A UNITED STATES DEPARTMENT OF COMMERCE

PUBLICATION /y

^M<X ^

NBS TECHNICAL NOTE 634

Lorenz Ratios of

Technically Important

Metals and Alloys

u.s. APARTMENT

OF

COMMERCE

National

Bureau

at

106

AJA1S%

fio.6)f
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates

that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics —

Linac Radiation - — Nuclear Radiation - — Applied Radiation '-' — Quantum

Electronics :! — Electromagnetics '• — Time and Frequency 3 — Laboratory

Astrophysics •" — Cryogenics 3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and

Government; provides advisory and research services to other Government agencies; and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry—Polymers—Metallurgy—Inorganic Materials—Reactor

Radiation—Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to pro- mote the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies upon request. The Institute also monitors NBS engineering standards activities and

provides liaison between NBS and national and international engineering standards

bodies. The Institute consists of a Center for Building Technology and the following

divisions and offices: Engineering and Product Standards—Weights and Measures—Invention and

Innovation—Product Evaluation Technology—Electronic Technology—Technical Analysis—Measurement Engineering—Building Standards and Code Services4—Housing Technology 1 —Federal Building Technology4—Structures, Materials and Life Safety4 —Building Environment4—Technical Evaluation and

Application4—Fire Technology.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts re- search and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center

consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of

the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader

aspects of the National Measurement System; provides appropriate services to ensure

that the NBS staff has optimum accessibility to the scientific information of the world, and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and

Publications—Library—Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted : mailing address Washington, D.C. 20234.

2 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.

* Part of the Center for Building Technology.
lational Bureau of Standards MAR 2 7 1975 art <&*- ' QC'OO

m3

Lorenz Ratios of Technically Important

Metals and Alloys

J.G. Hust

L.L. Sparks

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

*

' Teo-h* » <toJ> »ofc m ' ^^

NBS Technical notes are designed to supplement the

Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

„HJrt OF c,

v TO J

*"»e»u of *

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director

Issued February 1973
National Bureau of Standards Technical Note 634

Nat. Bur. Stand.(U.S.), Tech. Note 634, 133 pages (February 1973) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D. C. 20402

(Order by SD Catalog No. 03.46:634).
Contents

Page

1. Introduction 1

2. Theory 2

2. 1 Thermal Conductivity 2

2. 2 Electrical Resistivity 3

2. 3 Lorenz Ratio 5

3. Data 11

4. Predictive Procedures 1 3

5. Further Work 16

6. Acknowledgments 17

7. References 18

Appendix I Figures and Data Review Tables l-l

Appendix II Data Tabulation II

Appendix III Bibliography Ill-
List of Text Figures

Figure 1. Thermal conductivity of metals and alloys, (a) pure metal

(gold), (b) high conductivity alloy (aluminum- 7 039), and (c)

low conductivity alloy ( titanium -5A£- 2. 5 Sn).

Figure 2. Electrical resistivity of metals and alloys, (a) pure metal

(gold), (b) high conductivity alloy (aluminum-7039), and (c)

low conductivity alloy ( titanium- 5A£- 2. 5 Sn).

Figure 3. Electronic Lorenz ratio for pure metals and defect free

metals.

Figure 4. Values of (L-L )/L for several classes of commonly used

materials.

Figure 5. Values of the total Lorenz number for several classes of

commonly used materials.

List of Text Tables

Table 1. Debye temperatures of selected common metals
Lorenz Ratios of Technically Important

Metals and Alloys

J. G. Hust and L. L. Sparks

A comprehensive review and compilation of the world literature on Lorenz ratio of technically important metals and alloys is presented.

Lorenz ratio, electrical resistivity, thermal conductivity, and characterization data are compiled in tabular form and the Lorenz ratio data are presented in graphical form as well. Data are included here only if the

research reported both thermal conductivity and electrical resistivity of

the specimens. No attempt has been made to smooth data or present

recommended values.

Key Words: Alloys; compilation; cryogenic; electrical resistivity;

Lorenz Ratio; metals; thermal conductivity.

1 . Introduction

The development of new materials and a renewed interest in

existing materials by modern technological industry is creating a demand for thermal and electrical property data. These data are needed

for the selection of suitable construction materials and the prediction of

operating characteristics of low temperature systems. Apparatus are

available at this laboratory as well as others for the accurate measurement of thermal conductivity, electrical resistivity, and thermopower

of metals and alloys over the range from 4 to 300 K. However, the

measurement of thermal conductivity is slow and expensive; one cannot

hope to fill the immediate demand for data by measurement alone.

Furthermore, metals and alloys display a wide range in their conductivity values at a given temperature and a single material may exhibit

values varying over several orders of magnitude as a function of temperature. One cannot look to theory for these values, since, presently,

theoretical predictions represent qualitative guidelines only. However,
a strong relationship between thermal conductivity and electrical

resistivity of metals was observed many years ago and the nature of

this correlation has been studied ever since. This relationship, called

the Wiedemann-Franz-Lorenz law, makes it possible to predict approximate values of thermal conductivity from less expensive electrical

resistivity measurements. For this reason we feel a compilation of

Lorenz ratios of technically important metals is overdue. The predictive

value of these data is explained below.

2. Theory

In order to better understand the methods of predicting thermal

conductivity from the Lorenz ratio, it will be helpful to have an understanding of the general thermal and electrical properties of metals and

alloys. The following sections on thermal conductivity and electrical

resistivity are included as a review of the fundamental physical

behavior.

2. 1 Thermal Conductivity

The thermal conductivity, X, of a metal or alloy usually is considered to be the sum of two components- the electronic, X , and lattice, X

e §

X = X + X . (1) e g

There are other mechanisms of heat transport; however, they generally

are not applicable here. The lattice term designates the energy carried by the lattice vibrations, called phonons. The subscript g comes

from the German word for lattice, Gitter,

In "electrically pure" materials the lattice term is small (usually

less than 5 and almost never more than 20 percent of the total) compared

to the electron term. Electrical purity is characterized by the residual
resistivity ratio, RRR, between 273 K and 4 K (RRR = p /p ). The

electrical purity of a material is not specified uniquely by the chemical

purity of that material; it also depends on the distribution and location

of the impurity atoms and on the physical imperfections in the solid.

For example, whereas the chemical purity may remain essentially un- changed in annealing, the electrical purity of a material can, in some

instances, be changed by an order of magnitude or more. As will be

described later, such a change also affects the thermal conductivity.

In alloys, the electronic conductivity is so small, especially at lower temperatures, that the lattice conductivity no longer is negligible.

As a matter of fact, X is often much larger than X . The total conductivity of alloys is less than that of pure metals, and some alloys have

conductivities approaching those of thermal insulators. The general

temperature dependence and relative magnitude of the conductivities of

several materials are illustrated in figure 1. More details are given

by Powell El].

2. 2 Electrical Resistivity

For commercially pure metals and some alloys, the electrical

resistivity is described adequately by Matthiessen' s rule. This rule,

eq(2), states that the electrical resistivity of a metal is the sum of two

parts: the intrinsic resistivity, p., which is characterized by electrons

interacting with phonons only, and the residual resistivity, p , which is characterized by electrons interacting with the chemical and physical

imperfections of the metal.

p(T) = p + p. (T) (2) o i

The residual resistivity is assumed to be temperature independent while

Numbers in brackets refer to list of text references at the end of this

paper.
2000

1000

100

E

10

(a)

8 10 20 40 60 80 100

TEMPERATURE, K

200 300

Figure 1. Thermal conductivity of metals and alloys, (a) pure metal (gold),

(b) high conductivity alloy (aluminum-7039), and (c) low conductivit

alloy (titanium -5A Z-Z. 5 Sn).

4
the intrinsic resistivity increases rapidly with temperature. The

specific temperature dependence varies strongly but systematically

both -with temperature and material. Nevertheless, P^ is not dependent

significantly upon small composition changes for a given metal or alloy.

Thus, if one knows P- (T) for a given metal, P(T) for different compositions

can be obtained from eq (2) after measuring only p Q. The value of p is obtained by measuring P at low temperatures where P- is negligible (liquid

helium temperature is adequate). A few characteristic electrical resistivity curves of pure metals and alloys are given in figure 2. 2.3 Lorenz Ratio

In 185 3 Wiedemann and Franz formulated an empirical law relating

the thermal and electrical conductivities of metals, namely, that the

ratio of the electrical and thermal conductivities (WF ratio) at a given

temperature is the same for all metals. In 1872 Lorenz discovered that

the WF ratio is proportional to temperature. The result was the WiedemannFranz- Lorenz (WFL) law: — = XP = LT, (3) a

where a = electrical conductivity, L = Lorenz number, and T - absolute

temperature.

Drude gave a theoretical derivation of the WFL law for the electronic

component of thermal conductivity in 1900 and obtained a value of 2.228 X

10 i V

2

/ K

2 for L. Sommerfeld calculated the first order approximation

of L from the more recent free electron theory of metals. His value,

2.443 X 10"" V

2 /K 2

, is commonly designated L . Electron Lorenz

numbers, P X

e

/ T, other than the Sommerfeld value, will be designated L e to distinguish them from total Lorenz numbers, L = PX/T.
8 10 20 40 60 80 100

TEMPERATURE, K

200 300

Figure 2. Electrical resistivity of metals and alloys, (a) pure metal (gold),

(b) high conductivity alloy (aluminum-7039), and (c) low conductivity

alloy (titanium -5A^Z. 5 Sn).

6
For many pure metals the experimentally determined values of

—q 2/2 L fall between 2. 2 and 3.0X10 V /K at room temperature and only

slightly higher (2 to 3 percent) at 100° C. At very low temperatures the

experimental values of L are also near the Sommerfeld value. At

intermediate temperatures, values of L below L are observed. The

o magnitude of the decrease of L below LQ increases with increasing purity.

The values of L and L are nearly identical for pure metals since the

e lattice conductivity is small.

The decrease of L from L in pure metals is caused primarily

e o by the fact that the relaxation times for thermal and electrical conduction processes are different at intermediate temperatures. The electrical conductivity increases with decreasing temperature faster than the

thermal conductivity. As the residual resistivity decreases, L approaches

the value for a defect free crystal, thus, resulting in a curve with a lower minimum. The electronic Lorenz ratios of several metals as well as a defect free crystal are shown in figure 3. For alloys the measured values of Lorenz ratio are always higher

than their pure metal counterparts, in some instances considerably

higher. However, a similarity still exists in that the Lvs T curve tends

toward L at both extremes of temperature. At intermediate temperatures

o values of L vary from slightly below L for dilute alloys to more than

ten times larger than L for some highly alloyed structural metals. A

few typical curves for alloys are shown in figures 4 and 5. The large

values of Lorenz ratio observed for these alloys is caused by the pre- sence of a significant lattice conductivity as mentioned previously.

Often, knowledge of the magnitude of the lattice conductivity is so limited

that it is ignored in the calculation of L for alloys as it is for pure

metals. This is incorrect for alloys, of course, but until A. is known

g more accurately, our knowledge of L will also be severely limited.
Q

8 0l* 2

_>i 2 A' 9 l
8

K 2

&3&ZSZUZ*

At - 7039

-2

6 8 10 20 40 60 80 100

TEMPERATURE, K

200 300

Figure 4. Values of (L-L )/L for several classes of commonly used materials.
20

tj\^ji£r_

O

X

CM

CMO

<

orN 8

L±J o

Ai-7039

6 8 10 20 40 60 80 100

TEMPERATURE, K

200 300

Figure 5. Values of the total Lorenz number for several classes of commonly

used materials.

10
White [2] recently has compiled values of L as a function of

e reduced temperature, T/8 , for several metals (9 is the Debye temperature). Values of 9 for selected metals are shown in table 1 L3].

White's L data show a variation of only about ±2 percent from the mean

e values to temperatures as low as 0. 2 9 . White calculated X from eq (4) D g below, whose form was proposed by Leibfried and Schlomann [4] among

others:

X = 180 »A 9^

3 /y3 T Wm^K" 1

. (4)

In eq (4) a= lattice spacing, A = atomic weight, 9 = Debye temperature,

and y = the Griineisen parameter. For monovalent metals, values of

X calculated from eq (4) are only about 2 percent of the total experimentally

g determined conductivity. For the transition elements iron, platinum,

and tungsten, X values are about 20 percent of the total.

3. Data

Childs, et aL,L5] of this laboratory have recently made an extensive

compilation of thermal conductivities of materials at low temperatures.

From their work, publications which contained both electrical and thermal

conductivity data for the same materials were identified. These refer- ences were searched for data useful to calculate Lorenz ratos and for

citations to additional measurements. This search resulted in the refer- ence sources listed in Appendix III. The electrical resistivity and thermal

conductivity data from these reference sources were extracted and con- verted to a common set of units (SI). Lorenz ratios were calculated and

are plotted in the figures of Appendix I. The tabular values of electrical

resistivity, thermal conductivity, and Lorenz ratios as reported in the

literature are given in the right hand columns of Appendix II. The computed

values of Lorenz ratio in SI units are given in the left hand columns.

11
[3] TABLE 1„ Debye temperatures of selected common metals

Debye temperature, 8 Substance (K)

Aluminum 42 6 Beryllium 1160

Chromium 610

Copper 344

Gold 165

Iron 464

Lead 96

Magnesium 406

Manganese 47 6 Molybdenum 440

Nickel 440

Platinum 240

Silver 225

Tantalum 250

Tin 195

Titanium 420

Tungsten 405

Zinc 300

12
In many instances, data had to be read from small graphs. The

error introduced by reading these graphs was sometimes above 10%.

This is unfortunate especially in those instances where the uncertainty

of the original experimental data was smaller than 10%. In some

instances where data are closely spaced, curves were drawn to represent these data. No attempt was made to smooth the data or to present

best values. Considerably more work, both experimental and theoretical, must be done before smoothing can be done with confidence.

It is difficult to assess the uncertainty of thermal conductivity

data. Probably the best one should expect is about 1% and the worst

(except for blunders) is about 50%. Many sources list uncertainties

between 5 and 10%. The Lorenz ratios will have comparable uncertainties

since the uncertainty in electrical resistivity is generally much smaller.

Childs, et aX,[5] made estimates of thermal conductivity uncertainty for

each of the references. These estimates are not repeated here.

4. Predictive Procedures

In order to use the Lorenz ratio data presented here in predicting

thermal conductivities of new materials one must associate this material

with one whose L(T) is already known and measure the electrical resistivity of the new material. Then one may compute

P

It is stressed that obtaining p is significantly easier than measuring X. The association of one material with another may be done primarily

from a knowledge of its composition but also from other characterization

parameters such as electrical resistivity, hardness, density, or crystalline structure. The thermal and mechanical histories of the specimen

are important as well.

13
In the event that no similar material has been measured, generally

less accurate techniques of prediction may be considered. For purposes

of prediction, divide materials into the following classes:

( 1

)

pure metals ,

(2) high conductivity alloys,

(3) low conductivity alloys,

and consider temperatures in three ranges:

(a) T> & d

,

(b) t < e D

,

(c) t< e D. We will consider pure metals first. At temperatures above 9 or much less than 6 (say 0. 01 8_)» one can make reasonable estimates of

thermal conductivity of pure metals by calculating A as L T/p. The

lattice conductivity, A. , is computed from eq (4)and the total conductivity

g

A, from eq(l). The contribution of the lattice conductivity for pure metals

is usually negligible. The electrical resistivity, p(T), can often be obtained directly from the literature [6, 7] or from a measurement of p and values of p. (T), also found in the literature. At temperatures from

about 0. 2 6 to 9 L and L are temperature dependent but not appreciably

dependent on purity. Thus, one can use the L curve obtained by White

L2], shown in figure 3, to calculate A from L T/p. Between 0.01 EL and 0. 2 9 the electronic and total Lorenz numbers are dependent on

purity and temperature. No correlation between L and purity has been

mathematically formulated, although it is clear that one exists. It is noted that at temperatures above about 0. 2 9 , the thermal conductivity

of pure metals is not strongly dependent upon the chemical or physical

condition of the metal. Thus, if accurate conductivity values have been

obtained for a pure metal, these values above 0. 2 8 are applicable to other specimens to within about 10%.

