general boundary conditions and are

W

z = -c(3 z^/3 t) (39)

W

x

= eV(9 Z sL/ 9x) (40)

lV

= £V(3 Z sL/9y} (41)

( 3 z gL

/3 t)L

y

= -k

L [-(V*/K)G

L

Z sL

+ 3 7/ 3 z ]

+ k

s

[ - (V/K

s

^ G

s

z sL

+

3 V 3z] (42)

31
(3 z (43) sL/9 t)(l-k)(cyk) = kVGn

z cT -Cl-k)VC-(p T /pJD( 3 C/ 3 z) c sL L s'

G z T + T = G. z + T

s sL s L SL

(3 z sL

/3 t) = y(mG

c

Z sL + mC + - G^ -T }

(44)

(45)

From the continuity equation, eqs (40) and (41) can be combined to give

(3 W

z /3 z) = -eVV lZsL (46)

at z = 0.

The equations and the boundary conditions are homogeneous and

linear. It is convenient to represent the time dependence and the x

and y dependence in the form exp (at+ito x+ito y) . The quantities to and

X y X

to represent spatial frequencies and the general solution of the

equations will involve integration over all values of to^ and to . If

the real part of a is positive for any values of (to ,oo ), then the

x y

solutions grow exponentially in time and are unstable. If the real

part of a is negative for all values of (to^,to^), the system is stable.

The criterion for the onset of instability is determined by finding

the conditions for which the real part of a is not positive for any

(to ) and is equal to zero for some value of (to ,oo ). We write

x y

1 x y

W = W (z) exp (ot+ito x+ioo y)

z z r x y

T = T(z) exp (at+ico x+ito y)

x y

C = C(z) exp (ct + ico^x+ioo^y)

T = T (z) exp (at+ito x+ito y)

s s

r v x y

= z exp (at+ito^x+ioo^y)

,

(47)

(48)

(49)

(50)

(51)

32
where W , T, C, T are functions of z alone, and z is a constant. Subz

’ ’ s stituting these expressions in the differential equations yields

{(3

2 / 3 z 2

)-u)

2 }{v [(3

2 / 3 z 2

) -w

2

] +V* ( 3 /3 z)-a}W = goj 2 (aT+a C) , (52)

z c {x[(3 /3 z ) -oj ]+V*(3 /3 z)-a)T = W^G^ exp (-V*z/k), ( 53 ) {D[(3 2 / 3 z 2 )-w

2 ]+V*(3 / 3 z) -a}C = W G exp (-V*z/D) , (54)

(x

s [(3

2 / 3 z

2

) -oj 2 ]+V ( 3 /3 z)-a}T

s = 0, (55)

2 2 2 where oj = oj +oj x y

Since the equation for T

= does not depend on W , T, or C, it can be

solved analytically. Using the boundary condition (z->-°° = 0, we find

T" s = d

3 exp (Az) ,

where d_ is a constant and

(56)

A =(-V/2k

s

) + {(V/2x

s

) 2 + o) 2 + (a/x

s )} 2

(57)

We have three coupled differential equations for the functions W^,

T, and C. The boundary conditions, eqs (39-46), for W , T, and C at z = 0

also contain the unknown constant z and d^. However, we can eliminate

these constants, and obtain boundary conditions for W , T, and C at z = 0,

viz

,

W + (a/Vw ) ( 3 W /3 z) = 0,

z z

(3 W /3 z) + (eVw

2 k / a_) ( 3 7/ 3 z) - (eVw

2k A/a„)f

z Li o So

(a

3

+a

2 k

s A)T - (a ? k^)(3 T/ 3 z) - a^mC = 0,

-a

4

T + [ma4+ (l-k)Va

2 ]C + (a

2 DpL /p

s )(3 C/3 z) = 0,

= 0 ,

(58)

(59)

(60)

(61)

where

a

l - - ^ k

s G

s V/Ks

) (62)

33
(63) a = O/y) - mG + G T + T Jti) 2

a

3

= aL

v

‘ a

l ' k

s A(GL"

G

s

) C64) a

4

= o(l-k) (cyk) - kVG

c . (65)

Thus we have four linear homogeneous boundary conditions at z = 0.

We need four additional conditions in the liquid away from the interface since our differential equations are equivalent to a single eighth

order equation. We consider a rigid planar isothermal boundary at

z = Zj (a constant) . The boundary conditions are

A A A A W = ( 3 W / 3 z) = T = ( 3 C/ 3 z) = 0 (66)

However, in order to be able to treat a more general class of problems,

we will write the boundary conditions as W^ = 0,

b^T + b

?

( 8 T/3 z) = 0, (67)

b

3 C + b

4

( 3 CJ 3 z) = 0, (68)

b ( 3 W / 3 z) + b ( 3 2 W / 3 z 2

) = 0 (69)

D z 6 z where b^, b

?

, b^ , b^, b c , and b^ are constants. Clearly b^ = b^ =

b^ = 1 and b

9 = b_ = b^ = 0 corresponds to eq (66)

.

The boundary conditions at z = z^ are not rigorous. In many solidification experiments, there is a rigid boundary at z' = z (a constant),

Lj which implies that in our moving frame the boundary conditions should

be applied at z = z

T -Vt. In addition, if p ^ p , the unperturbed

flow is not zero at z . To take account of these effects would greatly

Li complicate the calculation. We are basically assuming that as long as

z^ is sufficiently far from the solid-liquid interface, the results will

be relatively independent of the precise boundary conditions. This

assumption will be investigated by numerical calculations.

34
Numerical Methods

It is convenient to convert the differential equations, eqs, (52-55)

to eight first order equations. We

Y 1 = W

1 z

Y

2 = ( 3 WJ 3 z)

Y

3 = 9 O

Y

4

= ( 33

W

z / 3 z 3

)

Y

5

= ^

Y

6

= (3 Tf 3 z)

Y

g

= ( 3 C/ 3 z)

define

(70)

(71)

(72)

(73)

(74)

(75)

(76)

(77)

and denote by Y(z) the vector with components Y^(z)(i = 1,2,... 8).

The differential equations are now

( 3 Y

x / 3 z) = Y 0 (78)

( 3 Y

2

/ 3 z) = Yg (79)

(3 Y

3

/3 z) = Y

4 (80)

(3Y

4

/3z) = - (V*/v)Y

4

+

[2o) 2 +(a/v)]Y

3 + (oTV*/v)Y

2

- [w

2 +(o/v)]a)

2 Y

1 + [gw

2 /v] [aYg + a

cY

7

] (81)

(3 Y

5 /3 z) = Y6

(82)

(3Y

6 /3 z) = - (V*/k)Y

6

+ [a) 2 + (a/<) ] Yg

+ (Y

1 G

l

/k) exp (-V*z/k) (83)

(3 Y

y /3 z) = Yg (84)

( 3 Yg/ 3 z) = - (V*/D) Yg + [oj 2 + (a/D) ] Y

? (Y^/D) exp (-V*z/D) (85)

or in a matrix form

( 3 Y/3 z) = A Y (86)

35
where the elements of the 8x8 matrix A are defined by eqs (78-85)

In general the functions and the quantity a are complex. A further

decomposition of the form Y. = IL. , + i U.. and a = o + ia. allows

one to consider only real functions and quantities. This results in

sixteen first order differential equations for the functions IL or in

matrix form

( 3 U/ 3 z) =A"U, (87)

where U is the vector with components IL and A' is a 16 x 16 real matrix

whose components can be determined from eqs (78-85)

Since the equations for Y^ (i=l,2,...8) are linear and homogeneous,

there are eight linearly independent solutions. We will determine these

T 30-33] eight solutions numerically . We define the k th linearly independent solution Y as a solution of the differential equation (86)

satisfying the initial condition (i.e., at z = 0) Y. (0) = 5 . , for

1 IK

i = 1,2,... 8, where <5., = 0 if i i k and 1 if i = k. The Y^ are solulk

tions of an initial value problem, and the numerical computer codes

r 34] developed by Shampine and Gordon 1 J have been used to calculate these

functions. The general solution of the differential equations is then

8 -k

y = y P k

^

k=l

( 88 )

where p^ are constants.

The boundary conditions, eqs (58-61) at z = 0 and eqs (66) at z = z^

can be written in the form

B

q Y(0) + B Y(zl

) =0, (89)

36
where B and B are 8x8 matrices whose elements are independent of z U Lj and are determined from the boundary conditions. For example, we can

order the boundary conditions in such a way that the elements in the

last four rows of B and the first four rows of B vanish. Substituting

U Lj eq (88) into eq (89) we obtain the vector equation.

= 0 , (90)

or in component form

P

k

[( Vij * C Vij Y

j

k

(*L} = °’ (91)

where (B_) . . and (B.).. are the elements in the i th row and j th

0 i] L ij — J —

column of the matrices B and B . Thus we have eight linear homogeneous

U Li equations for the eight coefficients p

. A trivial solution of these

K equations is p^ = 0 for all k. This is the only solution unless the

determinant of the coefficients vanish, i.e.

det F = 0 , (92)

where the elements F., of the matrix F are given by

8 lK

F ik = E t ( Vij Y>) + 'Vi)

1=1

(93)

Since Y. (0) = 6 , we can also write

1 3k 5

8 k

F.. = (B )

. , + V (B t ). . Y. (z T ) lk ^ 0^ lk L 13 3 V

3 = 1

(94)

Explicit expressions for (Bq)^ an<l ^p^ik are <Vn ' 1

(Bq)

12

=

37
1 ^0^22

(B

q

) 25

= -( £Va3 2k

s A/a

3

) tV 26

= t^l/V

^ B (p35

= ^ a

3

+ a

2ks

X

')

^ B 0^36

= " l' a

2 kL^

^ B (p37

= " ^ a

3m^

^ B (p45

a

4

( b

0

) 47 = ma

4

+ (l-k)Va

2

^ B(p48

= a2°p L /p

s

< B

L>51

= 1

< B L>62

= 1

( B

L>75

= b

l

^ B

lP 76

= b

2 ^87 = b

3

(B L^88

= b

4

tr\ r

with all other elements equal to zero.

Since F is in general a complex matrix, eq (92) is equivalent to two

equations, i.e., both the real and imaginary parts of det F vanish. For

particular values of the parameters occuring in the differential equations and boundary conditions, det F in general will not vanish. We

will vary two parameters, viz., and c^, until det F vanishes. We

use an iteration method developed by Brown as implemented by Gay^

Bb ^

to find values of c and a. for which det F vanishes. 00 1

38
Numerical Results

The differential equations and boundary conditions obtained in the

previous sections depend on a large number of parameters. Even if one

uses dimensionless variables, there appear to be thirteen dimensionless

parameters necessary to specify the particular solidification

conditions. A possible set of dimensionless parameters are r = v/k

(Prandtl number), s = v/D (Schmidt number), R = - gaG^z^/vx (Rayleigh

number), S = - ga G z^/vD (solute Rayleigh number), z V/v, e, k /k, k,

k /k, , VL /k T Gt , mG /GT , lAJVVv^G , V^/vyG,. » The first four r, s, R,

and S are the usual dimensionless parameters for thermo solutal

convection while the remaining parameters are related to the solidification process. Clearly, it is impossible to explore the effects of

more than a few combinations of these variables on the onset of

instability. In addition, the numerical code for performing the

calculations was only recently completed so that a very limited set of

results are available at present. Additional calculations will be

carried out in the future. In conjunction with the experimental

program, the first calculations have used parameters appropriate to the

solidification of lead containing small quantities of tin. The

specific values are given in Table 1. We have initially taken the

density of solid and liquid equal (e = 0) . In the usual morphological

stability theory the liquid density is assumed (1) independent of

temperature (a = 0) and concentration (a = 0) and (2) the density

change on solidification is neglected (e = 0). In order to distinguish
between these two effects, our initial calculations have taken e = U

and a and a non- zero. We have also neglected any kinetic effects,

c i.e., y-*».