14
Next we will consider high conductivity alloys. High conductivity

alloys are generally dilute alloys but may also be the result of alloying

similar elements. Ordered alloys also have high conductivities. The

values of L for high conductivity alloys are generally near L at all temperatures. Thus, a first approximation of thermal conductivity can

be obtained from L T/p.

o Last we will consider the low conductivity alloys. Generally, these are highly alloyed structural alloys. Prediction of the thermal conductivity is most difficult at temperatures T ^ 8 in the low conductivity

alloys. Here the lattice conductivity is comparable to and sometimes

much larger than the electron conductivity. If a comparable alloy has

not been measured, it is probably impossible to predict a reasonable

accurate value of \ f or this case. We presently are engaged in a program

to improve the predictive capabilities for such alloys. It appears reasonably obvious that to do this one must be able to calculate the electron

component from the electrical resistivity and the lattice component by

some other means. The lattice component probably will be obtained

from a modified form of eq (4), but additional research will be required

before a more accurate equation is found and its limitations are understood. At temperatures above 9 , one can obtain a first approximation

of thermal conductivity, usually on the low side, from L T/p. The above

methods of prediction are summarized as follows:

15
Pure

Metals

High Conductivity

Alloys

Low Conductivity

Alloys

T «eD

X m L T/p

o

X ft* L T/p

No

Valid

Predicting

Method

Known

t <e

D

A. m L T/p

e for o. 2 e D <t < e D

L from White [2]

e

A. « L T/p

Predictions difficult

for 0. 01 61 <T <0. 2 8

T >eD

\ «L T/p \«L T/p X ps L T/n

' M o

5. Further Work

It is seen from this compilation that the Lorenz ratios of pure

metals are near the Sommerfeld value, L = 2.443 X 10 V

2 /K , at low

o temperatures (residual region), fall to lower values at intermediate cryogenic temperatures, and increase again to near L at high temperatures.

At intermediate temperatures a dependence on impurity concentration is observed. For alloys one obtains the expected increase in Lorenz ratio

at intermediate temperatures instead of a dip as for the pure metals.

This increase in L is evidence of a relatively large lattice conductivity.

Somewhat challenging from a predictive standpoint is the large spread in

Lorenz ratios for the given classes of materials at each temperature.

This large spread will result in large uncertainties in predicted thermal

conductivities based on these curves. Further subdivision of materials

may be necessary to achieve a sufficiently small spread to be useful.

The objective of this Lorenz ratio compilation is to separate

materials into classes based on similar Lorenz ratio curves. From

16
these curves and a knowledge of the electrical resistivity of a new material from that class, it is often possible to approximate the thermal conductivity of the new material. This compilation has revealed some other

interesting possibilities for prediction of thermal conductivities. For

example, in several instances data exist in the literature which will

allow computation of the specific thermal resistivity resulting from

controlled addition of impurity atoms in a given host material. It has

been noted that some impurities are much more effective scatterers

than others. From a table of specific thermal resistivities, similar to

that compiled by Blatt [8] for electrical resistivity, one may be able to accurately predict the electronic thermal conductivity of metals and

alloys. Of the huge number of host-impurity element combinations which

exist, only a few have been measured. However, there is a good possibility that one can construct such a table from a knowledge of L(T) for

pure metals and Blatt's specific electrical resistivities. The measurements which have been compiled here and by Childs, et al., [5] can be

used to check the accuracy of such calculations. The available data will

also be useful in examining lattice conductivity.

6. Acknowledgments

The authors express appreciation to the many people who contributed to make this work possible. Most of the program was supported

by NASA (SNSO-C) Contract R-45. Steve Schmidt and Mark Prouhet

assisted in data extracted from the many sources. Gregg Childs and

Bob Powell were very helpful in providing a bibliography, as yet

unpublished, from their thermal conductivity compilation as well as opening their reference files for our use.

17
7. References

[1] Powell, R. L. , "Thermophysical Properties of Metals at Cryogenic

Temperatures, " Behavior of Metals at Cryogenic Temperatures , ASTM STP 387, pp. 134-148, American Society for Testing and

Materials (1966).

[2] White, G. K. , "Lattice Conductivity and Lorenz Ratio of Standard

Metals, " 8th Thermal Conductivity Conference, C. Y. Ho and R. E.

Taylor, eds. , pp. 37-44, Plenum Press, New York (1 969).

[3] Corruccini, R. J. , and Gniewek, J. J. , Nat. Bur. of Stand. (U. S. ), Monogr. 2_1, 20 pages (I960).

[4] Leibfried, G. , and Schlomann, E. , Nachrichten der Akademie der

Wissenschaften in Gottingen, Vol. II-A, No. 4, pp. 71-93 (1954).

[5] Childs, G. E. , Ericks, L. J. , and Powell, R. L. , Thermal

Conductivity of Solids at Room Temperature and Below, A Review

Compilation of the Literature, Nat. Bur. of Stand. (U. S. ), Monogr.

131 (1973).

[6] Clark, A. F. , Childs, G. E. , and Wallace, G. H. , Cryogenics ,

10, 295-305 (1970).

[7] Meaden, G. T. , Electrical Resistance of Metals , Plenum Press,

New York (1965).

[8] Blatt, F. J. , Physics of Electronic Conduction in Solids , McGrawHill Book Company N. Y. p. 199(1968).
APPENDIX I - FIGURES

AND

DATA REVIEW TABLES

The use in this paper of trade names is essential to a proper

understanding of the •work presented. Their use in no way implies

any approval, endorsement, or recommendation by NBS.

1-1
List of Figures

Figure 1 Figure 2 Figure 3 Figure 4

Figure 5 Figure 6 Figure 7 Figure 8 Figure 9

Figure 10

Figure 1

1

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17 Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Page

Lorenz ratio of beryllium 1-5

Lorenz ratio of aluminum 1-9

Lorenz ratio of aluminum alloys I- 11 Lorenz ratio of lead and tin 1-13

Lorenz ratio of gold 1-15

Lorenz ratio of gold-cobalt alloy I- i 7 Lorenz ratio of silver 1-19

Lorenz ratio of copper 1-21

Lorenz ratio of copper alloys (German silver and

brass) 1-24

Lorenz ratio of zinc and cadmium 1-26

Lorenz ratio of scandium and yttrium 1-28

Lorenz ratio of titanium, hafnium, and

zirconium 1-30

Lorenz ratio of titanium alloys 1-32

Lorenz ratio of tungsten 1-34

Lorenz ratio of molybdenum 1-36

Lorenz ratio of chromium 1-38

Lorenz ratio of manganese and rhenium 1-40

Lorenz ratio of iron 1-43

Lorenz ratio of stainless and alloy steels 1-47

Lorenz ratio of carbon steels 1-49

Lorenz ratio of cobalt 1-51

Lorenz ratio of nickel 1-53

Lorenz ratio of nickel alloys 1-55

Lorenz ratio of platinum 1-57

Lorenz ratio of palladium 1-59

1-2
List of Tables Page

Beryllium 1-4

Magnesium 1-6

Aluminum 1-7

Aluminum Alloys I- 1 Lead and Tin 1-12

Gold • 1-14

Gold Cobalt Alloy • • I- 1

6

Silver 1-18

Copper 1-20

Copper Alloys (German Silver and Brass) 1-22

Zinc and Cadmium 1-2 5 Scandium and Yttrium 1-27

Titanium, Hafnium, and Zirconium 1-29

Titanium Alloys 1-31

Tungsten 1-33

Molybdenum 1-35

Chromium 1-3 7 Manganese and Rhenium 1-39

Iron 1-41

Stainless and Alloy Steels I_44

Carbon Steels 1-48

Cobalt 1-50

Nickel 1-52

Nickel Alloys 1-54

Platinum I- 5 6 Palladium 1-58
COCO

S B

I- o ..

a i

a o

U

ffl

a.

o o o • *J 43 O si Is

£ £ 3 £

1-4
,',»'• »««'» ' 1- » t ' t > r > t > t

3.6"

3.2-- X

siCI

0)o

2.8 •

2.4.-

G

2.0"

:.6

n

A A &&A

Symbol Curve

O L

A PHG(II)

D PHG(I)

V WW (1) O WW (2)

«'!'« I » « i « 20 40 (0 eo too Temperature, K

2o; 4s^M 4

Figure 1. Lorenz ratio of beryllium

1-5
LAJ £ +> & 00 Sr £ Sr

'Y. oo "-- •4s "U "t: ^ % ^-* %• CJ -^ \ ^ ^ -^. uu

°? °?

<*> % *& % °t

"*i q «J °? °? CO °? LhJ x * H o 2 Si s « 3 8

CO

CDa

a1-6
CO

CO

* «

t; s s t: *• >

t

g S jj S °? 1 S

9 3 3 goo 5 5 6 'o o o b bo b 'o 8 o" % f: g „; "

& & &

i - f | - it

3 3 9 3

I I i I

3 5

1-7
cou

CO

Q=

3s

w

LjJ °^ I

as | CO cu l__ K o

r»»j i I.I-) *—

a

n

C-D s ^ E 1 1

C_D | = ~

l_a_l X ,_^ ii °

ic:

W OJ 8 H i p °° j: « a? °8 * I 1 %

+j -p a? §" a o CO ^ °^ S >> i > X "U ^ i i LU % <£

"a | o D Of O Q

a] 2 3 3 p i 8 I " « * 1

LhJ COCO 8 3 » 8

aJ

O S 5 O

W 1 '=1 1 * « "

JS ffi 1 I ! 1 i j j J -J o

sPo*-* 3E

d CO > »_CO § £ Q_3E Pn CD o

o^

g 3 * u .-» I

CD

d ^T £ - 8 d CO ~ X ^ ^ a *? N »

kl_l I

>i >>

d ! § j d s"

X ^ a s t £ g; CD H E 1 & ^ & 5 >> i s

tH -H

O CO >> rH ° S o E S H .. s 6 E P. d £-. . 1 ~ E -h | a < ON i i w- 8 §

•5 s & ? 8 S ON •S S -S SR -S > E s - 1 H £ W § - -

"-"

.H ,-< ^ 1 < •-a < PS < ^ < o: < 5n < < < <

"«* __! c\ £^ ~ 1 8 1

CO c> 9 oe *-* f» 1 1 J h'

CO 1 § 5 i 35 f 1 1

Ov kkJ 5 & o 5 = £ 1 1

fj S 3

u_l „

CD

a 1 g

J

g E E
Ml » t i t i i t t » t ' t i i i i » f *

1 i

2.2<-

> 18 +

0.6

% Q

©

B

N

a)H 1.4- Symbol Curve

O AMS

A AWS n FRW

V L Q O MMB

!.fl« © PHR (SO

+ PHR(IIOO-O) * PTW

©

7*

74

t

7 $

© e

' « i « i 4 i I i t « l > t l I I I 4 6 8 10 20 Temperature, K

Figure 2. Lorenz ratio of aluminum

40 60 80 100 200 403

1-9
o

CO I

OCS o o a

U_J " a ^ 1 3 s s

ac

a $ ^ Od ^ g s " * §

r--J rrT 8 o

l_kJ

g

t?Q

d I d

U i 1 8 S >o S o o 8

oe *T s " lo

O o d

Q at n d

C_3 a] >> £ a &,

N 4^ £ H

a CM 1 * I

i^

"S " SE Q 1 * m £ *

"3

a

"3 C3 3 r-l CkJ ^2 <0 » to to , w ^ „ CO M 5 I I a «

cu CO

M CO 1 S 1 i 1 w s £ w W co It ,_, S c s c c

l_kJ P 0)

+> 1^ 3 * 8 .. i I 1 3i 1

cea

a

Q

u

O £ 2 S p ^ 5

irt o u^ * CO § - z * 1

ii | 1 i • 1 ..

E-"K i I 1 1 i i 1 1 1

^^O o

""J o

E-<

g o o

*7 "?

M c 3 "P

d ^f

E-> o*^ 5

j3

J >

c" 3 H i s * < e*

E->

IS) ° «

Hj '"J *i

CO 5 „ j o ^ CO "-" "-* O 3 t^

f- c ^ ^ 5 3 £ U 5 N

SI ^

GO ^C ,-c .. " o ^ io

-^ CD o d 8 #

ae

HH 3 ^ , fc ^ to to o s -^ £ >

LfcJ C_3

d ,_; S?

m

h

d 3

to COCO £ £ d ^ 3 * 3 £

3E UA ^ . d ai C^ OJ __ X 3 d £ ^ o s 3 a

C-3 £ i -i ^ u s ^

•£ CM ^ ^ # "lo ^ - ^

CO i i 5 s A

o" ? I s g ^f H = 8 o 3 - u. IP o E ^ E-< S 8

-=* ^H ^r ^ o ^ M

cq -*

j. - 8 ^ ^c OJ ~ 8. J.

J o 8 i 8 i u s 1 s s s C\ s 8 8 & i 3 S 8 a: < o < < C < < < Kl < < <

ae* CM^' ' H

O o 8C\ 1 s I

CO * -—-

oe F± P. £ S TlJ 1 I 3 1 3 ^c '-' s - 1 1 s CO Jl ! 1 i Jri - 3

at ai 0] fr— a S "S 3 ,J ,_7 J rH- ^ ^

CO ft CM to P 0* 5 k

X s K

K z s 1 * 1 £ rH- " rjr rH-

-p

In

w « » » 3 » •x * X EC :•-

CM

oc „ "7

VD ^ S

fJJ ai C3 ? < i s1 s 1 O o

I- 10
2 3, .10'

» «i|ii»» i t r ' > > » » r »

2.6"

oj 2 4.-

$ 2-2t

Is)

o

2.0 +

:.6

Symbol Curve

PHR(6063)

A PHR(5I54)

PHR(5086)

V PHR(5052)

O PHR(2024)

HS (Ann.)

«»««.« i 4 & 8 10 -4-

20

> i i i i i m l « 40 (0 10 100 200 403 Temperature, K

Figure 3. Lorenz ratio of aluminum alloys

I- 11
s

o-> ae

3E

i_i_i ae^

r-a ^

o=^_

C_D

e_=> zUl_l 3FU

D° o Q_CO

co E

l_hJ

CC ^J .-l r^- C_3 •1 i • GO

gg

W T5 ° Q

o^

TT

CO

e3o_

3E^ua^

bhl U

COzk-kJ ^Eut_>-l Q-co 3 s

.o

X t, £ £ 2 £

be'

t_bj >-"—' _CO

ae

C0CO

l_l_l I S

SE ^ i g

.-1

i*J o £ 5 ^ hJ

1-12
2.5.??•

i > t i i > t » »

2.54-.

0)^2.52 >

«

N5 2.50 uo

Symbol

O

A

Curve

L(Pb)

L(Sn)

0A A

A A0

A 1

2.48--

2.46

i i i i «10

i »«»» 20 40 CO 80 !00 Temperature, K

400

Figure 4. Lorenz ratio of lead and tin

1-13
CO

'oo

* :*: m

O QQ OO QQ Q

Q ?

§ S

1-14
2,8.1 * i t » > ' 1 i i i > > i t i .JO

1

2.4-

>

m 2.

N

CI

O

iiiil i < i > i > i i i t i I 6 8 10 20 40 SO 80 100 200 400 Temperature, K

Figure 5. Lorenz ratio of gold

1-15
COCO

O

i—

i

OU

o

C3

co

S I

1-16
>

«

O

4.4-

Symbol Curve q

3.6-

1

2.8

r °

PBG

i i > i > i i i i i t >

' 6 e 10 20 40 (0 80 100 200 400

Temperature, K

Figure 6. Lorenz ratio of gold-cobalt alloy

1-17
>

I—

I

CO

go

GO

§ § 5

£ £

I? £

+ + < »^ E < <

S 5 S

I-li
.'„'•

3.2«

W

>

cd 2.4

N

CDu

o

1.6"

,e

c.e

i < » > » i » i i t i i ' > i r i i

+ +

t + + + + +

4 +

A &

Symbol Curve

o FRW (1) A FRW (2)

K(l)

V K(2)

O L

+ MW

*****

« I I I > » « I I 6 8 10 20

i i t i i i i i > 40 (0 i:ii 200 Temperature, K

403

Figure 7. Lorenz ratio of silver

1-19
u

(Ua

a,oU

CO

s«= 3J s 1 z 1 8 Q ^

ae

d >

°? >. z s +3 o

"3 s 1 O ^ 1

r-j 3 i 22 o 1 ee i a U-l 3 u •3 t- 2 1 W. 3 «J d I M 3

C_3 1>

-d3 oJ "

gj _N 1 |

1-hJ « *

"S 1 t? I § i P £ « g s» . J & 8 a i

TM. & S p 2 g * 1 *

CO TS o • o -P -P

d -h 8 3 P CO « "U ^ 3

COR « " p

d

d

is ta 38

>> "S >> o =3 ^ o * t "is 3 ^ ^ o ^ ^ en S p

to 1 o

CO "S E

x: LU =£" H E s ^ » £" % O CJ % g

*^ % "tS 1

tP- t

t. ^

^c

g § ° <£

g °? <? 1 "s

°?

h

°f °? J. S („ s cu i d COO o +J O q O 3 a ;; H 3 <H kl_l | -, X > o CO CO

S.X

x ° ^ x

CO ^ 1 ^ ° Q cjCO * a. a

-P 2 3 j J » <$» ON (0 ^O o in 1 § g

x: 8 z M h 1 d * * | A A

01 cu oj* -

cOA

-d > g

M

"3

J j < 1 O rH CU

JJ i " J 1 " j a i s 1 I 1 1 i

>. >. I 3 ^—. E 1 E o a o^ o 8 m ^ 5 < s >M

ai *B CO cc e & £ 5 1 1 IE to Eh u p

l-H 's' ^ I E ^ 5 3 >. 0) H H 3 « I 1

ee s 1 1 ^3 ^ O

•^ ^ 5 5 to 5" CO o o 8 o o d

>i ° & & a xi

l_i-l 9 3 0.

a- p- >

jj -P 5 u 3E p- --v 1 u 3 §

XI

A 3 •»

i_i_] „j o

"? "?

g ° 5 3

fiu o o CO

"S < 5 < < x: i \ I P fc. E ^ • S |

"S °

S\ S "a 1 t 1 s i

cc s

05 S 3 ^ s S P 8 S & s S^ 5

•d c 0> s R 2 s " ON s P

•? 5 « 3 5 ft 8 ft 3 £ % S 5 fi 3 g 5 s s

«£

g

ft O^ -£" >- ON

?* s

^. Sn {£

p x: ~i £

Ch CT\ CO 0> oc a

E-- E- Eh

d

t& CC i ^ s § 1 1 1 s

-d1 1

J= cs t3 „ e a B (D >> j £ "3 ^z £ 3 S £ § S ,_* ^ I t

Eh CO

l_lkJ 1 ES e S3 I 1 d — H 1 | E 1 1 £

fa 3 s < * a W M M ^ E a. & i

LftJ ae ,^ CJ

yl i e <

a.

g

1-20
2 4

<«-•

» « » I >

'.£>•

» t t ' r ' > Symbol Curve

o L

A MMG

D PRH (CD)

V PRH (Ann.)

O WT

• S

1

i*

0!

>

SIa

o

2--

$.

o

9

7

d?

6 8 10 20 40 60 80 100 Temperature, K

200 409

Figure 8. Lorenz ratio of copper

1-21
COCO

°k* w« %. %, °k °4= » ^ ^

°t> °t % %. It % - £ •£

as o o tf\ o O

o °? °f

<X> CO

pq

>

I—

I

COc

uO

tno s % <

a

exou

8 I

s B -

3 S3 S3 S3 % S 3 3

s §

1-22
% °u °u °w *!< % %. •t %. %.

°? °? °? <"? CO

E R

£ 3

1-23
W

>

O

.10

7

« tit i t i t

i

ill

t >ti|i>i| p——f r—

tit

:.2«

2 Z

a

5

:.8-

a 7

c

6

1 i

7

L

lit

7

Symbol Curve

*

:.< o

A

D

V

O

+

1 1 1 i

AM ** \

B (G-Ag)

B (Con) ******* KS(SB) t tt , t *** KS(NS) * l||m

L (G-Ag) and L(Ptd)

L

i i t ' i mi > 40 3 Temperature, K

Figure 9. Lorenz ratio of copper alloys

(German silver and brass)

I-Z4
C/9

U

X)c

o

.s

||| III

s s &

8 8 S S S

8 8^

1-25
2.8.1 » « ' t t 10'

2.4-

oj 2.

.

>

a!

O

:.2<-

: e

i i i » i > i > t i t t

6 8 !0

. * a-BB?3}

t 3

Symbol Curve

GG(Znl)

A G6 (Zn II

)

L (Zn)

V GG(Cd II) O GG (Cd 1)

+ L(Cd)

* I I I I t20

t i t i t i i i t 40 (0 80 100 200 Temperature, K

Figure 10. Lorenz ratio of zinc and cadmium

403

1-26
oo ^

t<o

"1= % %

s °t °fc %

» s °? °?o || q

a uCO as os H

3

-i-i

+->

+->

c

a

o

|-2

s &

1-27
.Iff

6"

5-- W

>

o«

SIa

<u

!-l OJ 3

2'-

6—i—•—

i

' t ' t ——i—t— i i—> i >

Symbol Curve

-t—

AC

• A

D

TCS (J.)

TCS (II)

'

* A

A

A

A

5 A

•

3

* * A *AAAAAA

3

3

a

B n

3 3

•

3 * 3P •

1

'

i » « 1 1

2 n _ r? S B

u g u w

1 >»!» 1 —*-

6 8 1C 40 SO 83 !33 233 4Q 1 Temperature, K

Figure 11. Lorenz ratio of scandium and yttrium

1-21
3 ,.

5 -

1-29
Jff"

4.4-

0)>

a

O

3.S--

2.8"

2.C

I

1 ——

>

Symbol

« t > 1 Curvet i t i i i i ' 9 '

O KKW(Ti)

A KKW(Zr)

n WW (Hf)

G G

B

3

U

C, ft

'

2

'

e E

S

n „ in •

3

a

a

•

fa

£

A

* i t 1 1 1

1

i t I 6 8:: 20 40 60 80 !00 Temperature, K

200 400

Figure 12. Lorenz ratio of titanium, hafnium, and zirconium

1-30
to

COo

1-31
0!>

«

o

! .4.

.10"

1 i t i l

i | i

° Q

-t- >!»'> 1 t »

1.2- "

!.0>

8 • Symbol Curve

O HWP

0.G- Y

aJ

C 4

t -»- t i i » i i » 20 200 400 Temperature, K

Figure 13. Lorenz ratio of titanium alloys

1-32
C3

CO

^1 °u °W °i* °id %. £ £ °t °f

CO

•A 'o °? 5

H 3

6

X

X

q q 1

q

& &

•s *

„ t

TJ -O Tj -3 T3 TJ

'd ? 's 'g '5 '5

C_3 a.CO

5 A

, 2 3 S

S £

& S

1-33
?.*

i i I > I » t » I i I < 1 > t t f r f i f '

2.8 ••

Symbol Curve

B

A DD

K

V MMB

O WW

+ WGB

>

id 2.0

PiN

c

<UU

O

.2"

J+ + +

+

+ + +

+

7

I7

Jo B

t

r

E

Temperature, K

Figure- 14. Lorenz ratio of tungsten

10 {30 400

1-34
3a

0) XI

oooe

3=

l-t-J ae^

r-»j

ij-j CJ«u

ae

1-3-1 z M ^

c-s

eft

W ^ ^

i_kj a. 1-1 o7

OJ OJ to 1 s a a CO *** <v

LJ_I 1

." <£

u <£u <£ « i 8 to l"3 8 \

_| „ "S ""* 3 X "S

X

l_l_l

X

C_5 CO rA

-3 £- I 3 * 1 i " < -5 <S J B " £ £ g 3 g

^<3 O^y i I CD s ^

_&<_ CO

Q. o 3= In o

•S3 u

Od ^ ^

LfcJ « ^J C3

ae ? ^J" o O CO i c w

LjuI i " s a£ w H >

C_3

J 5 S 3 1 a Q_ £ S (I? j CO 1 8 < < a a # 1 s a

i-i & P w

a

dl s- m. 8 s & & & S

8" $.

d 8 d > > ^ j |

""" *"*

w *~* """ > *"* > ""*' § w ^ E E 05 E EC S E K E O E

CE

LAJ ', , CO

acC3^ "P fo £ £ £, ro as CN CO

3» § ,3 3 3 3 2 5E 3 g 3 3 1 i 1 1 w w l I

bkJ

CO „ - «

1-35
.10 '

2.6"

2.4«-

>

2 2 2 + «

tqd

<DU

OJ 2.0

1.8"

!.6

Symbol

o

A

n

Curve

B

K(l)

K(2)

4 6 8 10

9

20 40 60 80 !00 Temperature, K

200 403

Figure 15. Lorenz ratio of molybdenum

1-36
CO

S I

2 3

O

u

siU

P a ~ s

~ 3

fc i*

l is s s is

1-37
M,

3.S2.8-

>

siC 2.0"

o

1.2"

0.4

i « i > i i i t i t >'>'»'? i > »

Symbol

o

A

v

Curve

G

HKKTW

MWM (68)

MWM(67)

8

4

! »

» ll|l|»« I | I > I > I > I > , t n—.- 4 6 8 10 20 40 60 80 100 200 400 Temperature, K

Figure 16. Lorenz ratio of chromium

1-38
CO

ac: ae

*g

i-u ae^C3

r-J ae

t-i-J o

CJz2

C_D

LfcJ S p. CO

ti to cos | 1 1 

O ^c s i ? 8 8

t- 5 si d C_5 CO 1 8 h 8 * CO * P 3 ,. * i E a i i 1 i

•vp a*- 3C

CO

e_^EC9Q^

t-l_l C9

CO53E s o O

l_l_l Q-CO ^ £ -! j o

1-1 ^z

wmM i I ~ i ^

>1 s s i 5 * s s £ 1 1 £ B Q Q p

<a " < EG < « < ec

LU

"~

—' .CO £. ? ? ?

C5|—

d 1 1 1 1 3 3 ^ s CO

t-I_l 1 1 1 1 1

-p

K § $ I s

Ue-1 ae 1 V 0) IU m

C_3

ffi § 1 s 3

1-39
! *7 .10'

1.2--

-q—7°~:;=

Symbol Curve

O R

A WW (Mn)

WW(Rel)

V WW (Re 2)

O WW (Re 3)

>

«

N

CIu

o

.8-

9B0

0.4"

» I I I f

fa

* *

Q 2C 3E

CO

C 8 10

I « i * I i I » t 20 40 (0 80 100 Temperature, K

200 490

Figure 17. Lorenz ratio of manganese and rhenium

1-40
CO OJ OJ OJ OJ OJ OJ

CM OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ Ol

o 'o 'o 'o o o

2 I £ S 5

8

% 5 5 § % i

1-41
CO

n 1

g

«

8 I

i |

C

oU

a

o s ^

- ~ 8

d, [l, pa [n &, e h h o u, tc

8 1

5 5

*j 'a

§ S

1-42
hh

4 4 •

5.S-- «

>

oh 2.8

G

OJoa 2.:

« i I i t i I I t i 1 r-t-rf-n i » i Symbol Curve

o B

A K

Be

V KKW

O KKT

+ KK

* L

-H- KS

• MMB

HPW (2a)

HPW(4) l"

1 '!'!*

2" HPW (2)

i i i i i > 4 6 9 TO 20I t !«*>» > » 40 (0 10 !05 200 400 Temperature, K

Figure 18. Lorenz ratio of iron

1-43
0)

<D CO

>^o1—I .—<c

nJ

tn

a) la

"(3 +j

co

=*= oe

3E

i-i-i °^

ae^

r-J UUuu

aEUJ

3Eu

Q_co

COC3 | ^ CM j. J. Ox 8 l/N o\ OS OJ ^ c*- « S ^

l-i_l CJ

co ~! 5& 15

-9 1 51 1 3 I 1 1 1 1 3E d

re

a.

b " a p o Q n a a

Q

a

a

Q

Q

-J3 O*- ^

CO

TF *"2

C-D ° ea ^

ac ^ ^ H

(-SJ C_3 oe ^V ^3 3

co

n ae •£

i_i_i ^ H 7J o C-3 LaJ Q_ " _^ s « o s £ _J CO ^ fl t^ ^ _^ J. CO o |

t-

+J § S & s

fi "S i ^ s J) ^ ro j^ in "?! £ 3 £ £ s o e 2* 3 5 o? CO +J o.

U •S1 c J. £l <n O

t- a? j? °i cu §<£ o 5 \o & t*- ^ 5 o! S OS 1

j= 3 < ft, < < <c ft. <s <: [x. "* fa ft. X ft. tn ft. J ft«

m ft, ^ ft.

K ft.

kkl s s

co 3 I ce 1 I

CO

cr

•d 1 CO

gg

r^ t- kkl ~ i i

£? S1 S1 2? S1 31 Os

£h 2" s S1 S1 ac E — a i E c c c c a c c p c c

.2 $ S & 1 | £ | 1 | § | & 1 m w H ft. ft. ft. '" ft. ft. ft. ft. ft. h ft. ft.

bki oe "rn

p tf\ 1a s " Q> "q"

TM 9 ^^ ^.

u ° "^i o g"

£?

w s= = 1 a | § a

nHa P, ft. * ft. ft. ft, ft. ft. », ft. ft.

1-44
co

iC dr oes " g

«*. oe 1 1 ^ I S 3 .H I § i

pa ON

r-j (0n to isS > q

AI o

PS

1-<_I §

c_d * ^ * A * tft "a

CU

K "2 ^ "3 cy «

Ol rH

*v ^ -**. fl

"S\ „ a ^c l

11 |11 | "

ON „ to e_s >> >i >* & -p >! « -P

LJ_I e) s->

n ^ B 1 1 1

"a 1

>» 1 Q 1 1 a c3

1-1-1 CO 8 ii a8 I 8 i ! 1i I 1i 1 J CO to o

CO

q » q 8 " i i s = » >» >> >» o +» o P d efL z a " c

11 8 n

11 5 q <J"

q J3 id

tu s S i Q S s i « d » d i

PS

Sn LJ-J to +* C_3 *? i ^ i

"?

a > H "S ,*J

H s a CO d " a " a " a s | 1 | I

(-i " 1 1 & 1 1 1 ? < & H i 1 i I 1 f d o ^ o 9 q d 8 ° o o „ < O ^ q £ ^y 3 o ^ ,-". o q q > — E o £ g • ? s K z "o" ^c ^ w 3 ^ ^ oi d d o CO s g •i

•~* to ^ c " 3 Si , ^ -2 o Q ol t\T t* ^ TM

E< C-5

5? o d tj-

"w"

w + r- ^E ,_^ to CO ^ ^ X a o ^^ "? «r S3 _^ ^C g £ ^ ^ w

t^-

O

Lkl ^ 8 8 ^ ^ ^ "to , d

w oe I => | j ri i € I s ^ t- CO a 1 ~ „ £ s E 2 z ^ H "^ I ^ ,_, "^ Q

£" CO* *? "2" "0

I_a— ^c I 1 o H h o H s d q d U d d B S5 o tto o_ 2 8

on CO s 8 8 £5 o O o o o & o £ o £ § 3 K

d 2S P p s s •S ' § 5 f i 5 OJ I < d q < tf q ^ d i-t rn 1 q ^ g *— o ,o ^ o o o 3 < B> fa 5= < a fa K < CD fa " < fa ° < fa ° '" fa e < fa fa fa fa

khJ S a a 1 ^o is i9 CO ,o jO T) ON <=>

on on ON C\ & p. Pi p.