A number of tests of the numerical program have been carried out.

Idie program was written so that the usual type of boundary conditions

can be used at both z = 0 and z = z^, i.e., of the type given by eqs

(67-59). A comparison of our numerical calculations with previous

analytical and numerical results for thermal and thermosol utal

convection is given in Table 2, and good agreement is found. Such

calculations correspond to V = 0 but G and G T finite (see eqs

(52-54)). When a = = e = 0, there is no fluid flow and the equations can be solved analytically. For solidification boundary

conditions, these are the usual morphological stability results (with

boundary conditions at z=z^). For this special case, our numerical

calculations are in agreement with the analytic results.

The calculations carried out correspond to unidirectional solidification upwards of a binary alloy which is rejecting (k<l) a solute

whose density is less than that of the solvent (a >0) . The density

change due to solute is such that heavier fluid is above less dense

fluid, i.e., the solute gradient promotes convection. The thermal

gradient is positive so that the density change due to temperature is

such that less dense fluid is above heavier fluid, i.e., the thermal

gradient is stabilizing with respect to convection. The solute gradient

falls off exponentially with a decay distance of D/V*, whereas the

40
temperature gradient is essentially linear since k/V* is typically much

larger than z^(see eqs (18-20)). We expect therefore that for sufficiently small solute concentration there will be no convection, and

the calculation will determine the solute concentration at which convection first occurs„

In carrying out a particular calculation, in addition to parameters

specified in Table 1, one specifies V, z, , and co, takes o =0, and

picks initial values of cm and c

ot

. The program then varies cm and c^

systematically until det F=0; more precisely until the real and

imaginary parts of det F are less than some prescribed value or until

the changes in a. and c

ro from one iteration to the next iteration are

less than some prescribed value. We have also written a program which

assumes that cm = 0 when o_^ = 0 (principle of the exchange of

stabilities). In this case F is real and c is varied until det F = 0.

If the initial guess for cm and c m(or c^ alone) is not sufficiently

close to the actual root of det F = 0, the iteration may not converge.

In addition, there are many roots of det F = 0, and although we are

primarily interested in the smallest value of c^ (which we denote by

c*) , the iteration may converge to some larger root. For a particular

V, we find c* as a function of w. The minimum value of c* as a function of go is denoted by c**. Calculations allowing both a. = 0 and c

to vary appeared to indicate that cm = 0; therefore most calculations

were carried out assuming cm = 0 since these require considerably less

computer time. However, as will be discussed, this assumption requires

further investigation.

41
The values of z

T were chosen such that z >>D/V* and wz >>1. For z

satisfying these conditions the results for c* were independent of z T ;

the results were also independent of the precise boundary conditions

imposed at z - z^, e.g., T = C = 0 boundary conditions gave the same

result as (37/ 9z) - (3C/9z) = 0. As coz T becomes large, the present

p computer program fails. This occurs because the functions become

very large, viz., roughly like exp (wz

L

). This results in long

computation times and decreasing accuracy. Hence, we choose z such

L that 1 <<ooz^<20 and z^>>D/V*. As can be seen from Table 2, accurate

results are obtained for ojz^=20. The program fails in a similar manner

if cm is not small, i.e., (oVD) 2 z^»l. This currently precludes investigating the existence of solutions corresponding to overstability

(cm/0) . In the corresponding problem with linear temperature and con-

[13 211 centration gradients and free boundaries 5 J it is known that

overstability does not occur when the temperature gradient is stabilizing

and the concentration gradient destabilizing as is the case in the present

[i3 21

1

solidification problem; overstability does occur L ’ J when the temperature gradient is destabilizing and the solute gradient stabilizing.

We plan to modify out numerical algorithm so that results can be obtained

for large wz and a..

Li 1 The results of our numerical calculations are presented in Table 3.

For c^ > c**, convection will occur. As the growth velocity V increases from l.Oym/s to 40um/s, c** increases and the wavelength \=2n/u

decreases. Clearly this is not a universal behavior, e.g., if V = 0,

4 2
convection would not occur and c** is infinite. The results of Table 3

00

can be rationalized if one assumes that the relevant length scale for

this particular problem is D/V. The independence of the results on the

precise value of indicates that this is reasonable. We therefore

define Rayleigh numbers based on (D/V), viz.

R' = - gaG, (D/V)

4

/ vk

S' = -ga

c Gc (D/V)

4/vD = (ga

c /vDk)(l-k)coo (D/V)'\

For the values in Table 3, j R j < | S ^ J and for V^> 2.5 ym/s | j << | S "

| ,

By assuming that the onset of convection occurs when S' exceeds a

critical value, one predicts that c** should increase with V. However,

although the critical values of S' given in Table 3 do not vary as much

as c**, they are certainly not constant. The liquid density decreases

with height as long as aG^ + a c^c

> ^ or C

oo <C co >E ( a G/a

c

) [k/ (1-k)] (D/V) =

1.896 (D/V)

+

; this value is given, in the last column of Table 3. Only

for the two largest velocities, viz., V = 40 and 80 ym/s does the

density increase with height at the onset of convection. For the other

velocities, convection occurs even though the liquid density decreases

with height.

For velocities much larger than 40 ym/s, the solid-liquid interface

is morphologically unstable for c

co >0.215 w/o . Neglecting surface

tension, the morphological stability criterion for interface stability

is c00 <[Dk(2k

LGL+VL )]/ [mV(k-l) (k L +k

g

) ] - 25.7 (D/V)

+

. For morphological

A A A instability C and T are non-zero; it follows from eq (52) that in

+ Here D/V has units of cm.

43
general does not vanish. Thus, morphological instability implies convective instability. Similarly if W, 7 is non-zero, eqs (53-54) imply

that in general T and C are non- zero and convective instability implies

morphological instability. Since in the morphological stability

criterion c** is proportional to V , for velocities somewhat greater

than 40 ym/s, c** will decrease with increasing V. The result in Table

3 for V = 80 ym/s illustrates the beginning of this trend; the value of

c** is in excellent agreement with previous morphological stability theory

which neglects convection. This may be related to the quite different

spatial frequencies at which morphological and convective instabilities

occur; the convective instabilities occur at large wavelenths compared

to the morphological instabilities. For the parameters chosen for our

numerical calculations, it appears that it is impossible to avoid

either convective or morphological instability, if the concentration is

greater than 0.2 w/o. In Figure 1 for V = 20 ym/s, we illustrate the

dependence of c* on to. The value of c** corresponds to the minimum

value of c*, viz. 0.0189 w/o at to = 24. When morphological and

convective instabilities occur at about the Same values of c , e.g. for

V = 40 ym/s, the corresponding plot of cto as a function of to is more

complicated and is still being investigated. For V = 20 ym/s, we have

also varied the temperature gradient. For Gj = 100,200, and 400 K/cm,

the values of c** are 0.186, 0.189, and 0.195 w/o with to = 23, 24, and

25 cm *", respectively. For this velocity and this range of temperature

gradients, increasing Gj has only a very small stabilizing effect.

44
At present the number of calculations is so limited that general

conclusions can not be drawn. There are a large number of areas that

require further investigation. Calculations for a range of Prandtl

numbers and systems for which the solutal and thermal Rayleigh numbers

are of the same order of magnitude appear worthwhile. The possibility

of overstability requires the development of a better computer algorithm, which is capable of handling wide variations of parameters. If

overstability occurs, the present results are only upper bounds

for the stability-instability demarcation, i.e., although instability

certainly occurs if c >c** it may occur for even smaller values. This

study has been concerned with the criteria for the onset of convective

and morphological instabilities. Of great interest is the effect of

convection on interface shape and the resulting solute distribution in

the solidified material. A limited amount of information on this can

be obtained from a linear analysis, e.g., the wavelength at the onset

of instability. A nonlinear analysis is necessary for understanding

the effects of fluid flow on solute distribution. In the near future

we will further investigate the onset of instability for a wider range

of parameters and develop improved computer algorithms.

45
III. EXPERIMENTAL INVESTIGATION

Experimental Procedures

The procedures of sample preparation, directional solidification

and sample characterization, which are being used to determine the

effects of solutal convection on the microstructure and macrosegregation of off-eutectics, are reported in the following three

sections

.

Sample Preparation - Half kg alloy melts were prepared from 99.999

pet pure Sn and Pb in evacuated and sealed silica crucibles. After

homogenization at 500C, crucibles were lowered quickly into H^O to

prevent any macrosegregation in the ingots. Ingots were swaged into 1

cm diameter rods, from which 12 gm pieces were cut for each directional

solidification tube. Five different alloys were prepared: Sn-35 w/o

Pb, -38.1 w/o Pb (the eutectic), -41 w/o Pb, -44 w/o Pb, -62 w/o Pb

.

Wet chemical analysis using a titration method yielded actual compositions of 34.7, 37.8, 40.7, 43.7, 61.1.

The samples for directional solidification are contained in 3 mm

ID, 4.2 mm OD silica tubes. In order to fill such thin tubes with

alloy without bubbles the following method is followed. A tube is

prepared with a 1 cm diameter x 3 cm long silica cup at the top with a

0.4 mm orifice between the cup and tube. The lower half of the tube is

coated with colloidal graphite and carefully dried. A thermocouple

assembly is inserted through a graphite plug at the bottom of the tube

and cemented in place with epoxy to form a vacuum tight seal. The

46
assembly consists of a commercially available thermocouple contained in

a 0.25 mm diameter stainless steel sheath coated with boron nitride.

The top 1 cm of the thermocouple is exposed and the lower portion is

held rigid by a 0.75 mm diameter Al o 0„ tube.

The tube is then inserted into a simple vacuum furnace with only

the cemented joint outside the furnace and a 12 gm alloy slug in the

cup. After evacuation the alloy charge is melted and the chamber is

vented with Ar. This casts the alloy down over the thermocouple and

fills the tube up to a level of about 18 cm. The chamber is quickly

filled with H 90 to freeze the sample from bottom up to prevent

shrinkage porosity.

Directional Solidification - The design of the directional

[4] solidification furnace is similar to that of Mollard and Flemings 1

Briefly, it consists of a bifilar wound cylindrical resistance heating

element with upper and lower sections and a circulating water cooled

chill zone. The silica tube containing the alloy is pulled down

through the chill sealed by 0-rings at constant velocity to accomplish

directional solidification. The cooling water comes directly in contact with the silica tube. The furnace is powered by an AC constant

voltage power supply and the water is cooled by a heat exchanger. The

vertical drive is powered by a synchronous motor with a multi- speed

gear box. Speeds from 0.5 pm/sec to 0.5 mm/sec are possible. The tube

is attached to the pull shaft using a device which permits the sample

to be suddenly pulled down about 3 cm to quench the liquid solid

interface.

47
The furnace is designed so that a permanent magnet with a pole

diameter of 8 cm and a pole separation of 11 cm can be slid around the

furnace to apply a 1 kilogauss horizontal magnetic field. Alternately,

an 11 cm diameter solenoid can also be placed over the furnace- chill to

apply a 700 gauss vertical magnetic field. The vertical field should

r 39

1

be the most effective in preventing convection 1 J

. These magnetic

fields will be used in future work under this contract.

A specific directional solidification experiment is conducted in

the following manner. A tube filled with the desired alloy is inserted

through the chill, with the alloy completely down in the chill section.

A vacuum is pulled on the tube from the top. The furnace temperature

is equilibrated for several hours. The temperature of the lower

winding is used to control the temperature gradient. The sample is

then run up quickly into the furnace melting about 12 cm of alloy. At

this point the top 1 cm of the thermocouple is in the liquid. The tube

is backfilled with Argon and temperatures are allowed to stabilize for

about 20 minutes „ The tube is then pulled down at the desired rate

until about 6 cm have solidified. The remainder of the sample is then

quenched delineating the liquid-solid interface in the microstructure.