l-l .H ^

<«c

a U3 n, to to ID

HHH cs ^s M id CO I 1

is

a I p 1 1 a

UbJ 1 1 a 1

•a3 9

|H 1 3 i p -p 3 3 3 = = K cc K M w a

l*j

C-3 ^ g "cu I s a t « « - £ g g £ ss ES = s g s

1-45
ou

CD m

a tvg

<v

<

C

en

<D

+-> m

I 1 5 2 5 s s

a £ J g 1 % . S ? s 9 £ ^ s s in (\i Eu ro ro

rH • • • O O X S 3 ° ° "^T

"""

"m 5" "o to" <D ir\

LT\ rH M rW O O O — d d d o o o

s a 3 3

J

1

§ a

S £ & If g^ggggggg

1-46
;*•

-i— » t » t i t » t » » » r ' 9 Symbol

8-

>

a!

o

6<-

4-

O

A

V

O

+

Curve

B

EZ (303)

EZ (347)

KK(I)

KK(2)

TW aTNW

KK(Mn)

HS(286A)

HS(286)

F(HM80)

\ F(LE42)

F(I0I5)

F(HP49)

i i i i i > t > » i i t > * » C 2! 40 SO 203 Temperature, K

400

Figure 19. Lorenz ratio of stainless and alloy steels

1-47
0)

<u COoUu

CO

atoe

^E

t-i_i ae^

r-j

CAJ CDoy

LU

^E

CO

1-kJ oo

co

d

l_hJ —J

kkl CO

co

p 3E aQ

--J3 O**- 3E^CO

Q3ECO^

«s

l_hJ CO

CO

ac

Ld_l Z

CO^CO

u£

fa

UkJ w—,CO

C9CO I

kkl ^^

w3

kfcj

CO j

1-48
3 56,

.10"'

3.28--

>

h5.2C-- «

N

CICDU

O

3.:2«-

3.04

Symbol

s

Curve

o

<

i

t

>

—

•

L

«

>

3

2

< 3

3 3 3 3

3

3

6 8 !C 2C 40 CO 10 !00 200 400 Temperature, K

Figure 20. Lorenz ratio of carbon steels

1-49
,QoU

*"3 O "D

1-50
},h

2.6--

re«

CO>

% 2-2

tsl

o

:.e<-

> 1 1 t ' t I 1 1 t

1

-T— I 1 » t ' t ' » - » » »

«

«

L

& -

&

Symbol Curve 3

3 3

' O RN

« A

WW

WPD

A A 3

A3

A

A

IS !3fl Temperature, K

403

Figure 21. Lorenz ratio of cobalt

1-51
CO 43 CO

te %: °U

(-1-1 TM> <£ <V

u

$ t»

-.1 g

5 I

i

: $

,. 1

1-52
.',.'•

» « » I » t I I I t » I » ' » » »

2.6«-

03>

2.2--

Symbol Curve

O FG

A GH

KKW

V L

O WT

?

7 7

?

77

c

o

6--

:.i •

ga n

a s

3 G*

* i « « « « At 4 A I i I i I e !c 20 40 (0 to too Temperature, K

Figure 2Z. Lorenz ratio of nickel

203 400

1-53
CX9

1 n

o

s?

<u X

<J 2

"; sr

- s

C\ O} <J\ CTv ^ S

1 2?

a |

I 1 J % 3

U 15 15

a a a a sa i

1-54
2 ? .10

5.8«-

>

«

O

.4"

C.2

I 1 I 1 > t.i

» »

4

+

t » > 1 ' t Symbol Curve

A

A EZ (MDT)

* V

O

EZ (MAT)

EZ (MDR) - EZ (IDT)

HS (7I8A)-/ + EZ (TAT)

\ + HPW (X)-» \ + 4

+

ft

•

HPW (718)-

A \^X -

+

e < -

<•>

G

i »

0^^.

% A

? —* i.i i »

i

1 « . i i i

3 ^s^^

3

« > i 6 8 10 29 40 (9 83 !03 Temperature, K

239 403

Figure 23. Lorenz ratio of nickel alloys

1-55
S «

i 1

s ?

I t

•-I

i—i ft

n 3 5

i-k-l

J S J 1 8 &

•d c W W

1-56

^^^^^^^^^^H
.toU

2.6--

o) 2.2--

o

I t 1 1»t 1 |

Symbol

' t

Curve

-t—•y—r ' t » t r——

o PTW

/» A WW 3

£J D MMB(I)

Y

V MMB(2)

L

^

L

L

L

k

'

» t i

* L

«

6 8 !C 20 40 (0 80 tOO 200 Temperature, K

Figure 24. Lorenz ratio of platinum

400

1-57
rt Ph

03

I > "W

1-58
hh

Z.2--

a

>

n5 «

a

o

:.< ••

* t tit 1 1

Symbol

' 1 1 t 1

Curve

i|t-} » t »

O KKSW

*

'

4 III 1 —i 1 i 1 til i | > 1 6 8 10 2C 40 60 80 T 00 Temperature, K

200 43:

Figure 25. Lorenz ratio of palladium

1-59

Appendix II - Data Tabulation Page

Beryllium II- 2 Magnesium II- 3 Aluminum II- 4

Aluminum Alloys II- 6 Lead and Tin II- 8 Gold II- 9 Gold Cobalt Alloy 11-11

Silver 11-12

Copper 11-14

Copper Alloys (German Silver and Brass) 11-15

Zinc and Cadmium 11-16

Scandium and Yttrium 11-17

Titanium, Hafnium, and Zirconium 11-18

Titanium Alloys 11-19

Tungsten 11-20

Molybdenum 11-22

Chromium 11-23

Manganese and Rhenium 11-25

Iron 11-26

Stainless and Alloy Steels 11-30

Carbon Steels 11-37

Cobalt 11-37

Nickel 11-38

Nickel Alloys 11-39

Platinum 11-4 2 Palladium 11-4 2

IIOOOOOOOOOOI

MINJIvjMNMhhmmi-.

•O -J CT1 -P" l\) O (BCT> *> f\J O -H •••••2 ooooooooooots

i\ji\Ji\ji\>r\j —.-- ^ .. — —--.— ... . CD O* X- I\J O <0(D>lff'Ulf'WfUHO-000)CD~J-JH ooooooooooooooooiouiouiom • ••••••••••••••••••••is OOOOOOOOOOOOOOOOOOOOO "D

i po r ro i ^f-UiO INJUJO JiOWHH J!

I I I i I i i I I I i -. m 0000000000002 OOOOOOOOOOO fN

00 03 CD CD 00 CD CD CD CD CD CD

i i i f I f I I I I I —• r oooooooooooo: OOOOOOOOOOO f 00000000000000000000002 000000000000000000000 fsi a: a) oo qq cd cd cd cd qjcdojcdcdcoojodocd oo oo qo

OOOOOOOOOON) TJ OOOOOOOOOOOT3

i^uu)roi\ji\)i\ji--(-ii-'i--

• • • • • ;o (- -j.p-r\j^0''-p-)-'^0CD-j-j>O

i i i I r I i I i i i

>—• j~n 000000000OC02 OOOOOOOOOOO M

03 O*1 *

, l\JO^Q3-4t>U'>Li)WHOsO'OtBa)>l-J1

ooooooooooooooouiouioaiom • • ••••••. •••••••2 COOOOOOOOOOOOOOOOOOOOTI

* ••••••••• ••• •••;(-

l\)t--i-'h-'OOOOM3»£>^0v£)«JD'J3OOCOOOO>O roouioa^-t'MOcD-g-j-g-jooi-'i— i-ii-'i-'O—(X

I I I I I I I I I I I t t I OOOOOOOOOOOC c cooooooooz OOOOOOOOOOOOOOOOOOOOO |M

O OOOOOOOO "O OOOOOOOOO "D OOOOOOOOOOI

-P- CD J> > O

O 0000000002 OOOOOOOOO M

QD 03 CD CO CO Q] CO CD CD OOOOOOOOO c z OOOOOOOOO INi coacococoaaicocD 0000000000002 OOOOOOOOOOO fsi cococococococococococc

OOOOOOOOOT3 OOOOOOOOO T)

,_.>-..-'>-'i-'i-"i-'>-"»-'C/im

• •••••••—

n

uii-'CD-f-Ovj'aivjiui-i^

I llllillf '—• — o oooooooo<ri OOOOOOOOO—> 00">CT, CTs O^<7,'C7*0N CT* —1|

roocDuii.oi-'OOO1 I I I I I I I I OOOOOOOOO- OOOOOOOOO- O*0s O*CJv Ov C7, 0', 0"1 h - OOOOOOOOOOI

wNHHHH-omur;i NfOHI_.HH^UlW

t-'OCDUi-C-i-'OOOn^O i-'OCDUi^-i-'OOO mOm'-POOOOO—t 2 moai'.pooooo

+ + + ++(-1 1 1 — > + + + + + + 1 i I o oooocooo<r— occ oooooo

O OOOOOOOO — OOOOOOOOO OOOOOt-'i-i-'-i OOOOOOi-J.-'i-'

rsj i\j i -J2 t~ CDCOCO-J-J-J-JC^-C-^i • > o OOOCDCDWOIVJ'OOI

I I I I I I I I I I I — m OOOOOOO 000002 OOOOOOOOOOO INi comcocococococoaicoCD
MAGNESIUM

SEE APPENDIX I - MAGNESIUM

IICO CO CO CO O O

(Si o o o o o o zooooooo

1 o o o o o

cocoao co co as co co <o co oooooooooo zooo ? DOOOOOO UJ •

I I I I I I I I I I

.-. --H (SI fSJ

0-T--10—'Oco^-Oc JK •HHHrlHHH(\IMN

aoooooooooo £:••••••••••

a: u

UJ =3 X O. i

OOOOOOOOOOO ooooccocooo OOOOOOOOOOO '+++++ + + + + + +

I O r-t U

i csi f r\J I

>sJ c o c o o o zooooooo LU — I I I I I I O<-3"Ov0f>(Sjcsj

0_ O O O O O O

1 OCOOCOCCOOO OOOOCCOCOOO

iS) <t •& O •

a oooooooooc

co co co co o cr> rsl O O O O O O

Z O OOOOOO Ul — I I I I I I orh-r-*or--d-oo

jq; • MfMH r-OCO

COCOCOCOCOCOCOCOCOCO

«sJ oooooooooo ^OOOOOOOOOOO UJ — I I I I I 1 I I I I ori— o J- —< OHoco-itMn 0< inin-or-cocT-O 00--H

CD CO CD CO CO CO 00 CD CO CO CO

rsl OOOOOOOOOOO Z O OOO OOOOOOOO UJ — I I I I I I I I I I I or — vDoc^u^cocoor--jco 0< Hm^ui'Ocoo'o-OHH

i or

rsl OOOOOO ZOOCOOOO LLJ —• I I I I I I CtHCDrHir\rH^(NJ O < -tf O nD CO (SI (SJ

1 CM (SJ (

j or

(M <

en o O O O o^

I isj la o m o (M a oooooooooo z

o_ oooocoooooo o. o c o o o cr

I

CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 00 CO CO CO o^ o o o> o o o <sj OOO rsj OOO rsl OOO -sJ OOO <sJ OOOOOOOO OOO 2 O O O O Z O O O O Z O O O O Z O O O D ZOOOO ooooo 1 1 1 UJ — 1 1 1 UJ — 1 1 1 LU — 1 t 1 LlJ —• 1 II UJ — 1 1 1 1 1 1 1 1 >JH^ QT 1— <sj CO O or i- -* -d- m or v- <f o o ori- r-icoN ori-mmtr\coooo

^- ^ ro O < J- en tr, o < -cr ** -* O < tr\ CO -J 0< -f com 0<-*fMiri i-, o^a>r-co

_i or • • • _i or • • • _j or • • • _i or • • •

(Si (SJ (si rsi rsj tsj CSI (SJ (SJ {SJ H r-H (SI •-* i-t r\i(sji-ti-tcor-coo

o_ o o o a o o o

3: • • • UJ (SJ CO Ji O O O O O O -tf unoinomom

or

CO CO CO

isl OOO Z O O O O

UJ ~ I I I * or i- & o o

o < m co ^r

_i or • • •

rsl OOO Z O O O O

IDCOCOCOO^(>0

fsl OOOOOOOO Z O

i CO N CO O1

a o o o a o o o csi in -j

i -d- •* o

i O O O O O O -J
CO CO CO CO CO CO CD CO COCO

rvj O O O O O O o o o o ZOOOOOOO z o o o o o

UJ — 1 1 1 1 1 | — 1 1 1 1 KK^^ooO'in tr I-0>^hO. 0<-J{n-Hr-m lf\ o < -fr r- o o

fsj tvj ^ _, _, ,_, - ^ h rg

a. o o o o o o Q_ O O O O

s: • • . • UJ (M o o o o o LU O O O O

f-J o o o o o o O ISl o o o o ZOOOOOOO 3 z o o o o o

ccK<f>oocotMn Q q: i~ o -^ —< o cx-a-m^r-m^

< O < -J r~ o oJCt • • • •

0. o o o o o o

I
cd 03 co co co co cocococoaDCOcococococococococoajcocorococococococococococoaorococotDco

i oooooooooococooocooooocooooooooocoooooooo :ooooooooooccooccooooo :>oooooooooooooooooooo I I I I I I i I i I I I

I I I I I I I I I I

^ o o ^ a> C ( CLOOOOOOOOO< ooooooooooooooooooooooooooooooo

i-j^moi llOvC^^lCCDc^Ol O' lOOOOOO ooooooo oo > O CM J" »£! CO

cococo cocdod aDc03!cococoiscoa)a}a3a}ii)coa)a]cococDcoaDcocDcocD(ScocDcococoaDcD(oco M ooooooooooooooooooooooocooooooooooooooooo zooooooocoooooooooooooooooooooooooooooooooo

oooooooooooooooooooooocoocoooooooocoooooo

m j) r— coo>OfMsf»£)cD Oiroi^OinOinOi

COo

<—

i

1—

I

I

rsJ oooocooooooooococooooooooocoocooooooooccc ZOOOOOODDOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOO

a o o o o o o £:•••••'•

lu m \D r- co cr> o iOOOOOOOOOOOOOOOOOOOOivT-£)COOu-iOLr>OiA omo lOOOOOOOOOOOOOOiAOiAOOOOOOOOOOOOODO ooaJOO'OHrvjmj-m^r-coootN^ica)

cocomcococococococococococococo co co co co co co co cocococococococococococococDCOCoajaD M oooooooooooooooooooooooooooooooooooooocoo ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO Ul — I I 1 I I I I t I I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I I cti-uiOHHrH>-irtHm^ ^ in j-h (D^ c\OfNO»0-jcMO{Dr->Oiri<fj--jiriv£)r-coo'-, -JCDom

J on

I (\J f rg in t rj i <N <M t t rsj r\j rsi (N ' J IN f\J ( I IN <N IN f r\J I I <\J ( I CM ( aoooooooooooooocoooooooooooooocooooooooooo s:
CO CD CO CO CD CD CO CD CO CO CO

r-J O O O C O O isj O C O O O ZOOOOOOO z :> o o o o o z o

ori— or-r- oifi« o: h- co o <-* r- r- o; i- 0<-tffO.-iO".BsO O < <-< o m co oj O <

-J «o _j q:

CD CD CO CO CO CO O O O O O C ZOOOOOOO I I I I I I M O O C O C O ZOOOOOOO lJ-1 — 1 I I I I I O<cr>%o«o-*mr\j

"si O O O O

Z O O O O D

a o o o o o o a. o o o o o a o o o o o o a. o o o o o o a o o o o

s: • • • • liJNOOO

CO CD CO CO CD ^ o o o o o

z o o o o o c

UJ " I I I I I cc t- co o •-< r- r- O < -< *0 ir> m r\i

CD CO CO CO CO CO

I o o o o o o

: o o o o o o o

CO CO CO CD CD CO

i o o o o o o

: o o o o o o o

M o o o o

z o o o o o

a. o o o o o o a o o o o o a o o o o c o a. o o c c o c

s:

UJ cm o o o o o

a o a o o

s: • • • *

UJ r\j o o o

c!oo

too

i

COCOCOCOCOCOCOCOCOCOCOCOCOCDCOCOCOCOCOCOCOCOCDCOCOCOCOCOCOCOCOCOCOGOCOCOCOCOCOCO

»^l ooooocooooooooooooooooococcooccocooooooo ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOODDOOO UJ — I I I I I I I I I I 1 I I I I I I 1 I I 1 I I I I I I I 1 I I I I I I I I I I I

I CM CM f\J <M f CLOOOOOOOOOOi

s ooooooooooooooooooocooooooooo

omomomomoinoirioinoi

cncn^j-mmyDvjDr-r-cocoa-CT'C'

COCOCDCOaDCDCOCOCOCOCOCOCOCDCOCOCOCOCOCOCOCOCDCDCOCOCOCOCOCOCOCOCDCOCOCOCOro

isj oooooooooooooooooooooooooooooooooooooooo zooooooooooooooooooooooooooooooocooooooooo LU -• I I I I I I I I I I I I I I I I I I I I I t I I I I I I I I I I I I I I I I 1 I

rxoooooooooooooooooooooooooooooocooooooooo £••••• •••••••••••• •••••••• UjNOr-cooofM^- sOCOOinoinOinoiriOiriOiriOi
•1-t H

00

I

COOOCOOOCOCOCOCOCOCO

I oocooooooo :ooooooooooo

aoooooooooo

CDCOIDCDlDCDIia) coco

rsJ COOOOOOOOO ZOOOOOOOOO OO

LJ ~ I I I I I I I I I I 0<-J-J-ir\inir\mir>un -* $• jq: • • • •

a oooooooooo ^... ••••••• LummclcO(*"\cotricorn.-i

r-ti-H^H.-ti-lrH(\jrM (\| f\J

CO CO CO CO CO CD CO CO CO CO

»sl oooooooooo zooooooooooo r*J oooooooooo zo cooooooooo LlJ '—> t I I 1 I I I I I I

f\j r\J i t\J c

Q. oooooooooo £:•••••••••• m m m m co m c a oooooooooo

<> <\i -r r- c*
fsl ooooooocooccoooooooocoocooooooocooocooo ZOOO D 3000000000000000000000000000 oooooooo UJ — I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Q:h-^ir»r^sDr-(no*0'^^mif\CT«(«itDc^c>tnou^oiri£>cNjiriO(n»ocDO'-'tri-3''fii^-Ci O'--<'-< 0<^^^^oo^r^^o»Otnininin*o^r^i^coo>c>ooO'-"'-tfNjf\irvjr\ic^icnmcn(n(»i(n<t'*-*

i or

I r\J < r\i r 1 f\l I aooooooooooooo o o o o

r •••«•• • bjr-tOO'OfNJ^-.OtDOmOinO LT\Oif»0 i ooooooooooooooooooooo

cococoDcococococosmcococococoaococococoaimcDcocDao^cococococococococococo

r-J ooooooooooooooooooooooooocooooooooooooo z o ooooooooooooooooooooooooooooooo oooooooo UJ — I I I I I I I I I I I f I I I I I I I I I I I I I 1 I I I I I I I I I I I I I o: i— >o iti r~- sor^mo-o,, ^>3- <TiiriOcTicotTioiriOLnoir!Oi<Mtn ocnvoco o--•c^-i-or-oo'—'^

I f\| c I C\J I i r\i i j pj r I (M I

a ooooooocoo<

IUM3JO- O <N -T «C CO O uH ( oooooooo<

moinounoinoi. coooooooooooooooooo

) CO o o o o o * CLOOOOOOOOOOOOOOOOO ^uj^or^coa.O'Mj-vocoomoi^oiAOm

oooooooooooooooo

o m o i

cococoiBcoajmmiDCDaicocococoiriiicDcDaDiDtDcDcocDCDffiajaDcocooDa]

r*J ooooooooooooooooooooooooooooooooo 20000000000000000000000000000000000 Ijj — I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ah-irimo^t^r^ifi^rn^r^^o^rni^^P^ryf^rvjr^^i^co^H-a-o^tNvOa'rvJrncn 0< n^fnmf\jHoo>ai^ •e*cc>c*or^r»coco(^CT- oooHHHNMMnmn J ct

Q.£:•••••••••••••••.•••. ooooooooooooooooooooo o

LU«iDr"-COO*OfM-d'»OCOOii"\OiXAOu"iOir!OLnOif^Oi OOOOOOOOCO
o

I

COOD00C0COC0C0C0CDa}COaDCOCDaDC0C0C0COC0C0C0COCOC0lI>CDCDCDCOC0CD COOOOCOOOOOCOOOOOOOOOOOOOCOCCOOO :003000000000000000000000000000000 I — I I I I I I I I I 1 I I I t I I I I I I I I I I I I I I I I I I

a. o o o o o

3:

UJ MD O- O M OOOOOOOOOOOOOOOOOi ooooooooo

co i I CD ( ) CO ( I CO < i CO < oooooocoooooooooooooooooooocoooo o zooooooooooooooooooooooooooooooooo -< UJ — I 1 I I I 1 t I I I t I I I I I I I I I I 1 I I I I I I I I I I — ct^^C>0<rocn^^rvj«0(vj^^v0^a>irir\icocncOf\j%Oorr>r~-'--i-j-r~-c>'-i(n

<S) 0<^^CTi ODr^if\<rr^mm<f^tniri*D*D^-aDCO^^OO^^^r\irMr\if\icnr<i

i r\j r i CNi I

Q-00000000000000000000000000000000
>>o

oU

I—

o

M ocooccococo iZOOOOOOOOO D DO

UJ — I I I III III II EhHCOiOHfMOinh r\JO O<o o-r\iOir>or--*r\j~-io

I CC

0. O O O O O O I o o o o

CL O O O O C ' o o o o c
,,-H,_l ,_t(-<,_( _l ,_, 000000 'OOOOOOOOOOOOO oooo ooooooooo

-H'-i-'OOOOOQ OOO 1 ocoooooooooo OOOOOOOOO OOO

-.-I.-IOOOOOOOO OOOOOOOOOO •O DJDOOOOOOO

'I I + + + + + + + +

0"» OO «0 <—i i—i <—< >C C- CT*

O o o o

o o

•ocooccoccoooo OOOOOOOOOOOOO • III CCOOOCOCOOCO OOOOOOOOOOOO

>flO>OHHi

cocococococococococ )OOCCCOCCOi >COOOOOCOO< I I I I I I I I iCO'DifiH

)C^c^Q", 0'»o"•oi, o", o% o", c^• o*- >

ClOOOOOOOOOOOOO X. ...... ...... ujfNj(^^^mo^-T-oa30w-tQ_ OOOOOOOOOOOO

LUrsjm<J-%D<DOtMvOCOOfNJ<r Q.000000000000 5:

'ii rvj «i J- >oa) O rj 4- i) CO O im

CDCOCOCOCOCDCOCOCDCCiCOCDCO M OOOOOOOOOOOOO 200000000000000 UJ -H I I 1 I I I I I I I I I I cc *— m •-• o O r- ^o —10 aim ^-^ m

jo: « 1 * • • • 1 • • • • 1 •

I I I I I

CD CO 3) CO CO CO CO CO CO CO CO CO M OOOOOOOOOOOO 20000000000000 UJ — I I 1 I I I I I I I I I a;h^inr\jcootn^>0>l-JinvO

O<*or-coco<7> o co r- r- in in .?

J cc

I f\J ( I (M <

a 0000000000000 a ocoooooooooo s:ujwm^^coorNvOcoocM^

Cl OOOOOOOOOOOO

I

en

03 CO CO CO CO

I O O o o c

: o o o o c o

CD CO CO

I OOO : o o d o o c

) o o o

CDCOCOCOCOCOCOCOCOCO

rj OOOOOOOOOO ZOOOOOOOOOO o

UJ — I I I I I I I I I I

1 CM f\j f\J IN CM a o o o o l 2: • • • • HI M J- CO st »

Cl O m 1 5: • • UJ O CO ( a in o x • • • UJ O CO cl

1— r- co

I *-+

I

Q.0000000000 5:

i— O'-'fN^'i^ChfM-tfr-c*

rsJ OOOOO Z O O < -tf (M m o C

M OOO Z O o o o

COCOCOCOCOCOCOCOCOCO

rsl OOOOOOOOOO ZOOOOOOOOOOO UJ <- I t I I I I I I I I 0<COHiMi\jnnnnn

_i cc •••••

Cl o c o C in

2:UJ (M ,J CO ^tf <G ClOOOOOOOOOO £:••••••••-••

1— o —«rNj-3-i*-Of\j-d-r-cr-
a

ou

u

9)>I—)

-.-I in

ooo-, '-, '-<-, '-,

i oocooooo oooooooo

1 C! o c c o c c c oooooooo -M — I I I I I

£L OOOOOOOO z

NJ oooooooo zooooocooo li_l~ I I I I I I I I 0< f— m »o i*- *o -J f\) o

j o;

CL OOOOOOOO s

UJf\JfT,.J- sOCOOfM-J
COCOCOOOO^COCOCOCOOO

tSI ooooooooooo ZOOOOOO D DOOOO LU — I I I I I I I I I I I

CO CO CO CT> O^ O^ 0> CDCDCDCOCOdiaDaDCDCOCOCO CO M ooooooooooooooooocoo ZOOOOOOOO ooooooooooooo LlJ — I I I I I I I I I I I I I I I t t I I I o; i— -o^ooooo 'OPior-cno^uirHf-r-ir-^-Hij-i 0<cnco(M(MvOCT>a'0<-<tNjf\jdm^-u-iir\j)>or^ri q:

rg i I o* ( CO CT^ 0.00000000000 £••••>•••••• LUir>oir>0 to m ir» m in m o

i_ .-H.-trNj<\jm^- tr\sOr--eo 0.0000000 OOOOOOOOOOOOO £;•••••••••••• ujinomomoinomo momt

COC0c00^C>CT'C0COCOCOCO

rsJ ooooooooooo 2000000000000 LU — t I I I I I I I I I I

<-t r-l .-H CO (

CO CO CO 0"» O1 CT- 0> COCOCOCOCOCOCOCOCOCOCOCOCO

fsT ooooooooooooooooocoo zooooooooooooooooooooo LU ~ I I I I I I I I I I I I I I I I I I I I crt— ^oinooooO'iDf'ior-tna-ir*—ii^-r-<r^<-Hir> 0< m a) rv r^ jj^ i> o<-<r\jrsjcnm.jir\if\v0^or-ri .-i QN CO CO o •

a ooooooooooo £

U-Jirou-\Oir\ir\i^tr\ir>if\o

i— ^H^nr\jr\(f<-,j-iri\Dr-co 0.OOOOOOOOOOOOOOOOOCOO 2:^jinomomoifi omomoinomomoino f— <-(rH(\jrMmfn<j-^-Lnm%osor-r-cocoo^o,i O

a)OhOu

I

•00000000000000 •ooooococccoooo OOOOOOOOOOOOO 3

) O O O ^h f 0.0000000000 2:'jjrnirirncomcomco m .-<

LU Z) X Q l

1 I. CO CO CO CO CO CO CO CO CO CO CO CO NJ occooooooooooo zooooooooooooooo LU — I I I I I I I I I I I I I I 0<--<O0r-mr>jrvjiMmma-1 j- <tio

1 •* <r <r <f J- I f\J r a o o o o c 000000000

jt- r— f- f- r- r^ !•- r~ r~- r— ^ *o *o -^ vD < — ooooccoc cccoco o>ooooooococcooo — -- I I I I I I I I I I I I I I

a o o o o o o c 0000000

ISl OOOOOOOOOO ZOOOOOOOOOOO LU — I I I I I I I I I I cti— mrxjr-h-r-mjjco o r\j 0< CDi>o>OH(Njf\j(\j^m

cocococococococococococococo

J 00000000000000 :o ooooooooocoooo

cocococococococococococococo

I 00000000000000 :o 00000000000000 I — f I t I I I I I I I I I I I

a. 0000000000 a oooooooocooooo q. oooooooooooocc xujino^om^inmo^Oinoir

h- .-<.-«r\jf\icn<rmOvor-r-coco
COCOOOCOCOCOCOCOCOCO

rsl OCOOOOOOOO ZOOOOOOOOOOO

Q.OOOOOOOOOO

M OOOOOOOOCO zooooooooooo

1— [T CM yfi o ,-1 CO H m -i *o

<r o *D o o a

m * •t «* m m m m r* cm

a. o O o o CD o o o o

cocococoao-DcoaDaD CO

rsl OOOOOOOOOO ZOOOO O O O O O O O

LtJ — I I I I I f I I I I 0<r-r-xOiniriir»j'^-j-j- jq: » • < • f\Jf\JfMfMf\JfMf\Jf\jr\Jf\J 0.0000000000 £•••••••••• ^jcnmmcomaDcntrim ^

cococdcococococococo

i oooooooooo 'ooooooooooo 1 I I I I I 1 I M OOOOOOOOOO ZOOOOOOOOOOO LU -* I I I I I 1 I I I I 0<r-r-*omirtifN<f.d-st j- _i a • •••• r\jc\jc\jr\jr\ir\jrMr\jr\j rsj

a ocoooooooo £••••••>•• ujo-imcnaomcomcom.-i - O'-'CN-jr-oroj-r-O'

a oooooooocc s: • • •

t- o--iiM-jr~-(^r\j^rr--a- aoooooooooo Z . . •••-•••

to

sa

in—

i

i

too

i—

i

i—

i

<

u

PkoU

1— C<1 tr, r\j r\j h- en CO CM r-t r-t — o o o o •— o o o o o

> o o o o

— 1 1 1 1 <

> o o

1 o o o

1 1 1 I- O O en m Z o o o o

U tn * -* * or U m co r- a> D • • • • Ort<THPl X O CO en (BHH

CO CO CO CO NJ o o o o

2 O O O O O

UJ — I I I I cr t- o o o o

O < -d- -d- e\j cm

_j or • • • •

o_ o o o o

CO CO CO CO CO M O O O O O Z O O O O O O

•4- j- r- o- a

CL O O O O O

; — c o o o

i > o o o o

i/i -j j- j- •* i

H o r a c n

> O

1 O cI c o

1 ~

•o ° •o o ^

a <r o o o a o o o o r z • • UJ * O O O -

a. o o o o t s • • • • JJ -J O O O r

J O O o o

: o o o o o

o_ o o o O c\j X

uj -d- o o o •-< a o o o o r\j £UJ J" O O O <H

D. O O O O D_ O O O O O
M oooooocooo ZOOOOOOOOOOO uj " r I i I i I i i i i

Q. ooooo ooooo £:•••••••••>

i— O'-<r\i.3-f-or\j*3-r--0^ _lr_,,_,,-,,_(,-Hf\J<Nr\J<M

x d :: cr x 03 co co co co

rsl OOOOOOOOOO ZO cooooooooo UJ — I I I t I I I I I I

I tNJ < I fM

a oooooooooo

u

u

a

si

s£5

1

i*J o o o

2 O O O O

UJ — I I I ex. t- *c -3- r» O < iT> O -J _j tr • • •

co co o

i coo : o o o ^

COCOCOCOCOCOCOCOCOCO

rg oocooooooo zooooooooooo ll>-« I I I I I I I I I I ori— oinomo'-to-finm

0<r\JfNJ<nr"\m-3- <T <f J- -J ja • • •••• ••••

f\l f\J f\J f\J OJ f\J f\J f\J f\J <NI

GO X CO

I o o o

: o o o o

aoooooooooo s:luro en mco r^co m co m .-<

r-J O O O

Z O O O O

I I I I I I I I M O O O

Z. O O O O

rsl O O O

2 O O O O

UJ — I I I

0. OOOOOOOOOO
Scandium and Yttrium

RAJS AND COLVINl 1964)

.

LORENZ

SC AND Y-AC

LORENZ

TEMP RATIO TEMP RATIO

4.2 7.00-008 4.2 7.oo-0n

20.0 6.00-008 20.0 6.00-00

40.0 4.20-008 40.0 4.20-uO

60.0 3.30-008 60.0 3.30-UO

80-0 3.10-008 80.0 3.10-00

120.0 3.15-008 120.0 3.15-00

160.0 3.30-008 160.0 3.30-00

200.0 3.60-008 200.0 3.60-00

240.0 3.85-008 240.0 3.85-00

280.0 4.35-008 280.0 4.35-00

300.0 4.65-008 300.0 4.65-00

AMARIN, CHUPRIK.OV. AND SHALYTI 1969)

.