The thermocouple in the alloy is used to determine the temperature

gradient in the liquid,, The silica is removed with HF acid and the

specimens are mounted in a cool -setting plastic for characterization.

Char acteri zation - Samples are routinely examined in a longitudinal

section (parallel to the solidification direction) using standard

48
metal lographic techniques „ When necessary transverse sections are also

taken. For each experiment the shape -of the liquid-solid interface is

examined to be certain that heat flow was unidirectional. Whether the

structure is dendritic, lamellar, or whether there are any signs of

growth rate fluctuations is also determined.

[71

As mentioned previously in this report, Verhoeven L 1 has shown that

considerable macrosegration occurs in directionally solidified offeutectics when solutal convection occurs. This macrosegregation is

almost impossible to detect by looking at microstructure alone. Therefore for the present work it was desirable to measure the concentration

as a function of distance along the growth direction in the directionally

solidified material. Since we are interested in macrosegregation, this

concentration must be averaged over the two phase structure and over

as much of the entire cross section of the sample as possible. For

this purpose a local energy dispersive x-ray fluorescence technique

is being employed. This technique differs from ordinary x-ray fluorescence techniques in one important way: diffraction from a perfect Si

crystal is employed to obtain a small monochromatic x-ray beam to

excite fluorescence from the sample.

AgKa radiation from a small focus conventional tube passes through

a vertical slit (0.3 mm) and a horizontal slit (1 mm) which sit 20 cm

from the source, and diffracts from the (220) plane of a perfect Si

crystal in the reflection geometry (see Fig 2) . The diffracted beam

then passes through a wide vertical slit (1 mm) and strikes the sample

to be analyzed. This beam is 3 mm high and 0.5 mm wide at the sample

49
position. The sample, which is sectioned longitudinally to the growth

direction, is placed with the growth axis horizontal and perpendicular

to the x-ray beam. The sample can be translated to perform a profile

in the growth direction,, Fluorescence from the sample is detected by a

Si (Li) solid-state detector. The 10 mm diameter detector window is

placed 40 mm from the sample surface and such that the scattering

angle to the centerline of the detector is 135°. The x-ray tube is

operated at 55 kev, 15 ma. This voltage is sufficiently high to

also excite the (440) diffraction from the Si so that the collimated

beam contains 22„1 kev and 44.2 kev components. This is done in order

to excite Snku at 25.3 kev. However, at the present time only data

from the Pb peaks is being used. The signal from the detector is processed by a multi-channel analyzer to form the x-ray emission spectrum

from a position in the sample,, A spectrum from a Sn-44 w/o Pb alloy is

shown in Fig 3. The spectrum in digital form can be transfered to a

computer for analysis. The integrated intensity is obtained for the

PbL, SnK and TDS (thermal diffuse scattering from the incident beam

peak). The latter serves as a monitor for the intensity of the

incident beam. The ratio of PbL counts to TDS serves as a measure of

the fraction of Pb in the sample. Results for runs on three different

compositions are shown in Table 4. At this point, composition resolution of 0.5 w/o Pb is possible. Further improvements are expected.

In order to determine the effective size of the incident beam,

spectra were collected from various positions across a planar interface

50
separating a piece of Au from a piece of Pb. The ratio of La counts to

TDS counts for Au and Pb uncorrected for background are shown in Fig 4.

This implies the effective size of the beam is 0.5 mm; i.e., less than

10% of the counts come from a region wider than 0.5 mm.

The reasons for using this particular technique are two- fold.

First, previous electron microprobe analyses 0 f composition profiles in two-phase structures have given very poor results presumably

due to the very shallow penetration (<1 ym) of an electron beam into

the alloy. The use of x-ray radiation for the incident beam greatly

increases the penetration; as examples, in pure Pb the characteristic

penetration depth (-jy) where y is the linear absorption coefficient for

AgKa is 10 ym and in pure Sn it is 60 ym. The higher penetration of

the x-ray radiation is necessary since the lamellar spacings are of the

order of 5 ym. Second, it is necessary for this application to have an

incident x-ray beam which is less than 1 mm wide and which is

monochromatic (or bichromat ic) . The small size is required so that the

profile can be measured with good spatial resolution and the monochromatic beam is needed to reduce the background to permit good

composition sensitivity. X-ray energy dispersive techniques not

employing diffraction from a first crystal are typically used for bulk

analysis

Further improvement will be obtained using a Ge crystal to increase

the diffracted intensity. Also by using a dual slit, a piece of the

51
diffracted beam will be monitored by a proportional counter. This

should prove superior to using TDS as a monitor because a larger number

of counts can be collected. This will improve the counting statistics

and improve the composition sensitivity.

Results

The experimental accomplishments of the first year's work under

this contract consist primarily of the development of the specific procedures of sample preparation, directional solidification and sample

characterization described in the previous sections. Using these procedures, significant advances are expected in the future. A few

preliminary results obtained from Pb-rich, Pb-Sn off-eutectics will be

described.

More than 20 directional solidification experiments have been performed on the 38.1, 41 and 44 w/o Pb alloys at solidification velocities from 0.9 ym/s to 32 ym/s. Many of these samples were solidified

to check the furnace temperature stability and drive mechanism and to

determine the relation between furnace temperature and temperature

gradient in the liquid at the interface. A problem encountered and

solved this year is demonstrated in Figure 5. This micrograph shows a

growth rate fluctuation during the directional solidification of an

off-eutectic composite. This type of fluctuation was found not to be

due to temperature instability or drive mechanism but by sticking of

[4i l the alloy to the silica tube as described by Verhoeven and Gibson 1 J

.

These fluctuations were eliminated by using a colloidal graphite

coating on the interior of the silica tube.

52
An interesting preliminary observation has been made. When samples

with compositions on the Pb-rich side of the eutectic (41 w/o Pb and 44

w/o Pb) are solidified at velocities high enough to ensure dendritic

solidification, the solidification starts out dendritic but changes to

composite after solidication distances of the order of centimeters.

For example, a 41 w/o alloy solidified at a temperature gradient of

280K/cm and a velocity of 31.7 ym/sec became composite after a distance

of 2 cm. Figure 6 shows the gradual disappearance of the dendritic

structure in a Pb-rich off-eutectic directionally solidified sample.

The composition of a composite region of such a sample determined by

wet chemical analysis was 39.6 w/o Pb; whereas the bulk alloy composition

was 40.7 w/o Pb. The change in structure down the length of a directionally solidified sample is shown in higher magnification in Figure

7 and may be typical of macrosegregation in dendritic castings caused

by solutal convection ^ ^ . In the future, measurement of composition

profiles using the x-ray method will confirm or deny this conjecture

of macrosegregation.

Future efforts will concentrate on an accumulation of reproducible

data on the microstructure and the macrosegregation present in samples

solidified under various conditions thought to produce solutal convection. The effect of the magnetic field on the suppression of these

flows will then be initiated.

53
Acknowledgements

We acknowledge the substantial contributions of Professor Robert F.

Sekerka of Carnegie-Mellon University and Consultant to the National

Bureau of Standards to the theoretical part of this research. We would

also like to thank J. R. Carruthers, D. T. J. Hurle, M. Kuriyama and

R. G. Rehn for helpful discussions.

54
References

[1] J. R. Carruthers, Preparation and Properties of Solid State

Materials , Vol. 3, Eds. W. R. Wilcox and R. A. Lefever (Marcel

Dekker, Inc., New York, 1977) p. 1.

[2] Do T. J. Hurle, Current Topics in Materials Science , Vol. 2,

Eds. E. Kaldis and H. J. Scheel (North-Holland, Amsterdam, 1977)

p. 549.

[3] R. M. Sharp and A. Hellawell, J. Crystal Growth 12_, 261 (1972).

[4] F. R. Moilard and M. C. Flemings, Trans. AIME 239 , 1534 (1967).

[5] J. D. Holder and B. F. Oliver, Met. Trans 5_, 2423 (1974).

[6] K. G. Davis and L. M. Hogan, unpublished results shown in K. G.

Davis and P. Fryzuk, Can. Met. Quart, 10 , 273 (1971),

[7] J. D. Verhoeven, K. K. Kingery and R. Hofer, Met. Trans. 6B ,

647 (1975).

[8] J. A. Burton, R. C. Prim and W. P. Slichter, J. Chem. Phys.

21_, 1987 (1953).

[9] J. D. Verhoeven, J, C. Warner and E. D. Gibson, Met. Trans.

1437 (1972)

[10] L. Vandenbulcke and G. Vuillard, J. Crystal Growth 36_, 47 (1976) .

[11] N. Streat and F. Weinberg, Met. Trans. 5, 2539 (1974) and

references therein.

[12] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability

(Oxford, London, 1961).

[13] J. S. Turner, Buoyancy Effects in Fluids (Cambridge, London, 1973).

55
[14]

D. D. Joseph, Stability of Fluid Motions I and II (Springer

Verlag, Berlin, 1976)

[15] G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of

Incompressible Fluids (Keter, Jerusalem, 1976).

[16] C. Normand, Y. Pomeau and M. G. Velarde, Rev. Mod. Phys. 49 ,

581 (1977).

[17] J. S. Turner, Ann. Rev. Fluid. Mech. 6_, 37 (1974) .

[18] R. S. Schechter, M. G. Velarde and J. K. Platten, Adv. Chem.

Phys. 26, 265 (1974).

[19] M. E . Stern, Tellus 12_, 172 (1960).

[20] R 0 L 0 Sani, Ph.D. dissertation. University of Minnesota, 1963.

[21] D. A. Nield , J. Fluid Mech. 29_, 545 (1967).

[22] P. G. Baines and A. E. Gill, J. Fluid Mech. 37 , 289 (1969)

[23] G. Veronis, J. Mar. Res. Z3, 1 (1965).

[24] R. L. Sani, A. I. Ch. E. J. 1_^, 971 (1965).

[25] G. Veronis, J. Fluid Mech. 34 , 315 (1968).

[26] J. M. Straus, J. Fluid Mech. 56_, 353 (1972).

[27] H. E, Huppert and D. R. Moore, J. Fluid Mech. 78 , 821 (1976)

[28] R. F. Sekerka, Crystal Growth : An Introduction , Ed. P. Hartman

(North-Holland, Amsterdam, 1973) p. 403.

[29] R. T. Delves, Crystal Growth , Vol. 1, Ed. B. R. Pamplin

(Pergamon, Oxford, 1974) p. 40.

[30] H. B. Keller, Numerical Methods for Two- Point Boundary Value

Problems (Blaisdel , Waltham, MA 1968).

56
[31] H. B. Keller, Numerical Solution of Two Point Boundary Value

Problems (Society for Industrial and Applied Mathematics,

Philadelphia 1976)

.

[32] D. P. Chock and R. S. Schechter, Phys. Fluids 16, 329 (1973).

[33] D. P. Chock and C.-H. Li, Phys. Fluids 18_, 1401 (1975).

[34] L. F. Shampine and M. K. Gordon, Computer Solution of Ordinary

Differential Equations - The Initial Value Problem (W. H. Freeman,

San Francisco, 1975)

.

[35] K. M. Brown, SIAM J. Numer. Anal. 6_, 560 (1969).

[36] D. M. Gay, CNA-109 (Center for Numerical Analysis, The University

of Texas at Austin) Dec. 1975.

[37] W. H. Reid and D. L. Harris, Phys. Fluids 1, 102 (1958).

[38] E. M„ Sparrow, R. J. Goldstein and V. K. Jonsson, J. Fluid Mech.

18_, 513 (1964).

[39] B. Lehnert and N. C. Little, Tellus 9^, 97 (1957) 0

.

[40] R. M. Sharp and A. Hellawell, J. Crystal Growth 5_, 155 (1969).

[41] J. D. Verhoeven and E. L). Gibson, J. Crystal Growth 10 , 235

(1971)

.

57
Table 1. Values Used in Numerical Calculations

v (kinematic viscostiy)

k (thermal diffusivity)

D (diffusion coefficient)

g (acceleration of gravity)

a (thermal coefficient of expansion)

(solutal coefficient of expansion)

k (thermal conductivity)

L (thermal diffusivity of solid)

k^ (thermal conductivity of solid)

(latent heat per unit volume)

m (liquidus slope)

T

M

r (capillary parameter)

y (kinetic coefficient)

k (distribution coefficient)

e (fractional density change)

r (Prandtl number v/k)

s (Schmidt number v/D)

k /<

s

2.43(10~ 3

) 2. cm /s

.108 cm“/s

3. 0 (10~ 5

) 2, cm /s

980.0 cm/s^

1 . 15 (10~ 4

) K1

5 . 2 (10~ 3

) (w/o)

1

.159 J/cmKs

.202 cm/^s

.297 J/cmKs

256.0 J./ cm

3

-2.33 K/(w/o)

1.0(10' 5

) cmK

oo cm/sK

0.3

0

2 . 25 (10~ 2

)

81.0

1.87

1.87

200.0 K/cm

58
Table 2. Comparison of Numerical Results with Previous Results

Case

+ w ERR

+ + R

R

(previous) Reference

1 3.117 io"

4

1707.35 1707.762 37

2 2.55 10" 4 1295.67 1295.781 38

R+S

Case to ERR R+S (previous) Reference

3 3.117 io"

4

1707.8 1707.762 21,37

3 3.117 io"

4

1707.5 1707.762 21,37

3 5.117 10

- 8 1707.762 1707.762 21,37

3 8.0 io'

6 7084.50 7084.51 21,37

3 20.0 io8 173573.47 173573.46 21,37*

3 20.0 io'

6

218625 218584.1 21,37*

3 20.0 io8 218584.1 218594.1 21,37*

4 tt/(2) %io"

6 657.577 657.5114 21

4 10.0 io8 943916 943864 21

4 20. 0 io8 172785 172138 21

+ Case 1: rigid; T=

at z=0 and z=l; C=0 for all z

Case 2: rigid; T= 0 at z=0 and (3T/9 z)= 0 at z=l; C=0 for all z . Case 3: rigid; T=C=

at z =0 and z=l.

Case 4: free; T=C=at z= 0 and z=l

rigidW = ( 3W

z z

/ 3 z ) = 0 at z =0 and z=l.

free W =(3

2W

z z /3z

2 )=0 at z=0 and z=l.

++ ERR is an error tolerance in the code for solving the differential

equations

calculated from formula of reference 37.

59
Table 3

.

Bulk Concentrations

,

c** at Which Convection

First Occurs as a Function of Velocity V

V c** X Dm/V S' c"

(pm/s) (w/o) cm w/o

1.0 3.16(10' b 2.4 0.8 1390 5 . 7 (10“ 1

)

2.5 4.10(10" b 1.0 0.7 116.0 2. 3(10

_1

)

5.0 8.39(10" 4

) 0.6 0.6 29.6 1.1(10

_1

)

10.0 3.10(10" b 0.4 0.4 13.6 5.7 (10' 2

)

20. 0 1.89 (10~ 2

) 0.26 0.36 10.4 2. 8(10' 2

)

40. 0 1.86(10" b 0.14 0.34 12.8 1 . 4 CIO'

2

)

80.0 1.16(10" b 0.0070 3.4 1.00 7.1(10“^)

See Table 1 for values of physical quantities used in the calculations;

S"=(ga

c /vDk) (l-k)c** (D/V) ^ and c''=(aGD/a V) [k/(l-k)] . For Cm

<c^' the

unperturbed density is a monotonically decreasing function of height.

60
Table 4. Check on Reproducibility and Sensitivity

of X-Ray Chemical Analysis Technique

Integrated Intensity

Analysis Composition (counts) Ratio

No. w/o Pb PbL TDS PBL/TDS

105 37.8 206,747 24,580 8.41

106 37.8 223,252 26,105 8.55

8.46+. 06

107 37.8 207,524 24,526 8.46

108 37.8 192,960 22,923 8.42

109 40.7 212,595 22,722 9.36

110 40.7 213,104 22,580 9.44

9.43+. 06

111 40.7 213,708 22,717 9.41

112 40.7 213,863 22,496 9.51

113 43.7 258,690 25,571 10. 12

114 43.7 256,742 25,762 9.97

115 43.7 263,423 25,948 10.15

116 43.7 245,714 24,410 10.07

117 43.7 232,170 22,874 10.15 10. 11+.. 08

118 43.7 225,439 22,135 10.19

119 43.7 222,242 22,094 10.06

120 43.7 229,763 22,897 10.04

121 43.7 244,851 24,006 10.20

A 0.5 w/o PELPb change corresponds roughly to a

1 JJo ratio change of 0.13.

ir

61
Fig. 1. The stability-instability demarcation as a function of the

spatial frequency w for a growth velocity of 2(10-3

) cm/s and

a temperature gradient in the liquid of 200 K/cm. For values

of the bulk concentration c^ above the curve, the system is

unstable with respect to disturbances of wavelength 2 tt/u>. For c

oo <0.0189 w/o, the fluid is stable with respect to all

small perturbations.

62
SILICON

H CD

K)O 4-> G

CO CD X o

•H 4-1

X og

0) 4-1 >

•H

G

W

O

g

4-1 -H <D

in

p

'H

rt rS

OX

CDOP£

aJCD

CD P -Q Oh O

i/I c3

X •h 4 ri

"C! 4-!

G

4-1 i X-H X

bo

Q

G

O

CD -H G • P

<U to ecS •H £ t—i to O

rt

X 4 O P X o rt a G o

rt

C

4-1OPG0£G ,G

bX>O

•H

GO

4-1

ajo

•H£

CD

ri

G

rH

CtJ aj "O P O CD G c/1 3

Gho

njG

G

<u -c G o

CD CD C3 P O

CD P 3

cr-G

CD £OG

4-i

CM

txO •rH tu

63

the

sample.
PbL/3 >

LU o

roO

c\J i

Fig.

3.

X-ray

spectrum

(intensity

versus

energy)

obtained

from a

single

position

in

Sn-44

w/o

Pb

alloy.

The

counting

time

for

this

spectrum

was

8x10 s

and

the

peak

intensity

is

about

10^

counts.

The

upper

half

of

the

spectrum

is

also

shown

with

intensity

magnified

ten

times.
65

Fig.

4.

A

plot

of

integrated

intensity

ratio

of

La

counts

to

TDS

counts

versus

distance

across

a

boundary

separating

a

piece

of

Au

from

a

piece

of

Pb.

This

demonstrates

the

spatial

resolution

of

the

chemical

analysis

technique.
Fig. 5. Longitudinal section of a growth

rate fluctuation caused bysticking of the alloy to the

silica tube during directional

solidification. The Pb-rich

phase is dark and the Sn-rich

phase is light. Optical

micrograph. Magnification 256

times
m

ijlwl'Ti'

'

; %§«

Mia

brlfe' yf : vri

-V |ip'3

;"

; ! 1 , •;i‘|

Wf$£W >

ililiilmi

-0

CU

I O *H \ ip

3 -HT3 Hr=Ho

to

o> X

p

fi *H

^rC

to"d

4)

* H

4h•H

m3

•H 10 r—) CD O P

10 *HP

<-H c

c

o

•HP

O

<DP

»HTJX

P

3

O

pu

4-1o

Pio

•H

+-> o

<uto

CO

0)S

• H

P

O

•*fr Co

«HP

<no

o

o

Pi

ajp

a

CD 4h

CLi *H

P4 Pi

cc$ bO

to 2

ci Pi p o

*rl bO P

P! O

H <D 3 P

PXbO

t3

aj

Pi •HT3 2 to p fl H X O M O 'H

P! h P

O <—» n5 J n! O

0) 4PP

OP

Pi3

O

4P

to

vO

bfl H

tu

67
Fig. 7. Longitudinal section of a directionally solidified Sn-44 w/o

Pb alloy showing the change in structure in the solidification

direction.

(a) Quenched liquid^solid interface, 4.2 cm solidified,

(b) 3.0 cm solidified, (c) 1.7 cm solidified, (d) 0.2 cm solidified. Growth direction shown* vertically. Magnification

256 times.

68
Task 3

Determination of Crystal Perfection

M. Kuriyama and H. E. Burdette

N Metal Science and Standards Division

Center for Materials Science

> r

* Summary

The objective of this year's task is shifted from the actual crystal

growth on Earth to helping NASA establish methods for evaluating spacegrown crystals with reference to nearly perfect crystals grown on Earth.

) For this purpose our intention is to perform Asymmeric (Double) Crystal

Topography (ACT) on a real-time basis so that any laboratory can evaluate

crystal perfection routinely with the same accuracy using an ACT camera.

In this report Section II includes the crystal characterization work on

nickel single crystal growth with emphasis on the interpretation of

observed imperfection images including a new rule of image invisibility.

Section III covers our activities on real-time imaging, which are aimed

toward improvement of resolution and brightness.

69
I. INTRODUCTION

The previous objectives dealt with the assessment of crystal perfection as crystal growth conditions were deliberately changed, so as to

obtain the relationship between resultant crystal perfections and crysn-31

tal growth conditions . In order to do this it was necessary to

introduce a new technique for the evaluation of crystal perfection by

x-ray diffraction topography, namely Asymmetric Double Crystal

Topography (ACT) ^ . With this technique, we were able to evaluate

the crystal perfection of a large number of Czochralski grown crystals

(about 20 boules a year and more than 50 crystal slices) routinely but

more accurately than the ordinary topographic methods.

The objective of this year's task is different from those of previous years. This year's goal is shifted from the actual crystal growth

on Earth to helping NASA establish methods for evaluating space-grown

crystals in comparison with crystals grown on Earth. Our intention is

to perform ACT on a real-time basis so that any laboratory can evaluate

crystal perfection routinely with the same accuracy using an ACT camera.

In the past, we demonstrated that ACT is best suited to the characterization and assessment of crystals and is superior to other

well-known topographic techniques, such as the Berg-Barrett technique

I 7 8

1

and Lang techniques 1 *

. This is because the ACT system is more

sensitive to strains and imperfections in crystals than the other

methods. A well-considered use of the x-ray diffraction effect makes it

possible to obtain improved x-ray optical resolution and strain-
sensitivity. Although this ACT system is versatile and simple to

operate in that it requires neither a- micro-focus x-ray source and

generator nor a scanning device, this system still suffers from one

problem common to other topographic systems. This problem is that it

takes a long exposure to record high resolution diffracted images, in

which all the information necessary to characterize the crystal is

delivered. This cumbersome problem deters many people from characterizing their crystals accurately.

In this task, we aim at obtaining improved real-time imaging systems

with sufficient resolution and intensity-sensitivity „ These systems,

once successful, will be used not only with the ACT system but also

with x-ray or y-ray radiographic systems for material flaw inspection.

Since the work on this task was at a reduced level this year, the

results reported here are by no means final and should be considered as

a starting point for further work.

Section II includes the crystal characterization work on nickel

single crystal growth, which has thus far been unreport ed 0 Section III

covers our activities on real-time imaging.

II. CHARACTERIZATION OF CRYSTAL PERFECTION

In x-ray topography, the visibility or invisibility of imperfection

images is quite important for the characterization of crystal imperfections. The direction (and sometimes also the magnitude) of atomic

displacements can be determined by just looking for the existence or

non-existence of images. One of the unique features of the ACT system

71
enables us to observe imperfections deep in the interior of quite thick

Olmm) crystals. In the x-ray topography of thin crystals kinematical

scattering processes dominate the formation of topographic images. By

contrast, in the x-ray topography of thick crystals, the conditions of

invisibility differ considerably, depending upon the nature of imperfections-^. Here the product of thickness and linear absorption

coefficient, yL, is greater than 10. These conditions had never been

studied before the ACT system was fully developed. The recent availability of synchrotron radiation will now provide the same opportunity

as the ACT system.