SC AND Y- TCSIPAR

LORENZ LORENZ

TEMP RATIO TEMP RATIO

5.0 4.20-008 5.0 4.20-00

10.0 4.70-008 10.0 4.70-00

17.0 5.00-008 17.0 5.00-00

20.0 4.90-008 20.0 4.90-00

30.0 4.50-008 30.0 4.50-00

40.0 4.10-008 40.0 4.10-00

50.0 3.95-008 50.0 3.95-00

60.0 3.90-008 60.0 3.90-00

70.0 3.80-008 70.0 3.80-00

80.0 3.77-008 80.0 3.77-00

90.0 3.75-008 90.0 3.75-00

100.0 3.72-008 100.0 3.72-00

110.0 3.70-008 110.0 3.70-00

120.0 3.68-008 120.0 3.68-00

130.0 3.67-008 130.0 3.67-00

140.0 3.66-008 140.0 3.66-00

150.0 3.65-008 150.0 3.65-00

TAMARIN, SHUPRIKOV, AND SHALYT ( 1969 ) . SC AND Y- TCS PERPENDICULAR)

LORENZ

TEMP RATIO

5.0 3.00-008

10.0 3.05-008

14.0 3.10-008

20.0 3.00-008

30.0 2.47-008

40.0 2.00-008

50.0 1.95-008

60.0 1.90-008

70.0 1.95-008

80.0 2.00-008

100.0 2.03-008

120.0 2.47-008

140.0 2.50-008

150.0 2.53-008

LORENZ

TEMP RATIO

5.0 3.00-00

10.0 3.05-uO

14.0 3.10-00

20.0 3.00-00

30.0 2.47-00

40.0 2.00-00

50.0 1.95-00

60.0 1.90-00

70.0 1.95-00

80.0 2.00-00

100.0 2.03-00

120.0 2.47-00

140.0 2.50-00

150.0 2.53-00

II- 17
CEC0<BCOC0<DCOCDCOCO

rsl OOOOCOCCOO ZOO DOOOOOOOO IU — I I I I I I I I I I

ooN

lOOOOOOOOO

»oo ooooooo

i cr

I CM r i ry i (M I 'OOOOOOOOO

V > coooocco oooooooo I I I I I 1 I I

i i/> <r * •* •*

•H

a

Q. OOOOOOOO 3:UJOiAOOOOinO

00

I

>NJ OOOOOCCOOO eoooo oooocoo

COCOCDCOCOtDCOCDCOCI} m oooooooooo ZOOOOOOOOOOO UJ — I I I I I I I I I I CL \— & o *D in >—i r— en in r- ce

_.. Q • a * • e o . • • . f\jf\iro<M(\ir\ir\ir\jr\jr\j

CL^OOOOCCCOO OOOOOOOOl Q.OOOOOOOO 2:. ....... UJOiTiOOOOLf>0
( r— f— r— r— i— f— r

-— r~— r— i— r— f~— i— ooidcococdcococococccoscocdqiicocdoccooocoocc

isj oocooooooooccooocoooococoooccooooocccooo ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O DOOOOOO I I I I I I I I 1 1

* f- yC O O O L **•*** CLOOOOOOOOOOOOOOOOi 'OOOOOOOOOOOOOOOOOOOO

1—

I

T—t <

B

d

G

1 f- CO O- O (

I

^l~-^^^•^^^^^^^^^(DcomcoaDalcDcDaD!tlIla:KlIlcD(B^I)a)<D^Dcoa!mcotDco

fsl oooooooooooooooocoooooocoooo o-o oooooooooo ZOOOOOOOOOOCOOOOOOOOOOOOOOOOOOCOOOOOOOOOOO I I I I I I I I I I

f- O \D \0 •£> l

CLOOOOOOOOOOOCCOOOOOOOOOCCOOOOOOOOOOOOOOOO 2: • • • • • • kJMCffOf\IJ>DiDOinO^OifiO^O^Oi'iOL
-ooooooooo ooo 'COOOOOOOOOOO ooooooooo ooo

-o oooooooooo •ooooooooooo OOOOO 3>DOOOO

• + + + + + + + + + + + -O-S-OI^-J-rsioO^O-JfM

ioo*ocncococop-i--r~r~

l-0'-«'-< 00000 — oooooooo _i>oooooooo

1 COOOOOOOOOOO COCOOOOGOOCO I I I I I I I I I I I I Ovta3^J^O-}03MJ3C>r 004-(?>^cO(\JvOHif\0-t

^^rtHiNNmn^ -j in m

OOCCOOOCCOO OOOOOOOOOOO

ii— fflcococor-r^-r- \0 :--oooccocc >>oooocooo ' ~ I I I I I I t I :(--3-f-rjir\i-i-<-HsO i/)Nmr-(^O(0-* o

I t/) I <n i

a oooooooooooo Q-00000000000 CL OOOOOOOO x ••• UJOino oooino

CO CO CC CO CC X (E CO CO CO CD CD M oooooooooooo 20 oooooooooooo UJ —• I I ( I I I I I I I I I or i— pj ci -j -jcooror-mjjr-in O<f-r\jmr—coo o^r\jf\it\jt\j J LL , . . . . HMCNMCMrgcnrnmrnmriCDCDCOCOCDCOCOCOCOCDCD

rsl OOOOOOOOOOO ZOOOOOOOOOOOO iU — I I I I I I 1 I I I I

CO CD CO CO CO CO CO CO

J OOOOOOOO :o 00000000 I — I I I I I I I I

a oooooooo- CL OOOOOOOOOOO a£••••>•• 00000000

ujomooooino

in

H

o

I

t- o o o o o —0000c I > o o o o o oooooooooooo^-''-'^-' •ooooooooocooooo ooooooooooooooo rsl o C O

z o o o o

S *~ r-> co -h r- m 51 1- Q:ua>^ ^ j) vO or u «o -o

iNI o c c z o o o o

LJ — I I I C£ I- <£> O O

o < o o o

1 or

1 r\j t

II— iD vO <D "O ^0 < — C O C C C w "> o o o o c

—'OOCCOOOCOCCOCOC >ooooooooc cooooo

or h- o o so -

I 1 1 1 1 1 1 1 1 1 1 1

1 <-i eo r— iTi -J (

a. o o o o c

I tT* CO O O 1

I O CO fNJ -J -J I

CO CO CO CO CO

isJ OOOOO Z O

CDCOCOCOCOCOOCOCOCOCOCOCOCOCO

I OOOOOOOOOOOOOOO :oooooooooooooooo I — I I I ( I I I I I I I I I I I

CO CO CO

fsJ OOO z o o o o

a 00000 £••••> UJ o o o o o
M ocoooooooc ZOOOOOOOOOOO UJ — I I I I I I I I I I cc t— r- f^- m o o o co r-- r- 0<^00c0sommr\i.-«o

J Q.

'"J oooooooooo 300 ooooooooo UJ — I I I I I I I I I I 0<~HO*l^ir\-3-rM^HOf^-^

<\l [\J r CM . i o <?•

X- x 'X ix x x x x x 3

>SI oooooooooo zooooooooooo UJ — I I 1 I I I I I I I trt— (\icooomr\icnr-oo

_j Q ......... *

i en ^ -a* in in *o

i O u"> o m o

i .* <r m m %o a»nomomoinomo

s:

X a: "D x- x a: x <x x CD

rNJ OOOOOOOOOO zooooooooooo

S) CO S) CO CO S) CO COO s "^ oooooooooo zooooooooooo

CO I 3 CO I I o

fsl oooooooooo zooooooooooo UJ -• I I I I I I I I I I orf-fsico ooinf\jc^p- oo 0<o-r-*£).3-mr\j'-< o o r-

_i a: • •••

-

cou

4)

COGOa

dH

I

rsl OOOCOOOCOO 2 DDOOOOOOOOO -

I I I t I I I I

r\J OOOOOOOOOO ZOOOOOOOOOOO UJ — I I I I t I I I I I or f_r\j,-ior-c\jocooom 0<cri(M^tj'CO^omin^-cn JC • • • » t

I oooooooooo :ooooooo dooo

i o co «£i in -r (

Nl oooooooooo ZOOOOOOOOOOO UJ ~ I I I I I I I I I I cr i— (^ a tno> oi/> a ohn

i\j i J c\j i

CO CO CO CO CO CO CO CO CO cc M OOOOOOOOOO ZOOOOOOOOOOO UJ «-" I I I I I 1 I I I I an- (Mf-.oM^f>cooom 0<t^f\jHO, co*ifiin-3-m jq: • • •

COCOCOCOCOCOCOCOCOCC

rsj OOOOOOOOOO ZOOOOOOOOOOO UJ — I I I I I I ( I I I OC t— co rvj co OCNJO"!—>r>j<MCO O<i\'-icrco^in^wr\jrt

. o m o in o m .
Molybdenum

BACKLUNDl 1967) »M0 LORENZ ELECTRICAL THERMAL

TEMP RATIO TEMP RESIST IVITY CONDUCTIVITY

100.0 1.74-008 100.0 1.05-006 1.66+000

150.0 2.24-008 150.0 2.30-006 1.46+000

200-0 2.36-008 200.0 3.35-006 1.41+000

250.0 2.53-008 250.0 4.55-006 1.39+000

300.0 2.54-008 300.0 5.60-006 1.36+000

KANNULUIKI 1933' • MO- Kill LORENZ

TEMP RATIO

273.1 2.63-008

194.6 2.38-008

90.1 1.94-008

NNULUIKI 1933 ) . MO- K< 2

1

LORENZ

TEMP RATIO

273.1 2.61-008

194.6 2.35-008

90.1 1.76-008

LORENZ

TEMP RATIO

0.0 2.63-OOE

-78.5 2.38-006 -183.0 1.94-00E

LORENZ

TEMP RATIO

0.0 2.61-008

-78.5 2.35-008

-183.0 1.76-008

11-22
-"•OOOOOOOO ooooooo oo

•ooo oooo oo

o o

o c

o o oooooo ooooo ooocoo ooooo •OOO DOO OOOOO

H d <-* rr\ <t <t

OOOOOOOOOOO -OOOOOOOOOOO •OOOOOOOOOOO • + ++ + + + + + + + + -Offlm^J-rsiOrgOcgcO'O

-r-r-r-r-r-r-r-r-r^i£»o •OOOOCOOOOCC OOOOOOOOOOO • I I I I I I I I I I I ircoiNM^oifMninrMM

irvir«jp"i>a-ir»f--cn-tf-*«o*£>

jt— oococor^f^r-r-r-r-*£)«o [^-OOOOOOOOOOO ^>ooooooooooo • — i i i i i i i i i i i : i— ooor^-om c o o o o*

- i/) o en r- o •-< co o •-< -! ir. m >—••••••••••• j oi 1 ct» o> h r-i h r\j m r- —I -J

OOOOOOOOOOO OOOOOOOOOOO ' 1 I I I I I I I I I I

aooooooooooi lOOOO ooooo

lOiflOinirifiinoo

a.£. ooooooooooo •••

y lAm omomaMniiiao

i^J OOOOOOOOOOO ZOOOOOOOOOOOO Ll_I —— I f I III I I I I I a;>-cor\jcor-in~H<\jmr^co o 0<mcr»i-«OOC0<0<0C0 iT> c

M OOOOOOOOOOO Z O OOOOOO ooooo I I I I I I

fsl OOOOOOOOOOO Z O

Q.OOOOOOOOOOO a. oooooo ooooo Q. OOOOOOOOOOO

s

o

uu

M

I

rsj OOOOCCO ZOOOOOO D D

LU —> I I I I- I I I 0<^nHO(D^CD

I ooooooo :oooooooo

j o:

1 rsj t f\J -* (

-'OOOOOOOOOO OOOO OOOOOOO OOOO

O in en r- ifi J \0 M rg (\ o )••••••••*•

-—OOOOOOOOOO OOOOOOOOOOO O 5 OOOOOOOOO

aooooooo a ooooooo

r-r-i^r- r- r- r- r- r- <o %o ccooocooocc OOOOOOOOOOO I I I I I I I I f I I u >

I- U)

r^r^p-r^-r-r-r-r^r— «J3\C coocooecccc ooooooooooo

Q_ 0000 ooooooo Q_ OOOOOOOOOOO s:LuminOLnoiniTiinmOO

I CD 1 I CO M ooooooo zo

LJ — I I 1 I I I I a: t- ocinoifi^N 0<£-3"mi-iOCC\OCO

CO CO CO CD QD 00 CO

fsl OOOOOOO z o ooooooo UJ — I I I I I I I

cococoao co co cq co (C co co

rsl OOOOOOOOOOO Z O O O O O OOOOOOO LU — I I I I I I I I I I I

oooococococoQDcoaocoec M OOOOOOOOOOO Z O

I CO

Q. OOOOOOO a. ooooooo a ooooooooooo 2: • •••• ummomooMnininoo

Q. OOOOOOOOOOO 2:UjiniAOinoinif^^OO
cou

ad

•t-l sou

(N(\jt\j(\;rM<MfNj(M<Mr\iojf\ifvji—it-Hr-i^Hi-H —i —i —i —

t

cooocoooooo coooocooooo OOOOOOOOOOO OOOOODOOOOO

i 0"> O"1 O^ s Q" 0" n) CD CD X o

(VJM(\C\t\J(NJt\Jf\JrHrtH oooooooooooo OOOOOOOOOOOO ++++++++++++ f\iir\-j*oo(\jr-fsjm,joir\

l-( 1-iI r-f f-4 t-li—tr-H^HOOO O'

u >

a)ctcoaDcocotDcocoaDcoaDcoc>r--h-r-r-h-h-r-i^ ccccccoooooocooccooooo cooooooooooooooooooooo — — I I I I a: i- (

UJ lO • _) bJ UJ (X

J I— COCO0OC0CDCO00COr*-r--f^-r^-

' — ccoooocoocco i>OCOOOOOOOOOC •— I 1 I I I 1 f I I I I I

cocoaococococoaor-r-r- oococcccoooc oooooooooooo ' I I I I I I I I I I I I

Q- OOOOOOOOOOOOOt oooooooo

JOOOOOOOOOOO OOOOOOOOOOO

rtHHHHrH^HHHMMfMcntvjfSirvj (M (M CM m

a oooooooooooo s.UJOOOOOOOOOOOO I— O-OfM^ J)tD O c\j -J •£ CD O

~*.-irH.-i.-ic\ir\jc\ic\icgr*"\ aooooocoooooo

CDCDCOdlCOCOCOajCDCOCOCOCDCXDCOCOaJOOCOCDCO

fvJ oooooooooooooooooooooo zooooooooooooooooooooooo I I I I I I I I I I I I I

isj oooooooooooo zo oooooooooooo I I I I I I I I m oooooooooooo zooooooooooooo UJ *- I I I I I I I I I I I I

I <t <t <t <t -d- -* I <t -a- <r <r * i

i <t <T <T <T <t i -* <t * -* -* <r tn

Q. OOOOOOOOOOO OOOOOOOOOOO XUJOOOOOOOOOOO OOOOOOOOOOO v— oO'-'fNjm^'injir-coo o-i (NitM4^vD^a}{> o

HrHHrHrHiHrHHi-lrH{^rjfM(^t\jrjf\J(\Jf\J(\jm

Q. oooooooooooo *£••••••••••• UJOOOOOOOOOOOO t— t> ON •* »OC0 Of\l -tf £> CO O .—i.-h.—i.—ir-tr\jf\jr\jf\if\jc*ia oooooooooooo z • • • • • • UJOOOOOOOOOOOO i-cr>o<M-d-NOco of\i >f >Dco o