We continued the characterization of nickel single crystals grown

under different conditions. Since nickel is ferromagnetic, magnetic

domains form in it. The magnetic domain walls between the domains are

usually strained due to a magnetostriction; in other words, the domain

walls can be thought of as crystal imperfections. When magnetic domain

walls extend all the way through a crystal, and the crystal is thick,

topographic images are usually produced by the domain walls. These

images are called disruption images or shadows.

We have observed a new rule for the visibility or invisibility of

[91 these domains . These rules relate crystal and defect orientations to

diffraction condition, as described in reference 9. This new rule is,

in general, applicable to a non-isolated thin planar defect which has an

extremely regular atomic displacement. One such defect could be a

stacking fault.

72
The methods of interpreting topographic images in ACT have been explained elsewhere ^ - through the application to nickel crystals.

When bulk crystals are used for the true assessment of crystal imperfections, the interpretation of images obtained with the ACT systems or

synchrotron radiation requires different rules from the familiar ones

for the ordinary Lang topography. With ACT system, for example, it is

possible to identify crystal imperfections whose identities would not be

uniquely determined by ordinary Lang techniques.

III. RESOLUTION IMPROVEMENT IN REAL-TIME IMAGING

For the rapid and accurate assessment of crystal perfection, an

improvement in resolution of a real-time imaging system is required without loss of image brightness 0 As in ordinary optics, two principal

problems will be involved to achieve improved resolution: one is the

collimation of incoming beam, and another is the spatial resolution on

an imaging detector. If one could make the size of the beam source truly

a mathematical point, the first problem would be solved. However, this

is not possible. One has to devise a method of controlling the spatial size

and angular divergence of the incident beam regardless of the size of

the beam source — this is the problem of collimation 0

We deal with two objects each of which has a finite size and which

are located a given distance apart. Tentatively, resolution will be

defined by the minimum distance between the centers of these two objects

before the images from the two objects start overlapping in the imaging

detector. Before describing the method used in the current work, other

73
methods of improving angular resolution will be described for comparison. It is concluded that the method being developed in the current

work provides major advantages over these other methods.

Collimation

The earliest attempts at spatial collimation of an x-ray beam

consisted of an arrangement of single slits to define beam direction,

sometimes followed by Bragg reflection by a crystal. The beam colli-

[121 mated in this way was, generally, quite small. Soller L first

suggested collimating an x-ray beam by using multiple long foils, each

spacing defining a narrow beam divergence, over a rather large area. It

is interesting to note that Soller's original plan was to study microscopic changes due to thermal, mechanical, or other physical influences

on materials. The first Soller slits were made with lead foils, with a

length to spacing ratio of 166:1. Although lead is not the ideal material for Soller slit foils because of its mechanical properties, it does

illustrate several other important considerations in the manufacture of

this device. It is very important to avoid K- fluorescence and surface

reflection by the foils. There are clearly two ways to avoid the first

problem: either the foil materials must have a higher K-excitation energy

than the energy of the penetrating radiation, or they must have such a

low excitation energy that, although much fluorescence is present, it is

absorbed either in air or the detector window or can be discriminated by

the pulse height analysis system. The best collimation will be achieved

if the foil material can be chosen such that it has an absorption edge

74
near the energy of the x-ray beam. The problem of surface reflection on

the foils has been at least partially .solved by roughening the foils

[ 13 ] with emery, with a reported 1 20% increase in resolving power for the

case of FeKa x-rays collimated by A1 0

The common Soller slit ratio in use today is 30:1, resulting in an

angular divergence of about 2°, compared to Soller' s 1/3°. The ultimate

collimation the device can achieve is the order of 1 to 10 arc minutes

angular divergence,,

Another collimating device, originally designed to study grain

boundaries, inclusions and details of histological specimens, utilized

surface reflections in order to improve the ratio of transmitted to in-

[14] cident flux. This device consisted of bundles of glass capillaries L J

from 2-12x10 6 m in diameter and 0. 5-1. 0x10" z m long. Although the

apparent "best case" collimation is of the order of 1 arc minute, the

angular divergence is significantly greater because of the reflections.

One can make a similar statement where a single wedge-shaped glass

arrangement is used to collimate CuKa x-rays. An actual collimation of

15 arc minutes was achieved, with an ultimate limit of 5 arc minutes

predicted .

A novel approach to the mechanical collimation of x-rays -- the

multiple slit array 1- J -- eliminates entirely the internal reflection

of off-axis radiation. This device was conceived for x-ray astronomy,

where it is desirable to have a large percent transmission over a very

narrow angle so that x-ray fluxes from neighboring sources in the galaxy

75
could be resolved. In this collimator, identical grids, which are prepared from a master by precision photomicrographic techniques, are

spaced in a progressive pattern. That pattern is designed, based on

simple geometric considerations, to eliminate all possible off-axis

paths. The overall length determines the angular resolution. The first

intermediate grid (j) is placed midway between grid (i) and the right

end grid; grid (k) is placed midway between grid (j) and the right end

grid, etc.. The geometry allows a minimization of the number of grids

actually needed to achieve the desired overall angular resolution, based

on the number of slits in each grid. McGrath 1 J has estimated that the

best collimation that can be achieved with this device is 30 arc minutes

with 40% transmission.

There are several problems inherent to the above device especially

when viewed from the application to hard (over 8 kev) x-radiation. One

would require that each grid be opaque to the radiation of interest because some beams are blocked by only one plate thickness. Also, this

apparently simple instrument requires very close alignment tolerances,

especially for the closely spaced grids near the beam exit. This makes

the device quite difficult to construct. A collimator in which the

[ 17 ] grids contain a random array of apertures has been suggested and

r 1 8 1 constructed 1

- , which to some degree eliminates these problems. With

an array of identical grids with random apertures, each part of the beam

must pass through the same hole of each grid, and the grid plates are nsi evenly spaced. Tests 1 J of this device using 8 plates, 1.27x10 2 m

76
apart, yielded an angular response at AlKa (8.34A°) of 15 arc minutes

and 27% overall transmission. These plates were 25x10 6 m thick stainless steel with 2000 holes, 0,36x10 3 m in diameter, inside 2x10 4 m2.

The random hole pattern was derived from a random computer output and

photographic etching techniques. A similar output could be used to

prepare a tape for a tape operated drilling machine and much thicker

plates, suitable to hard x-radiation.

r 19 ] An offshoot of this device, the modulation collimator 1

- , is the

current favorite of x-ray astronomers. Used in its rotating mode-“^,

F 21

1

it can be used to reconstruct the location of celestial x-ray

sources down to a few seconds of arc. The multiple set of grids is replaced with multiple grids of wire. The spacing and the wire diameters

are determined by the same geometrical arguments as above. The resultant collimator has multiple angular transmission planes. If the

modulation collimator is rotated about the line of sight, the x-ray

signal from each source is modulated with frequency components and with

a phase characteristic of each source's location in the field of view.

The resultant time varying signal can be Fourier analyzed to reconstruct

the source locations. Clearly, both the actual alignment and the

precision calibration of a modulation collimator are quite complex.

While these developments were underway in mechanical collimation,

another very successful means of collimation was also being explored.

r 2 2

1

This method, first suggested by DuMond 1

, makes use of multiple

parallel reflections by a very good crystal near the Bragg angle to

77
achieve highly collimated, very monochromatic x-ray beams. The Bragg

condition for one crystal can be represented by a band. After successive diffraction by two or more crystals, a very narrow-range of

wavelength and angular divergence, corresponding to the overlapping of

the several bands, is selected. With asymmetric diffraction, the very

[1 4 5 7 23 24] parallel beam can also be magnified in area L * 5 J * 5

This is the principle used for our asymmetric crystal topography

(ACT). The angular collimation from a two crystal arrangement using

this principle was found to be much less than 10 arc seconds in the ACT

system. Also the collimated beam still was sufficiently strong, as

demonstrated by the successfully imaged topographs mentioned in Section

III. Using a multi-crystal arrangement, the narrowest angular spread

actually measured was 0.16 arc seconds, well beyond the usual limits of

mechanical collimation. Unfortunately, the collimated beam in this case

was quite weak after two or three reflections. Nevertheless, the 10 arc

second collimation achieved from two crystal arrangement is much better

than that achieved by other techniques.

In sum, it is concluded at the present time that the collimation for

the ACT system is the best among those above mentioned collimation

methods, particularly because the collimated beam is sufficiently

intense (or bright) for practical use.

Resolution With Various Screens

Currently, image intensifiers for visible light are commercially

available at reasonable cost. These can be made into x-ray image

78
intensifiers by placing a fluorescent (phosphor) screen in front of the

[2 7] fiber-optic input faceplate as described in previous papers 1 1 J

.

Obviously, the resolution of the x-ray image depends strongly on the

properties of the phosphors 0 We have tested various phosphors, such as

polycrystalline cadmium sulfide and gadolinium oxy-sulfide, and single

crystal cesium iodide.

For the previous topographic work, a 0.1 mm thick Ag-activated

(Cd,Zn) S fluorescent screen was used. This material was selected

simply for its adequate intensity yield of visible (green) light after

the conversion from x-rays. Therefore, the resolution was not good for

real-time imaging. We tested five additional (Cd,Zn) S phosphors for

resolution and intensity- sensitivity (brightness) with CuKa(8kev),

MoKa(17 kev) and AgKa(22 kev) radiation. Nichrome, Sn-bronze, stainless

steel and gold meshes of various sizes were placed in the path of a beam

collimated by the method described previously. We were able to achieve

a resolution of 250 ym with all of the phosphors, but their intensitysensitivity varied enormously. As expected, the brightest image was

obtained using the coarsest phosphor.

A series of gadolinium oxy-sulfide (Gd202S) and yttrium oxy-sulfide

(T 20 2 s) were tested next. Their particle sizes were quoted to be 6 ym

and 3 ym, respectively. The thicknesses of gadolinium phosphors were 17

mg/cm2 and 19 mg/ cm2

, and those of yttrium phosphors are all 19 mg/cm2

.

Their resolution reached 125 ym, but the brightness from yttrium

phosphors was so low that they were considered to be impractical. It

seems quite difficult to prepare thin phosphors from fine particles for

79
the further improvement of resolution. Therefore, we attempted to

prepare phosphors from single crystals.

We chose cesium iodide (Csl) single crystals for this purpose. For

slicing and polishing, we modified the acid saw and the acid polisher

which were used for copper and nickel single crystals. Cutting was made

using nichrome wires carrying a solution of 5 to 10% distilled water in

ethyl alcohol „ The proper speed was chosen by trial and error for each

boule of a different diameter „ Polishing was tried in two ways:

1) Mechanical polishing - crystal slices were polished first on

abrasive papers to obtain a desired thickness and then on a lapping

wheel to produce an optical finish on the surfaces.

2) Chemical polishing - slices were polished with 5 to 10% water in

alcohol on a precision polishing wheel attached to the modified acid

polisher. Even though considerable efforts were made on the precision

for the flatness and the rotation axis of the polishing wheel, this

polishing method produced lens shaped samples due to the chemical

reaction around the edge of the slice.

It was important to hold slices securely without straining them

during polishing. Various methods were tried; for example, "Opticon

UV-57" optical cement* was used with only partial success. This produced uneven bonding. Dow Corning "2-3067 optical couplant"* was found

to be satisfactory. This is particulary suitable for mounting a crystal

on fiber optic plates. The polished crystals were finally mounted on

Use of the trade name does not constitute a product endorsement.

80
fiber optic plates which matched the plate on the front of the image

tubes o

In spite of all these efforts, resolution was not improved much from

the one (>125pm) obtained with polycrystalline phosphors , The brightness was not improved either. Some of single crystal phosphors yielded

less brightness than polycrystalline ones, probably due to the uneven

thickness of single crystal wafers. The very thin single crystals

showed a marked decrease in brightness. They were impractical for use

in the image tubes, even though the resultant resolution was better than

that achieved from others.

In conclusion, the present approach in the improvement of resolution

for real-time imaging always encounters two opposing problems simultaneously; if one improves the resolution, then the brightness decreases,

and vice versa. The best resolution which is easily obtained by the

ordinary preparation of phosphors can be said from our experience to be

about 150 ym, without loss of significant brightness. If one uses

commercial inexpensive image intensifiers like the one we used, they

have a resolution limit determined by the size of the fiber diameter in

fiber optical plates. They may be about 50 pm down to 10 pm at best.

Therefore, the present approach or any similar approach would not

succeed in reducing the resolution for real-time imaging to less

than 10 pm or to a submicron range. As a result, we have since taken

a completely different approach mostly based on reexamining existing

collimation techniques to overcome the resolution problem. This new

approach including a two crystal arrangement mentioned above has been

quite successful.

81
References

M. Kuriyama, J c R. Early and H. E„ Burdette, NBS report 10873

(1972); NBSIR 73-402, 3 (1973).

Mo Kuriyama, W 0 J. Boettinger, H. E. Burdette and R, M. Eaton,

NBSIR 74-611, 3 (1974).

M. Kuriyama, W. J. Boettinger, and H. E. Burdette, NBSIR 76-980,

3, (1976); NBSIR 77-1208, 3 (1977).

M 0 Kuriyama, J. G. Early and H. E. Burdette, Proc. AIAA 12th

Aerospace Sciences Meeting, Paper No. 74-204 (1974).

M. Kuriyama, J. G. Early and H. E. Burdette, J 0 Appl. Cryst. 7_»

535 (1974).

W. J. Boettinger, H. E. Burdette and M. Kuriyama Phil. Mago 34 ,

119 (1976).

W„ J. Boettinger, H. E. Burdette, M» Kuriyama and R. E. Green, Jr.,

Rev. Sci. Instr. 47 , 18 (1976).

W. J. Boettinger, H 0 E. Burdette, E. N. Farabaugh and M. Kuriyama,

Advances in X-Ray Analysis , Vol. 20, Eds. H. E. McMurdie, C. S.

Barrett, J„ B. Newkirk and C. 0„ Ruud (1977) p. 207.

W. J. Boettinger, H. E. Burdette and M. Kuriyama, Phil. Mag. 36 ,

763 (1977).

M. Kuriyama, W 0 J. Boettinger and H. E. Burdette, Advances in X-Ray

Analysis , Vol. 20, Eds c H„ E. McMurdie, C. S. Barrett, J. B. Newkirk

and G. 0. Ruud (1977) p. 245„

M. Kuriyama, W. J. Boettinger and H. E. Burdette, J. Cryst. Growth

43_, 287 (1978).
[12] W. Soller, Phys. Rev. 24, 158 (1924).

[13] J. Drahokoupil, Czech. J. Phys. 6, 35 (Jan. 1956).

[14] F. Fournier, Compes Rendus de l’Acad. Sci. 227, 833 (1948).

[15] J. A. Lely and T. W. van Rijssel, Acta Cryst. 2, 337 (1949) and

Philips Tech. Rev. 13 , 96 (Oct. 1951).

[16] J. F. McGrath, Jr., Rev. Sci. Insto 39, 1036 (July 1968).

[17] J. H. Underwood, Rev. Sci. Inst. 40, 894 (July 1969).

[18] R. S. Wriston, Rev. Sci. Inst. 45, 1566 (Dec. 1974).

[19] M. Oda, Appl . Opt. 4, 143 (1965).

[20] H. W. Schnopper, R. I. Thompson, and S. Watt, Sp. Sci. Revs. 8,

534 (1968).

[21] H. Bradt, G. Garmire, M. Oda, G. Spada, B. V. Sreekantaw,

P. Gorenstein, and H. Gursky, Sp. Sci. Revs. 8, 471 (1968).

[22] J. W. M. DuMond, Phys. Rev. 52, 872 (1937).

[23] K. Kohra and S. Kikuta, Acta Cryst. A24, 200 (1968).

[24] M. Kuriyama and W„ J. Boettinger, Acta Cryst. A32, 511 (1976).

83
Task 4

A Thermochemical Study of Corrosive Reactions in Oxide Materials

H. S. Parker, R. S. Roth and C. D. Olson

Ceramics, Glass and Solid State Science Division

and

E. R. Plante

Chemical Stability and Corrosion Division

Center for Materials Science

Summary

The system KFeC^-Fe,^ has been examined over portions of the

subsolidus region. The occurrence of a B-alumina structure-type at

a composition K

9 0 : 5 . 75Fe 7 03 (85.2 mole percent Fe^O^) has been

observed. Little corrosion of platinum by this composition at a

temperature of 1475°C was detected. Vapor pressure measurements of

-4

KFe0 o showed an equilibrium potassium pressure of the order of 10

atmospheres in the 1200°C range.

84
Introduction

The major objective of this work is to further the understanding

of the reactions of alkali oxides and iron oxides with other oxides

common in MHD and fuel cell environments. The alkali oxides as a

class and the transition elements, with iron oxide as an example, are

extremely reactive, particularly in the liquid state. Because of

sample-container reaction in laboratory studies, a further objective

is to investigate the nature, extent and limitations imposed by this

reaction and to evaluate containerless techniques for melt and solid

state studies. At the present time, severe problems associated with

chemical reaction, corrosion and erosion exist with electrode-insulator

materials in the current generation of MHD channels as a result of the

K^O derived from the required potassium seed together with various

combinations of K

? 0 , SiO^, Fe^O^, Al^O^ an<^ ot^er oxides in those MHD

channels operated with slagging electrodes (coal combustion).

Additionally, one proposed fuel cell concept envisions a molten alkali

carbonate eutectic cell with a ceramic matrix, again with a concomitant

corrosion problem. However, the study of reactions with alkali oxides,

iron oxides and other ceramic oxides is severely hampered and results

often vitiated by corrosive reaction with the necessary container

material, whether it be ceramic or metal. Thus, it is suggested that

the ultimate studies could best be performed in a zero gravity environment where containerless studies might more easily be performed. It is

anticipated that such experiments could provide data of importance not

85
only to the technological community concerned with alternate energy

sources, but in addition provide fundamental data on the basic

equilibrium assemblages in such systems. Studies in the K^O-A^O^-

Fe^O^-SiC^ system are currently in progress at NBS as part of our

program on materials degradation in an MHD environment. Complementary

investigations in a containerless geometry would enable measurements

otherwise unobtainable to be made as well as an estimate of the effect

of container reaction on properties of importance in MHD applications.

As indicated above, the problems of greatest urgency are those

involving iron and alkali oxides in contact with ceramic oxides,

primarily Al^O^ and MgO , with the resulting degradation of properties

through compound formation or eutectic melting. Attempts to investigate

potential solutions to these problems in the laboratory are severely

hampered by the simultaneous reduction of iron oxide and alloying with

the platinum container and the reaction of the alkali oxides with the

platinum container. Both of these reactions severely compromise the

bulk composition of the sample under investigation. Al^O^ and MgO

crucibles have both proven unsatisfactory containment materials, reaction with these oxides either forming compounds or penetrating the

crucible walls with subsequent disruption on cooling. For limited

studies, containers of a silver-palladium alloy are of some use at

temperatures up to 1200-1400°C. However, temperatures well in excess

of 1400°C are of interest in MHD environments. A further problem

urgently requiring investigation is associated with the geometry

86
and materials in current MHD channels. Iron oxide is one constituent

of the electrodes which are in contact with aluminum oxide or MgO

insulators. A further complication is associated with the slag which

contains potassium, silica, alumina and iron oxide. Reaction of slag

with the oxide insulators and electrodes degrades the performance of

both and is a major problem at the present time. These reactions

include compound formation, melting and vaporization.

The initial system chosen for investigation is the KFeO -FeO

Z X

portion of the K^O-FeO^ system, in part because of its immediate

applicability to the study of slag-electrode reactions in MHD systems.

Of further interest in this system are those phases with the 3-alumina

structures which may exhibit high ionic conductivity as well as high

electronic conductivity. During the period covered by this report,

the major effort has been directed towards a general survey of the

subsolidus phase equilibrium assemblages and vapor pressure measurements of KFeO^.

Experimental Procedures

In order to prevent hydration of both starting materials and

heated samples it was necessary to perform all handling operations

including weighing, blending and grinding in a drybox. Transfer of

materials between laboratories was done in small dessicators.

Potassium carbonate and a-Fe20^ 9 ignited to constant weight, were

used as starting materials. All calcinations were done in air,

using gold containers. The heating schedule followed for all

87
compositions was an initial heating at 625°C for ^18 hours followed

by an 800°C heat treatment for ^90 hours, with periodic grindings.

A total of 16 compositions, as shown in Figure 1, were prepared.

For heatings above 800°C, it was necessary to use sealed containers to prevent potassium loss from the specimens. In order to

determine if the tubes leaked during heating, specimens were quenched

into paraffin oil. Oil was used instead of water to prevent the

introduction of moisture into the drybox in case of failure. Attempts

were made to use gold tubes for 1000°C heatings but the high failure

rate necessitated the use of platinum tubes. At temperatures so close

to the gold melting point the gold tubes appeared to fail from internal

pressure rather than from any corrosive reaction.

All sixteen compositions were heated at 1000°C for 72 hours in

sealed platinum tubes, 5 mm O.D. x 25 mm long, to provide well-reacted

materials for higher temperature heatings.

Characterization of specimens after heat treatment was by powder

x-ray diffraction methods, using a high angle goniometer equipped with

a bent graphite crystal monochromator. Scanning speed was 0.25° 26

per minute. The goniometer shield was sealed and a thin plastic

window provided for the x-ray beams. In this manner a dry nitrogen

atmosphere could be maintained over the sample, preventing hydration.

Both optical and scanning electron microscopy were used to evaluate

the nature and extent of reaction with the platinum container. In

this case, a special heavy-walled tube, 2.54 mm I.D. x 6.0 mm O.D.,

88
was used. A separate end cap was welded on after filling. After

heating, the sample was mounted in epoxy resin and cut with a diamond

saw at right angles to the tube axis. The halves were ground and

polished using gamma Al^O,., and methanol for microscopic examination.

Experimental Results

A. Phase Equilibria and Corrosion (H.S. Parker, R.S. Roth, C.D. Olson)

The compositions and temperatures investigated are shown in Table

1 and Figure 1. Figure 1 includes several high temperature points

obtained prior to the start of this investigation. These points were

obtained in sealed platinum tubes, with severe attack of the platinum,

failure occurring for all compositions within moments when liquid was

present. The dashed lines in Figure 1 are estimates of the solidus and

liquidus values primarily from Takahashi, Kuwabara and Kase [1], modified

by the MBS measurement of the melting point of KFeO^ as 1615°±10°

(C.L. McDaniel, personal communication). The observed phase assemblages

are, in general, in agreement with reference 1, although the composition

range of 8+6" structures appears to be slightly different.

The K? 0 : 5 . 75Fe202 composition (85.2 mole percent Fe^O,) in

the sealed heavy wall platinum tube was heated at 1475°C for 19 hours

and rapidly cooled in paraffin oil. A low magnification SEM photograph after sectioning, polishing and carbon coating is shown in

Figure 2. As is evident, no gross attack of the platinum is visible.

As shown in Figure 3a, the specimen was at least partially melted

and separated into two phases on cooling. Figures 3b and 3c indicate

89
Table 1. The System KFe0

2 -Fe

2 03

.