11HHr-IHMf\|fSJ(\J(Njm
cooooooo 'OOOOOOOO

-<-«.-'300--''-< — •OOOOOOOO OOOOOOOO

- f~~ r

-— r— r*- p- vO >£ <o COOOCCOO OOOOOOOO ' I I I I I I I I

t— cococor--r--r— \0*o — OOOOOOOO >oooooooo

a oooooooo 0-00000000 £•••••••• LUOifiOOOOmO

COCOCOCOCOCOCOCO M OOOOOOOO ZOOOOOOOOO

CH h- <-• ( O < co r jq: •

D_ OOOOOOOO sUJOinooooino

a oooooooo £•••••••• UJOinOOOOiTiO

PI0)

I

GO

CtJ

I I I I I I

CO CO CO CD CO CO

fsj O O O O O o zooooooo UJ — I I I I I I 0<h^)0\000

jq: ••••••

•-OOOOOOOO _i>oooooooo < -- i i i i i i i i st-oooooooo KUChmr-urifNjfMcn^H X Q ( v -o r- r- \D i

oooocoooo ooooooooo I I I I I I I I I

0_ O O O O O O £:•••»••

h- co <\j r- rvj r- o> OOOOOOOO OOOOOOOO I I I I I t I I r-r-mr-o-j-.d-o

Q. OOOOOOOOO £

UJ'n OOOOOOOO

a. oooooooo £UJOinooooino

r- cocor-r-r-r-f-i^ri: N o o o f-J ooooooooo i. z o o o o a zo ooooooooo UJ — 1 I 1 (EI-HH^ cei— coincn--i-*mr-<-ir- O < <t <t m ^ O < H CO OH HMHHO _l or * • • Q m •£ sO o O

I I I I I I

CL ooooooooo a o o o o o o OOOOOOOO
I I I I I

< — o c o o o

u > o o o o o

-— «—* i 1 I 1

- i/) O rsj J- r» to

cococococoooeococorocoooooco

fsl ooooooooooooocoo ZOOOOOOOOO oooooooo UJ— I I I 1 I I I I I I I I I I I l OTi— cocoininminmo inMOifiininow 0<<ror-inmfNjrH^oooP^njr-inir>

jq: •••••••• • ••••••• fMWiHHHHHHHHH^ffiCOIDM

CLOOOOOOOOOOOOOO-*!

u - uj lq rsj rsi t

_J 1— & -O *C ^O sQ < •— o o o o o

VJ > o o o o o — — I I I I 1 or y- o o o o o

rsj ( UJ <S) , i |/1MJ>

a. o o o o o £••••• UJ o o o o oo_ o o o o o

s:UJ o o o o o

CO CO CO CO CO CD 00 CO CO CO CO o o o o o 1 M O O O O O

o o o o o o UJ z o o o o o o

U_

i— >-< o r~ fH en or i- -a- m m nj rj- < iTiM O1 COh O < O r-i O" vO vC —

COCOCOCOCOCOCOCOIQCOCO^C, Ov O>CO

i oooooooooooooooo :ooooooooooooooooo

O < -3- o r-~ i

I I I I I I I I 1 I I

a o o o o o

X

UJ o o o o o

a£•••• o o o o o

UJ o o o o o

CL OOOOOOOOOCOOOO-Jrn

— o o o o o

-J > O O D O O

< -* I I I I I s: i- o o o o o aUH -J MHO

— o o o o o

_1 > o o o o o

< TM I I I I I 2: i- o o in o o au vooi?^ cr X Q >£> I •o>o -o

5: t- o o o o o

UJ 3 • • • • • IQ-jinmin-o

< - c- o o o o

u > o o o o o — « I I I I I or t— o o o o ^ ^o«

UJ l/l ( , r- ^ ^h

< — o c o o c u > o o o o o

' I I I I I CZh- o o c & -

i— lQ co o O O rsj

I t— O O O in if\ :—< o o c o o

i > o o o o o

j I- vO J) in m in < — o o c c c w > o o o o o ~ — I I 1 I I Or I- O O CI O IT: h- <s) co o o m -r u — • • • • uiflmajHHHii— vom m in m — o c o c o 1 > o c o c o -< I I I I I

a. o o o o o

5TUJ o o o o o

i— o in o m co —i -t cm rsi rsi

a o o o o o

s

UJ o o o o o

CL O O O O O a o o o o c

SiUJ o o o o o

a o c o o o £••••'•

UJ o o o o o

i— o m o m co

.-i —i rsj cm ou

i co ( CO

INI o o o o o

z o o o o o o

UJ — I I I I I or i- &• •-> .* -4- o

O < -J- r- r- co c> _j or • • • • • CM CM CM (M rM

CO CO CO CO CO NJ o o o o o

z o o o o o o

LU *—

•

I I I I I or h- cm in m r- m

O < O O O O-h JK

CO COCOCOCO M O O O O O

Z O o o o o o

LU — I III I or t— -3- a >f r- h

O < CO O C O r-l _i or • • • • • cm c\j m en en

I I I I 1

a. o o o o c

s:

UJ o o o o o

a o c o o o £••••• UJ o o o o o

Q- O O O O O a o o o o o

s:UJ o o o o o

o_£•••• o o o o o

UJ o o o o o
COCDCECETOrofflCGCDCOfflCOffl^COffil x i x j\ i; x.' cr x x x X x : x t: x X x x x 2o§§§f§§gg?§§§8§§gg§§ggggg°§g°googooooogoo

I fsj <M <M r\j (\i r Q.00000000000000000000

i cm r\j (\j r\j r\j < oooooooooooooooooooo

iT\OiT\OiTiOOOOOOOOOOOOOOO

z o o o o OOOOOOOOOOOOOOOOOOOOt

n + LiL'''' 1 ' 111 I III I I I 1(1 I I I I I I I I llll

OtMJ O1 ^ O" O 0>i

Q. oooooooooooooooo OOOOOOOOOCOOOOOOOOOOOl

I

isl oooooooocccooooooooocoocooooooooooccoooo ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOSOOOOOOO UJ — I I I I I I I I I I I I I I I t I I I I I I I I I I 1 1 I 1 I I I I I I I I I I

j <N r\j f\j r\j rsi i CM I CM I i rsj c I f\j f\j (N f\J I CM C j cm rsj aoooooooooooooooooooooooooooooooooo< £uoMD^Of\jj^coOinoir\Oinoir>O^Oi

o o o o o

fnJ ooooooooooooooooooooooooooooooooooocoooo zooooooo ooooooooooooo oooooo ooooooooooooooo UJ — I I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I 1 I I I I I t I I I

aooooooooooooooooooooooooooooooooooocoooo £••••••••••*•••••••• •••••••••••• ijjNOr-xtoorM-jsoa)Oif\OinOinou-ioiriOiriOinoir>oooooooooooOOOO

»— t^^i^rH^rgr^imf<i^j^^vOvor^p--ro(Dc>CT*0'--<fMcr*-JiA>or~coc>OfM-d'^)m

,_i,_, 1_«,_, 1_t 1_i 1_i r-<,_i,-,r\J (\jf\jc\ir\j
ooooooooooooooooooooooooooooooooooooooooc 3.00000000000000000000000000000000000000 000

I CD O O O r

I t I I I I I I I I I I I I

J f\J f\l <N fNJ I txooooooooooooooooooooooooooooooooooooooooo

i vO r— oo o o < lOiTiOiAOOOOOOOOOOOOOOOO ODcoi>a>OHrvjrnj-iniOhQDij>oiN-d-^ff) O

MHHHHHHr-IHtHM(\J[\J(\|N(^l

CO CD ID COCOCOCDCOCOCOCOCOCOCOCOCOCO CD CO CO CD CD CD CO CDCOCDCOCDOOCOCO COCOCOCOCOCOCDCOCO

I OOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOO :o OOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I — I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ;i-Hf\j(\j(Ti(^(riMmmcvjco OOO 1-' ^aomrvj'-*>-if\irnir\r~-0>d-o*0<MC j<iriiriiriiri^u^ir\iriiri^^^cor\j^oc>c>o^c>c>o>t7, c7'C>c>0'--<'--trNj(

rsj i

I r\J ( I ry < C\J I i co r J f\l I

CLOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO s:ajvOr-cooocN-T'DcooinoinOinomoi

oo

CD 00 CO CD CO CO

rsl O O O

z o o o o ggSSSS5SSggS55555555 555oooooooooo

i \0 >o o ^~ 0.00000000000000000000000000000 lOOOOOOOOOOO

COOOtM^^OOOOU^Oi

CO ( o o <

I CO ( I CO < I CO c ) CO CO CO CO c CO < I COCO ( CO I I CO ( CO I ) CO ) CO ( CO ( ooooooooooooooooooooooooooooooo

D^^irljrljAjAj^ iii^Ui<fini^rvjco<)iri^or^coo ^Anmo&Ot-* p^^o^rsjoa ( vi^o* t ^^^^^w-^^"'^-;~ -J o<r a* ^cO^OmcOHr^ HOCT'OCOQDCCCOCOCOOCMJ'OOHHW^Cim^ <t m <£>•£>•£> r~

I CM C I t\J ( I (NJ (

I t\J (

Q.000000000000000000000000000000

Lu^r-cooooj-j-^cooifvoir^oi

ooooooooooo
at >J UJ 3

I Q

000000'H--''-<-< oooooooooo

+ + + + + + I t I I otDP-^ir-^oooo

J-cOcg.-HOOmo-O'-i

'OOCCCOOOCC •oooooooooo > I I I I I I I I I I Oco >0 JO 5> O- O 0"» iTi J-J-OO-OHMOiAO

rsl OOOOOOOOOO ZOOOOOOOOOOO tu — ( i r i i i i i i I orf-Oin-Jf-icoinm.jh-a'

i ......... - cneimcnrM<M(Mr\i(Mr\j a 00000 00000 s

i— o--<oj<j-r-0">rvj-Jf-0'-

>-i 1-<.-( 1-i.-[.-ir\jr\ir\ir\j

•OOOO'-'^'-*-'^-'-'^ •OOOOOOOOOOOO •OOOOOOOOOOOO

^l in h r(cnr\jr-0"*C0O(\jr\j tcn<M.-iOOiMC0inm^HOC0

I CD CD rii— r-io>0s0>O'O^>0v0i0'0ifi — OOOOOOOOOOOO >>OOOOOOCOOOOO

a oooooooooo e:uj in m co i*- o %o -jd o co ri— cocor-»cii"\mor-<fc\j

a oooooooooooo s: • UJOOOOOOOOOOOO

HrtHrHrHtNJI\f^(\JC^(n

inJ OOOOOOOOOO ZOOOOOOOOOOO UJ — 1 I I I I I t I I I q;i— (\jr-fNjcncnif\CT>cor\jrM 0< (\Jt\jf\jr\jcnmm.Jir\co

j or

COODCOCOtDCOCOCD coco M OOOOOOOOOO Z O

U-l •—• I I I I J I I I I tti-Cin^-mcomrn.jf-O'- 0<--, ococha!7>aaa

ir\jrsjr\j<\j<\jr\jr\ir\jr\i

COOOCOCOCOCOCOaDCOCOCOCO

iNI OOOOOOOOOOOO ZOOOOOOOOOOOOO iLl — I I I I I I I I I I I I cr — r-a>ocno'-H'-'0^'0<\ir---< 0<-d^^lcoc^o<\Jc*^ o-. ^ ^ m >o ............

0. oooooooooo £•••••••••• ujc^mmcoeicomood—t

I— OHN 4-M^N.J M?- OOOOOOOOOOOO

rvl O C O

Z O O O O

UJ — I I I

CO CO CD CO

ISI O O O O

z o o o o o

CO CO CO CO CO M O O O O O Z O O O O O c

UJ — I I 1 I I

CO CO CD CO CD CO C00DC0COCD M OOOOOOOCCOO ZOOOOOOCOOOCO

OOOOOOOOOO 'OOOOOOOOOO OOOOCO D D O O

<SJ f\J r\J tM r MM J J-. a o o o o a o o o o o aooooooooooo

_ii— comr-r-r-r-r-r-r-.£> <— ccocoooooo ^>oooooooooo — — I I I I I I I I 1 I orf-oOi-ir-i^C'-'OOj

t-i/jrvj-JOO-^-JO^OJO

uj ul O 0*> —i--i.-i.-ir\jciir\i-i

Q. OOOOOOOOOO sLJ-JOO^OfMOOOOO

CO CO CO ~ CO 00 CD CO _ CO CO CO CO CO

is) o o o or M O O O O Oi ISI o o o o o

z o o o o Z O O O o o z o o o o o o

UJ •- | II

or i- r- <~> o < CC 1- o o o o < a: i- o o o o o

O < < t-t *C X o < r- -j- -d- <r X O < u-i m m tn o

_j or • • • u . j !••• . U

rvJ OOOOOOOOOOO ZOOOOOOOOOOOO LU — I I I I I I I I I I I o:f-o~'cno-j-'-«(N'-, r- oo >o 0<-d-m-?or-ir\iriir>r^O'-<ixl OOOOOOOOOO ZOOOOOOOOOOO

a o o o o a o o o o o a. ooooooooooo a oooooooooo £•••••••••• uj-d-oo«or\jooooo
<sj O O O

z o o o o

LU — I I I Of i— <N o in O < CO -J <N jd: • • • m m m

03 CO co

ISJ o c o

Z O O O O

CO CO CO

fsl O O O

Z O O O D

*J o o o

z o o o o

LU -H I I I iri-vomo

fsl O O O

z o o o o

rsj O O O

z o o o o

a o o o

lu in o o

t- (M O O

r-i (\l CI moo <N O O

r-H f\l t^

CO CO CO M o o o

z o o o o

CO CO CO M o o o

z o o o o

UJ — I ) I or i— o m o

O < rH *D <f

i or

* m

z o

o

o oo

O

JJ .-. o <

a

CO

O*

I o o o

: o o o o

i - i 1 i

LU m o o

y- <m o o i-< <\j m

a o o o

s: • • • uj m o o

v- <n o o

a o o o

2 • • • UJ in o O

i- <N O O

a. o o o

s: • . • uj in o o

I- f\t o o

CL O O O

2; • • •

uj in o O

I- IN O

i-i rvi m

j in o O

- OJ O O

H (\J n

O

CO

co

CO

r—

(

.9

+-> en

o

CO

1— m fo rg f\l (M — o o o o o

f > o o o o o

: — i i i i i

coaococococococococoGOcocococococo

rsj oooooooooooocoooo zoooooooooooooooooo UJ — I I I I I 1 i I I I I I I I 1 I I orf-ooooooooooomooooo 0<omi>-j'C>covor-invOinco<rr\jp^h--irsl OOOOOOO ZOOOOOOOO

or n m 3- « n n in m n m r\j N en m in in in

a. CNJ - <f »o o* O I*- m 00 O *o (^ - <j- m in co

o < in i\j f-»

a o o o

< — c o o o o

u > o o o o o '—' I I I I 1 or i— in o cn m in

I— i/> p- CO CO O IN u— • • • • • uj ui J- -3- -* m m

lu en

0- o o o o t £ • • • •

LU * O O O r

oocococococooococococococococococo

rsl OOOOOOOOOOOOOOOOO ZOOOOOOOOOOOOOOOOOO lu — i i ) i i i i i i r i i i i i i i or >- ooooooooooomooooo 0<orrio^j'a'CO\or-in*£imco^-<Ni^r-<-

i or

CO CD CO Q) CO CO CO

isj OOOOOOO ZO

UJ •— I I I J I I I or k- ooooooo

i IN ( r\j j- i i in i

a. o o o o r z • • • • LU -J O O O ' J vOO O f- I a o o o
ID<a

o

T3

»sl ooooooooooooooooccoooooooooooooooooooooo ZOOOOOOOOOOOO 3 DO OOOOOOOOOOOOOO OOOOOOOOOOOO UJ — I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I CC h- -J m-O 0-JO«l> r~i-3-(M(> or*OOCT^NOc^O%OOJOs^j^f-H003(rrgNOtnoa'0'0-*'-'OC> 0<r-coc7>~-r\j.nr-co0^cnm •d-tnmr\jo0^oof^ir»-Jrg^Oa'NO-3-rNJ^iJ>oor- ir» .J .* eg ~* o co ii^iO^^^or^r^r «C^O*00'00<0<D. -*-3--3--J-3--3-J--*- a oooooooooooooo oooooooooooooo oooooooooooo £••••••• . . . • U*OMDff'ON'*>DCDO^O iflO iA O if O in O

isJ oooooooooooooooooooooooooooooooooooooooo ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I I I I I I I I I I I I I I I I I

i iO i0 *o >o "O r* ^ i -i— r~h-\0-£ivOvO iO'OiO'fli ' -4" -J -J J" <

aooooooooooooooocooooooooooooooooooooocoo s:UJ^MDO-OiN-J^HOiriO i

CO

«—

I

a M OOO z o o o o

O < r\J C> rrsi OOO Z D D O O

UJ — I I I

a o o Q. O O O a o a. o o o

z 000

or 1-< O O -d- ,J -t ~H

CO CO CO

J OOO : O o

CO CO CO

I OOO : o o o o

O < c*i a* I sQ. O O O Q. O O O
OCDSC0C0(CXCDUCDa}<Sll0O(D(D(DC0CC(Da)C0<COC0(DC0CDa)C0Sa)CDC0C003C0C0C0a]CD

INI ooooooooooooooooooooooooooooooooooooooooo ZOOO 300000000000000000000000000000000000000 UJ — I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I t I o;^-j^looc^>Ol^'Dlnc^a'>0(Tl>j''-•Jln4'(\lo^(^lO^J'^t^^Oln>oo4HC^co(^0'Cc^t^JH 0<iT>-j^coaiHj'iOiDOOMfnr'im(\jHOO, cDvOir''*rMHOceiO'*fNH(ji(DOiri-*-J ,N H Ot>

j a

i *o *o *o »o *o r~- i r- r- i r^r-r— "0*DvO'0>o ,o*o>oii .•*^^*-t4*-j*i

Q.00000000000000000000000000000000000000000 £*•••• • • • tuiror-a)^o(M-J vocDOinoinoinoii^omoioo^omoo ooooooooooooo t_ ^ r^^rH^-tfNjf\irnfn^-j-ifAu-isO'£!(~-^ooeoO^O^O'--t<N(rlJ'i^*Of^COO, 0{N|j-\OCO