Composition a/ Temperature— Time Results

Mole percent °C hrs

K„0 Feo 0 o 2 2 3

50 50 1000 72 KFe0

2 33.33 66.67 1000 72 KFe0

2 + (6+6")

25 75 1000 72 KFe0

2 + (6+6")

20 80 1000 72 (6+6") + KFe0

2 1200 19 Leaked badly

16.67 83.33 1000 72 (6+6") + KFe0

2

15.4 84.6 1000 72 (6+6") + trace KFe0

2 14.8 85.2 1000 72 (6+6")

1200 19 Single phase 6 1308 18 Single phase 6 (small leak)

1475 19 For SEM examination

14.3 85.7 1000 72.5 (6+6") + trace

1308 18 Single phase 6 (small leak)

12.5 87.5 1000 72 (6+6") + trace Fe^

1200 18 Single phase 6 11.1 88.9 1000 72 (6+6") + Fe

2 0

3

10.0 90.0 1000 72 Fe

203 + (6+6")

1200 18 Leaked badly

9.1 90.9 1000 72 Fe

2 0

3 + (6+6")

8.3 91.7 1000 72 Fe

2

0

3 + (6+6")

7.7 92.3 1000 72 Fe

2

0

3 + (6+6")

5.9 94.1 1000 72 Fe

2 03 + (6+6")

4.2 95.8 1000 72 Fe

2 03 + (6+6")

0 100 1000 72 Fe2°3

- All compositions calcined at 625°C for ^18 hours and 800°C for

^90 hours . All heatings above 1000°C used material heated at

1000°C for 72 hours.

90
the lamellae to be a potassium-rich phase. Again, little or no interdiffusion between Fe, K and the platinum container is evident.

In Figure 4a, a dark area is visible at the interface between

the platinum and specimen near the upper center of the figure.

Analysis of this area, Figure 4b, by EDXA showed that a slight reaction has occurred, the dark area being composed of K, Fe and Pt as

contrasted to the spectrum obtained in areas immediately adjacent on

either side, Pt in one case and K plus Fe only in the other.

B. Vapor Pressure Measurements on

sl KFeO ^" (E.R. Plante)

Results of mass spectrometric measurements of the vapor pressure

of KFeO^ (series 1) were summarized in a previous report [2], In the

series 1 data an abnormally high ratio was observed

which was thought to indicate that significant reduction of the KFeQ 0 took place during the vaporization experiments. However, this

observation was contrary to results obtained by x-ray diffraction

studies of the residual sample which indicated that the evaporation

process was consistent with a reaction forming a non-stoichiometric

phase which can be approximated by the following:

7/6(K

2 0-Fe2 03

) = 2K(g) + 1/2 0

2 <g) + 1/6 (^0 - 7Fe2 03

> .

The possibility that a high 0 pressure was due to reaction of FeO^

with Pt allowing release of 0 was considered but SEM examination of

the Pt Knudsen cell indicated only minor interaction.

91
Because of these conflicting observations the mass spectrometer

constant could only be determined within a factor of 3. If it was

assumed that the x-ray diffraction data were correct the mass

spectrometer calibration factor for K would be a factor of 3 greater

than that obtanined assuming the ratio was correct.

More recent observations on unrelated K^O-containing slag samples

•f +

have shown that the data were probably incorrect because of

misalignment of the molecular beam with the ion source. These

observations showed that the I^/l^g ratio could be varied over a

factor 3 depending on the ion optics adjustments of the source. This

effect is possible because 0 o is non-condensible and can bounce off

surfaces into the active volume of the ion source while K is condensible

and will be effectively removed from the molecular beam.

New measurements on the vaporization of KFeO

? have been undertaken. The measurements were made in our modulated beam, quadrupole

mass spectrometer using a platinum effusion cell having a 0.343 mm

diameter orifice. The experimental arrangement was essentially the

same as previously used except that a new thermocouple was used. As

before, measurements of both the K+

and 0^ion currents were made as

a check on the vaporization stoichiometry. However, within experimental

error the vaporization reaction is that previously noted.

Certain non-equilibrium effects were observed during the experiments.

Measurements of the ion currents were made at constant temperature, but

-f -(- the initial ratio of 132/^39 depended on whether the temperature was

92
increased or decreased in going from one constant temperature to

another. When the temperature was increased, after the initial

increase in the K intensity, there was a tendency for the K

+

ion

current to decrease with time and the 0* ion intensity to increase

with time until a steady state was reached. The opposite effects

were noted when the temperature was decreased but the same steady

state was eventually achieved. It appeared, however, that a shorter

period of time was required to achieve steady state pressures if the

temperature was increased from point to point and the data presented

was taken in that direction. Above 1300 K, equilibration rates were

quite rapid and steady state pressures were observed within 10-15

minutes , while at the lower temperatures periods of about an hour were

required

.

These effects could be due to a phase boundary dependence on

temperature. For example, the "K^O . yFe^O^" composition might become

0^ deficient at higher temperatures. Other possibilities include

instrumental problems with the mass spectrometer or kinetic factors

in the diffusion of K and 0^ from the evaporating phase (insufficient

equilibration time). At steady state conditions, the ratio

indicated a deficiency of 0^ at low temperatures but at higher temperatures the O^/K pressure ratio appeared consistent with the proposed

decomposition reaction.

Some selected data from the measurements are shown in Figure 5.

Curve A shows data for the K pressure series 1 data using the mass

93
spectrometer sensitivity constant obtained by assuming that decomposition

took place according to the reaction cited. Curve B is the K pressure

observed during the later experiments and Curve C is the oxygen

pressure. The ratio of the K pressure to the 0^ pressure is based

on previous experience which indicates that the mass spectrometer

sensitivity constant for K is about 5.6 times that for 0^ a The

difference between curves A and B is probably due to a systematic

error in temperature of about 30 K. Different thermocouple probes

were used for the respective measurements. The curve B data is

thought to be more reliable. Curve D represents the K(g) pressure

over KAIO^. The order of magnitude increase in the K pressure over

KFe0 0 compared to KA10

? confirms the general idea that K^O interacts

more strongly with Al^O^ than with Fe^O^.

Conclusion and Discussion

The compositional range of the B-B" alumina structure types

appears to be centered at a composition of K^O : 5 . TSFe^O^ (85.2 mole

percent Fe^O^) with the B" disappearing at higher temperatures as +2 +3 the Fe :Fe ratio increases. The possibility of high ionic and

electronic conductivity in these structures, including the B"

structure should be investigated.

The attack of platinum by compositions in the 85 mole percent

^e2^3 re8^on does not appear to be extensive at temperatures up to

1475°C for times of 19 hours. Failure of thin-wall platinum containers

at temperatures in the 1200°-1300°C range may be due to internal

94
pressure from released oxygen from the sample rather than from

corrosive effects. Future Mossbauer and magnetic susceptibility

studies should help establish the cause of failure. At compositions

higher in potassium content, it is expected that corrosive attack

will become a factor.

The potassium pressure over KFeO^ is roughly an order of magnitude

greater than that over KAIO^ , approaching 10 atmospheres in the

1200°C range. As a result, shifts in bulk composition occurring during

extended heat treatments at higher temperatures in open systems must

not be overlooked.

References

[1] T. Takahashi, K. Kuwabara, and Y. Kase, "Formation of K-BFe^O^

and Phase Diagram of the System KFeO^-Fe^O^" , Denki Kagaku 43_

[5] 273-7 (1975). In Japanese,

[2] Quarterly Progress Report for July - September 1977, NBS

"Properties of Electronic Materials", E. Passaglia, NASA

Government Order H-27954B, October 1977.

95
1600

96

mole

percent
1 1 mm

Figure 2. Scanning electron micrograph of section of heavy wall

platinum tube containing specimen of K^O :5

,

75Fe203

(85.2 mole percent Fe„0») after heat treatment at

1475°C for 19 hours. 1 5

97
I

1 0.02 mm

Figure 3. a) Scanning electron micrograph of interface of specimen

of Figure 2.

b) Potassium map of 3(a).

c) Iron map of 3(a).

98
0.01 mm

Figure 4. a) High magnification micrograph of platinum-sample

interface of specimen of Figure 2.

b) EDXA spectrum of small dark area near upper center

of 4a and spectrum of immediately adjacent specimen.

99
PRESSURE,

ATM

TEMPERATURE K

Figure 5.

7.0 8.0

Pressures over KFeO -K O' 7Fe 0„ vs. 1/T compared with

KAlO ? -3 alumina. A; P over KFeO-, series 1, B; P over KFeO , C; P over KFeO , D; P over KA10.-3 alumina.

Z Up z K. z 100
Task 5

Gravity Effects on Flame Inhibition

J. W. Hastie

Chemical Stability and Corrosion Division

Center for Materials Science

Summary

The first year of this project has emphasized the development of

new or improved techniques for the detailed molecular characterization

* of laboratory flames. This development has progressed very satisfactorily, with the following main achievements:

a. Design and nearly complete construction of a High Pressure

Sampling Mass Spectrometer facility, suitable for transient species

analysis in diffusion and particulate containing flames.

b. Development of optical absorption spectroscopy for OH concentration and rotational temperature measurements in optically thick

flames

.

c. Application of the new technique of rotational Raman spectroscopy to flame temperature profile measurements.

d. Initiation of thermodynamic and chemical kinetic modeling

predictions of flame temperatures, post flame species concentrations,

and flame inhibition and promotion.

e. Design, construction and critical evaluation of new burner

systems having potential utility as standard devices for interlaboratory

comparison of flame diagnostic procedures.

101
f. Critical evaluation of various optically based flame temperature measurement techniques including, OH-absorption , N^-rotational

Laser Raman, NaD-line reversal methods.

Introduction

Previous experimental and modeling studies of gravity effects in

clean or non-inhibited combustion by NASA and NASA-supported research

laboratories have considered the fluid-dynamic and thermodynamic aspects

and obtained partial agreement between experiment and theory. A significant conclusion from this early work is the recognition that a more

satisfactory agreement between observed and predicted gravity-effects

cannot be expected until more detailed combustion kinetics are included

in the models--even for clean unperturbed flames (e.g., see NASA CR120921, 1972). Such studies have however established that, for gaseous

flame mixtures, readily observable phenomena such as physical shape and

combustion efficiency are known (NASA CR-120921) and can be predicted

(NASA CR-143350) to be strongly modified under zero-gravity conditions.

Similarly synthetic polymers, such as polyesters and polyurethanes,

exhibit marked differences in flame propagation rate at zero-gravity as

compared with normal 1-g conditions (NASA Conf. Mater. Impr. Fire Saf.,

1970). As these and related flame properties are also known to be

affected by flame inhibitors under normal g-conditions , we can therefore

expect the degree and perhaps the mechanism of flame inhibition to be

gravity dependent. This means that the control of fires in space by

flame inhibitors should not necessarily be dictated by terrestrial

experience. Nor should existing standards and test procedures be assumed
to be valid measures of fire hazards in space. Another aspect to the

problem is that the eventual study of laboratory flames in space under

essentially zero-gravity conditions would provide us with an added

variable (i.e., g-level) for testing and mechanistic details of flame

propagation and inhibition in general. This is significant since our

present understanding of flame phenomena is limited by the difficulty of

uncoupling the physical (e.g., mass and heat transfer) and chemical

(e.g., reaction rates) components in flame theory. As gravity can be

expected to influence primarily the physical transport properties, a

comparison of earth-bound and space-laboratory flame data should reveal

the relative importance of physical and chemical effects and aid in

their decoupling for development of a generalized flame theory. Thus

the study of flames in space impacts both on the reduction of spacecraft

fire hazards and in the fundamental understanding of flames under any

gravity condition. In the latter instance, the development of a generalized flame theory incorporating chemical or physical perturbations

leading to inhibition or promotion will certainly advance the flame

retardant and energy conservation technologies. Development of such a

far reaching theory will require the most detailed experimental measurement

effort possible, so that non-unique mechanisms are excluded as far as

possible

.

Experimental Procedures

I A comparison of flame inhibition processes under both 1-g and zerog conditions will be made to test gravity effects on flame inhibition,

A leading to a generalized model of flame inhibition. From practical and

103
fundamental (i.e., availability of basic chemical kinetic data) considerations, a halocarbon such as the commercial fire extinguishing agent

CF^Br in diffusion and premixed flame configurations, will be required

under normal 1-g conditions to establish a predictive preliminary model

for flame inhibition in a spacecraft environment. The limited availability

of basic chemical kinetic data limits the flame compositions for which a

theoretical analysis is presently possible to those containing or

CH. as fuel and 0_ as oxidant. These flame mixtures will be subiected

4 2

J

to detailed earth-lab mass spectrometric and optical spectroscopic

analyses for the spatial determination of species concentration and

temperature profiles, including both radical intermediates and stable

reactant and product species. These profiles are the net result of

chemical kinetic and transport processes, and, using the well known

flame equations, such data can be unfolded to yield a set of reactions

describing flame propagation and inhibition. Thus the profile data will

be used to establish a flame inhibition model for 1-g conditions. This

predictive model will then be used to define the experimental parameters,

such as flame composition and flame type (diffusion or premixed) , best

suited to zero-g conditions. Such an a priori optimization of experimental

conditions for a spacecraft study of flame inhibition is essential, due

to the limited measurement tools that can be applied in space. Thus the

use of a sophisticated molecular-beam-sampling mass spectrometer, for

instance, in the terrestrial experiments would be contrasted in suggested

space lab studies by application of relatively simple optical spectroscopic

methods for monitoring macroscopic flame properties such as luminosity,

104
and the spatial distribution of CO^ and CO species. Eventual comparison

of these sky lab data with those obtained in the 1-g environment would

be used to test, and modify where necessary, the predictive flame inhibition

model

Experimental Results

The main objectives for the first year of this project (just completed) were as follows: (a) Using molecular beam mass spectrometry

obtain temperature and species concentration profiles including radical

intermediates for premixed CH^ , , 0^, flames at atmospheric pressure,

(b) Develop optical spectroscopic absorption methods to supplement mass

spectrometric technique. (c) Design and construct a separate molecular

beam sampling mass spectrometer system for species characterization of

relatively weak premixed and diffusion flames. Objectives (b) and (c)

were essentially met and objective (a) was modified to include the

application of Laser Raman spectroscopy to the monitoring of temperature

and species concentration profiles.

Optical Spectroscopy:

Classical optical spectroscopic methods have been utilized in our

laboratory primarily for spatially resolved concentration measurements

of H and OH and the temperature profile determinations. Current work

has emphasized optical absorption spectroscopic measurements of the OH

visible-U.V. system in a series of fuel-rich H^-O^-N^ ^^ ames • Particular

attention was given to the rotational line intensities and their dependence

on the degree of optical thickness of the flame. The basic expressions

for deriving temperatures and OH concentrations from the OH rotational

105
fine structure are valid only for an optically thin system such as for

very weak (and difficult to measure) transitions and for flames with

relatively low OH concentration. By noting the dependence of absorption

intensity as a function of the number of light beam traversals (i.e.,

optical path length) through the flame we have been able to correct for

the effect of optical thickness. The multipass optical system used was

based on the White cell design. A linear dependence of the fractional

absorption on the number of beam traversals was found thus enabling an

accurate extrapolation to zero passes to be made from which line intensities of the ideal optically thin condition are obtained.

With this correction procedure, we have determined average postflame temperatures and OH concentrations for several H^-O^-N^ flame

compositions. The importance of the optical thickness correction was

evident from the approximately 200K temperature difference between the

corrected and uncorrected values (too high) . Comparison of the corrected

temperatures with those obtained by the Na-D line reversal technique

indicated a disparity of 100-200K. At least part of this disparity may

be due to the lower spatial resolution of the White cell optical system.

Laser Raman Spectroscopy:

Laser Raman spectroscopy has the particular advantage over other

optical methods of high spatial resolution and sensitivity to major

species not having readily accessible electronic transitions. Our

current interest in this technique is based on its potential for accurate

temperature profile determinations throughout the whole flame. This

contrasts with other optical methods, such as the Na-D line reversal

106
approach, where moderate resolution data can be obtained only in the

post flame region.

Vibrational and rotational Raman measurements have been carried out

on small premixed H^/O^/N^ flames premixed initial compositions of 4/1/4

and 3. 4/1. 0/2.0. Measurements of temperature profiles in the fuel rich

4/1/4 flame with and without a concentric gas shield flow indicates

that diffusion of air into the unshielded flame can raise the flame

temperature by 125K (2150K unshielded, 2025K shielded at 5 cm distance

from the burner face). Comparison of Na-D line reversal temperature

data from the capillary type burner (used for the other optical measurements) and Raman measurements from the shielded torch flames gives

temperatures in agreement within the uncertainties of the two measurements

(^ 20K for Raman)

Computer profile calculations of and vibrational Q branch

lines have been obtained as a function of temperature. These calculations

are essentially the same as those used by others (Lapp, Setchell, etc.).

The effects of rotational-vibrational line strength corrections, 0 and S

branch contributions, and the anisotropic component of the Q branch on

these predicted profiles (and hence, temperature measurements) are

currently being investigated. For example, including rotationalvibrational line strength corrections for H^-Q ^ ranc h spectra lowers the

calculated temperatures by only 1.5K at 325K but more significantly by

80K at 2400K.
Mass Spectroscopy:

The mass spectroscopic component of our flame characterization

program relates to the spatially resolved identification of virtually

all the molecular species present. As the method involves use of an

intrusive molecular beam sampling probe, care must be taken to avoid

perturbing the system being sampled. Previous work in our laboratory

has demonstrated the conditions for which such a perturbation is negligible.

A second high pressure sampling mass spectrometer system (HPMS) is

currently under construction in our laboratory and is near completion.

This system will be more versatile than our existing HPMS facility in

that it will allow sampling from vertical gas flows (i.e., flames) and

from diffusion and particulate laden flames.

Associated with both the mass and optical spectroscopic phases of

our work is the development of reproducible flat flame burners capable

of handling inorganic additivies . We have obtained commercially a metal

honeycomb material from which we fabricated a shielded flat flame burner.

Unlike the more conventional sintered brass burner-type this burner

produced visually flat flames of CH^-Cb^-N^ over a wide range of fuel

rich and lean stoichiometries. This burner so far appears very satisfactory for generating atmospheric pressure flat flames suitable for both

optical and mass spectrometric analysis as well as eventual theoretical

modeling

Modeling

With the increasing availability of high speed computer facilities

and the development of new mathematical techniques for solving the basic

108
flame equations, theoretical modeling of kinetically complex experimental

systems is becoming feasible. The potential value of modeling combined

with a comprehensive combustion diagnostics program is now well recognized

by researchers in the field. While at the current level of effort we

cannot generate original modeling computer programs ourselves, we are

making every effort to obtain usable programs from other sources as they

become available. In the interim we are, and shall continue, modeling

selected aspects of the experimental systems.

For instance, the burnt gas region of the hot flames that

we have obtained experimental data on can be very well approximated as a

thermodynamic equilibrium system. The Gordon and McBride NASA multicomponent equilibrium program has been revived for this purpose. Calculations

have been made of the adiabatic flame temperatures of methane and propaneair flames of varying stoichiometry in an attempt to rationalize the

different behavior of inhibitors in both these types of flames. The

calculated flame temperatures differ by less than 50K, with propane

yielding hotter flames. This trend is in accord with the observed

effect of inhibitors in diffusion flames where smoke suppression effects

appear more predominantly for the hotter propane-air flames.

In an attempt to rationalize, in at least a semi-quantitative

manner, the experimentally observed reversible inhibition-promotion

effect of phosphorus-containing additives we have developed a simple

kinetic argument based on the rate limiting reaction;

H

2 0 + PO ^HP02 + H.

109
Our previous determination of the heat of formation for HPO^ , using

Knudsen effusion mass spectrometry, combined with the known thermodynamic

data for PO , H,

; 0 and H indicate this reaction to be exothermic by about

22 kcal/mol. To a satisfactory approximation we can therefore assume

the activation energy for the reverse process to have a similar magnitude.

The pre-exponential factor in the Arhenius rate expression can be estimated

by analogy with similar processes, e.g., those reported by Jones and

Jensen (1975). With this information we have estimated rate constants

for the forward and reverse processes as a function of temperature.

From our mass and optical spectroscopic analyses of flames containing

phosphorus, we know the concentrations of the species involved in the

above rate processes. Hence, the reaction rates can be calculated. We

find that the calculated reaction rate vs temperature curves for the

forward and reverse processes should cross in the region of 1700 ± 300K

with the forward process being favored above the cross over temperature.

This forward reaction creates H atoms and is therefore flame promoting

whereas the reverse process is flame inhibiting. Our earlier reported experimental observations of phosphorus-induced H-atom removal below

about 2000 ± 200K and H atom production above this temperature regime

can, therefore, be rationalized by this simple kinetic scheme involving

the PO and HPO^ species

.

Conclusion and Discussion

The first year of this project has emphasized the development of

new or improved techniques for the detailed molecular characterization

of laboratory flames. This development has progressed very satisfactorily,

110
with the following main achievements:

a. Design and nearly complete construction of a High Pressure

Sampling Mass Spectrometer facility, suitable for transient species

analysis in diffusion and particulate containing flames.

b. Development of optical absorption spectroscopy for OH concentration and rotational temperature measurements in optically thick flames.

c. Application of the new technique of rotational Raman spectroscopy

to flame temperature profile measurements.

d. Initiation of thermodynamic and chemical kinetic modeling

predictions of flame temperatures, post flame species concentrations,

and flame inhibition and promotion.

e. Design, construction and critical evaluation of new burner

systems having potential utility as standard devices for interlaboratory

comparison of flame diagnostic procedures.

f. Critical evaluation of various optically based flame temperature

measurement techniques including, OH-absorption , N^-rotational Laser

Raman, NaD-line reversal methods.

Ill
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»

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 78-1483

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

NBS Properties of Electronic Materials

5. Publication Date May 1978

6. Performing Organization Code

7. A UTHOR(S)

J. R. Manning and R. L. Parker

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

NASA - Marshall SFC

Huntsville, Alabama

13. Type of Report & Period Covered

Annual Report

4/77 - 3/78

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Annual Report

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This report describes NBS work for NASA in support of NASA's (Materials Processing

in Space) Program covering the period April 1, 1977 to March 31, 1978.

The results obtained for each task are given in detailed summaries in the body of

the report. Briefly, in Task I - Surface Tensions and their Variations with Temperature and Impurities - surface tension measurements have been made for gallium using the

pendant drop technique and some complex effects ascribed to impurities were observed.

In Task 2 - Solutal Convection and Liquid Diffusion Coefficients - the onset of con- vective and interfacial instabilities during the vertical directional solidification of

a binary alloy has been determined theoretically by means of a linear stability

analysis. In Task 3 - Determination of Crystal Perfection - a study has been performed

on the improvement in resolution of x-ray imaging systems for real-time assessment of

crystal perfection. In Task 4 - A Thermochemical Study of Corrosion Reactions in Oxide

Materials - the system KFe0^-Fe o0^ has been examined over portions of the subsolidus

region, and the occurrence 5f a^beta alumina structure-type at 85.2 mole percent

Fe 2°3 has been . observed. In Task 5 - Gravity Effects on Flame Inhibition - a high

pressure sampling mass spectrometer facility has been designed and construction on it

is nearly completed

,

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Convection; corrosive reactions; crystal perfection; flame inhibition; microgravity;

solidification; solutal convection; surface tensions

18. AVAILABILITY Q Unlimited

For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No, Cli

py) Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

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UNCLASSIFIED

21. NO. OF PAGES

116

22. Price

$6.50

USCOMM-DC 29042- P 7 4


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