,_i^lr^^, 1_i^, 1_( f_(r-,^-tr\jr\](M(Ni(M

oDcocoaDiiiajmcoaDcoajoDwcoaDcocoaDmcfflCDcoQDmcoojajcocomajmajiDajmccmiiia) M oooooooooooooooooooooooooooo ooooooooooooo zoooooooooooooooooooooooooooooooooooooooooo I. I I I I I 111 I I I I I I I I I I

i vO O >0 ^ "O I >fliOiO>0 ,i)»OvD'Dt '^^r-d-j--*-*-*'*'

a oooooooooooooooooooooooooooo ooooooooooooo

\ •£> r— co o o (

(-» CO

>>o m

I

T3a

CO<B

1—1

PI

• iH

+-1 CO

co co co co cococococococococococomcocococococococoa)cocoa)roQ3cocoa)cococoa) co co co

i ooooooooooooooooooooooooooooocoooooooooo :ooooooooooooooooooooooooooodooooooooooooo I I I I I I I I I I I I I I I I

i<f -5-J-J<I<f * <f i aoooooooooooooooooooooooooc o o o o o « ooooo ooo

I vO P- CO O O (N .^vot-r— cocooo O' lOOOOOOOOOOOOOOO

M OOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOO ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO Ijj — I I t I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I tti— l^c^o^^N^c^co>J^oc>^l^Jl^l^c^rH^^ol t^^«r^tn^^^oJl^^JC^^-^o^O'i)•Jcn 0<^^c>rgJ^Ol^r^^^l(^^^n^^lr^IJ^^^n^(^JOcoNlO^^^Jr^co^^rfvJOC>^'Ol^^*rl^^oc^

•£) sD I • r- co < CO CO < t~~ r— \0 >© vO vO • , .* -J J- -d- . <* *

O.OCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

i O iT\ O iTi O ii"\ < <j- <t tr\ m «£> -O r
M oocoooooooooooooooooo cooocococooooooooooo ZOOOOOOOOOOOOOOOOOOO OOO OOOOOOOOOOO 3DOOOOOOO

t I I I I I I I I I I

'(I)(OCOCD(CaD(DCOCOII)(Cr *£ \C -O <G -0 «C l <r -r -j -* c 0.000000000000000000 ooc o o o o o c 'OOOOOOOOOOOO

CDC3KCCCPC0CPCPCCCCCCtX1 <X)C0C0CncnC[> C0C0CCCOCCCCC0CCQ0 C03JCD(DJ)DC0CCCC(UIX(DI

isj ooooooooooooooooooooo oooooooooooooooooooo zoooooooooooooooo oooooo UJ — I I I I I I I I I I J I I i I I I I I I I I I I I I I I I I I I I 1 I t I I I t I Q;i-a)(fi(D4iDOifco^-jotM'7iM'Oa, HiMin^ 1oo) o -J r- r\j f- omc^.j-.O'-'r-m.T.a-r-rNoo' C< vD co o ^ i^ co r-<c"\if\sOf-r— ^ in o —I oco ^) ^ i\ o cr> r^ m .j inj or^-mci-^ocor-jDmrncM'—ic>

•£ O f I CO I i co r >C >£ vO >0 £ >0 i

0.000000000000000000 ooo oooooo oooooooooo oooo 21Lumvor-cooo'NJ.j.ocoomomomoin o m o in o i

<D

<D +>co

o

a

nJ

CD

CDCD

r-Hs

•t-t nt CO

M oooooooooooooooooooocooooocoooocooooooo ZOOOOOOOOOOOOOOOOOO^OOOOOOOOOOOOOOOOOOOOO LU — I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0<r-roo^minsONOi^i^i^'0^^r^<^^oc>a3^iA^mr\joo^r^vi5^fn(%j^-i^-.oc>cor-»o

i<0<0' \0 •& \Q --C: -O £ -C- £} • m i •*•**•* •* -T -J J" < aoooooooc oooooooooooooooo ooooooooooooooo

jj I*- CO O O f socooinomoinomomomoLnomooooooooooooooo ^i^i>jrjtrim^^inir\x0^or^r^cococ>c>o^^tn^in'Or^coc7'orsJ<f^oco HHMrSHHHHHMfSJMPjNtM

m oooooooooooooooooooocoooooooooooooooooo zoooooooooooooooooooooooooooooooooooooooo I I I I I I r- a a aDr-mmrMoaor-^\0%or-

•O in -d- c ifMi-H OOcO^Omj-mtMO

I I I I I

i -O iO >0 >0 >C vO >o ' vO >0 vO i£) iD -O if) >0 I -* ^ -j- -j -* <r (

a. o o o < s . • • lu r- co on c ooooooooooooooooooooooooooooooooooo

oj-4- voa)Oinoii>o^Oino
cocoiEaDaaaDcoaaajaDxcococoajooeDcocococococDcocooocDcDaDajcocDcococotDcocoooco

>NI oooooooooooooooooooooooooooooooooooooooo ZOOOOOOOOOOOOOOOOOOOOOOOO DOOOOOOOOOOOOOOOO - I t >\0-4" ^oj^\Of^r^cococbt>oror-f\ic^*b«b'ijh-cSrvj{>coi(b

ir\jrvi^i-HOO^cor-«Oii^'*(ncnf-iCTvco'Om^-mrsj>-H'-t0^cor-sO

•t <f -J -J ITM i -C -J) -O \0 %0 <£ vO >i) i ^^I^^-t^44(

Q.0000000000000000000000000000000000000000

i %o »o r~- r*- co i

COCOCOCOCOCOCOCOCO OD (D CD ID CO CO COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCO

NI oooooooooooooooooooooooooooooooooooooooo Z O ooooooooooooooo ooo cooooooooooooooooooooo ^J — I I I I I I I I I t I I I I I I I I I I I I I I 1 I I I I I I I I ( I I I I I I Q^k-*Dco<f0^^orvJCr'^(^CNj(>j>o^^c>c\j^sOl^l^cooococ>Oc^l^r^c>^NO^l^^rge>coa3cD 0< -3-ir*r-coomm*oco o-nryr\ic\jrg.^^oc>a)i^voa^<rm<^^c>co*Oiri<r<ncsi^.^o>cor-vo

_) or •t^-J^fl i\OvO*0*Oi£\OxO^Ci i tn i -* <f -* <r -3- •* <ja. oooooo oo ooooooo ooooooooooooooooooooooooo

i«or-coo>Of\jj->o< 3inOiTiOOOOOOOOOOOOOOO icooo o-—<c\im-d-in\or-co o OfM -J -jd co

^-1 ^-, r_1 ^H^ l_H ^Hl_,^HrHrVj (NJfNJrVj fN1

4)

<a

*-• COo m

I

c

tn

tfl <D I—

I

a

+->

CO 03 CO COCOCOCOCOCOCOCOCOCO COCOCOCOCOaOCOOQ COCOCOCOCOCOCOCOCO COCOC0C0C0C0C0C0COCO

ISJ ooo ocoooooooooooooooooooooooooocoooooooo ZOOOOOOOOO^OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO uj -' I I I I I I I i I i I I I I I I I i i I I i I I I I I I I I I t I I I I I I I I Oil— m -3- o LAO(^t>%oo ,-, o^coOir>ooco \Ocnc>»Of\jO'»*ocn'-<cQr--cO'-*vO<\i ooo--i<C<nHH 0<%o^coor^^%ocoo^fNJ^c^c^i>Jf^OC>co«Oiri^(\irHOOO^rg^c>a:r-iAiri^-f\jr-ioc>

J en m l vO >0 vO J) ' - r- r- r~-r-r~i— jd o •£> \c to >o >c ^ i m l t un -3- • -J -3" -3" •*-*-*( 0.0000000000000000000000000000000000000000 z: • • • ••••••••••••••••••••••••••••••••••••• uj^or-cochorsj-jxocoou^omoinoin oinom omomooooooooooooooo t— t^i^^iMrtf\jrocAmj^inir\>ONor^r-ci)coc>oo^^rnj-ino^-coc>orsisj\Oco HrtrHi-li-IHHHHH(\J(\Jf\|(\JIN

CO X CO cocococococococococococococococococo cococococococococococococococococococo m oooooooooooooooooooooooooooooooooooooooo zooooooooooooooooooooooooooooooooooooooooo uj - i i i i i i i i i i i i i i i i i i i i i i i r i i I i i i i i i i i i i i i i Q:hm^OiriOM3'>OCH^CD(7'inO>OCOvOP10>0'Nl>iOmHCDMDHvONOO'0 H 'DdHH

0<^or^coorjsjsOcoo--"<>jrnrnmrM>-HOC>co»c^^rvji^oc^^^ry^o>co^-intr\j-(\ii-too>

, vD vO vJD vO • h-t— i^h-f-r-r-r"-r-%C\OJ3^^>£>j3vOi i -* -* -3" -tf <1- -tf •**-*<

a ooo ooooooooooooooooooooooooooo ooooocoooo £•••••••• • uj^r-cooofMj-^)coOtr.omomom Oinoi
I I I I I

X O -*-**•* i

C£ «J in O < UJ D • • X Q r\J iM (

— o o o

-J > o o o

< — I I I 2: t~ (M O P- auotM jj UJD • • • X Q ^ (M cm

I- 2

_i - in m in m z _l 1— m m m m m Z _j t— in in in m m

< — < — C O O O < — c u > < U > C O O O O < u > c — — 1 1 1 11 "—- — 1 1 1 ft 1 — — 1 1 1 1 I cr h- m m en r- 10 q; 1- in co in to CT 1— i-> «© O f- -J 1- t/) O i-l en in t— tO -J *o O -h -j- 1— 1/) r— —t en f- O

UJ 1/) J, H H ^ H z Uj ui ,-« .-1 ,-< e\j rg z tU Ul .-1 _t CM CM CM

< •_. c r O O C r. u > a O C O c

ir ifi E f- rr.

,K

~, U] 33 O rH m *

UJ Ifl H <-<• rsj CM CM (M

< — O O C

\J > O O c

1 1 ir O tO IT 10 CM 1- w

UJ 1/) f\l CM CNJ

0_ O O O O O a 00000 £:••• >jj %o o in in so

CL OOOOO a c o

Cj

rsj n O

Z

cc < CM CM

-1 or

CO 00 CO X CD

I OOOOO : o o o o

CO CD CO CO CO

I OOOOO : o o o o o

CO CO CO CO 00 CO M OOOOOO ZOOOOOOO

O < co 1-1 r-~ \ O <£ O O co

<D

(0

+-> in

o

in

ro

I

I—

I

.2

co

*z O

-J > 3 D O

< — 1 1 1 X t- CO

0£ U >t UJ z> X .-1 .-1 •-* r-c rsj

•—OOOOO 1 —' O c O

-J > O :> -I >oooooo < — 1 1 1 1 1 i/3 < — 1 1 1 1 1 1 E; •— c- ^O O en St-mr-oooin CtUOlN^MM crum^ocoo-jrr O ,-. -1 n-C ^ CM H XQ^r^r-Jininin

< — c c, c c o

u > o o o o o

— — I I I I I <— coocooooo u>ocooooooo — — I I I I I I I I I — c _ < — c

> c < l_/ > — 1 1 1 1 1 — — 1 1 1 1 1 t— O en r\j j- en to or 1- *o j- r- r- 00

to *o CM J) in h- to m co cm m cm Q

to m no *© no r- Z uj to -o *o r— r- 00

<—oococo o>ooocoo

a 00000 z

jj o f- r^ r- -r

t- O <t V m o Q.OOOOOOOOC a o o o o CL O O O O O

i— co j- CT- m o

a o o

CO CO GO CO CO

J OOOOO : o o o o o

CD (3D CD CO CD CO CO COCO

I 000000000 :oooooooooo

CO CO CO CO CO N OOOOO Z O O O O O O

LU — I I II I or i- I s- o so o m

O < o m oen rvO t m t

M OOOOOO ZOOOOOOO UJ — I I I I I I

Q. OOOOO £

uj r- r- r- j- aooooooooo a o o o o o a. o o o o o

z

uj 00 r- co m m
+->

o CO

I

1—

t

CO N O O O O O O ZOOOOOOO

1— rg rvj r\j (N — OOOO J > O O o O

IQhhimi X Q -< -1 ^h (\l a o o o o o o

_j 1— in m m in < — o c o c w > o o o o

Ljj <S) >O^M

a o o o o a o o o o

I I I I I

1SI OOOO Z Oisi OOOO z o o o o o

LU — I I I I CC I— in m O O O < iH t\j j- so j cr • « • »

0. O O O O O O a o o o a o o o o
>-* >-> * o o o

' o o o o o o

O O O 3 O O

1 oooooooo oooooooo oooooooo < + + + + + + + + oooomooo «c^in«oeooor-

- cy (M r\j c\j *-* — o o o o o

I > o o o o o

:« + + + + +

I ftj I I J- J- < I CM r UJD • t • X O -• ^ -< r »- z

— — 1 I I

coeocor-r-r-r^r- ccooccoo ooooocoo I I I I I I I I r-(\if\jr^ocoo

ll/) l> O1 C H H (Ml o

II— CO CO CO CO CO

: — c o o o c

> > o o o o o

I— i/) O —» fi ^ o u — • • • • •

nloU

Q. O O O O O O

z

uj •-< <N cn -3- in «o

CO CO CO (D CO CO N O O O O O O

Z O OOOO OO UJ — I I I I I I

CL OOOOCOOO

COCOCOCOCOCOCOCO N OOOOOOOO ZO OOOOOOOO

i tr

J CO CO j- -* O

O O O O O O O O O O

oiTi oin o

.-h ^h c\j rsj m

O < vO CO C* O^ O

I f\J t r\i i

Q.£••••• O O O O O O

UJ H M m 4 ^ <fl a ooooocoo s • LUOinOOOOiTNO

a o o o o o

s

UJ o o o o o

I

(M ooocooococ ZOOOOOO 30000 UJ — I I I I I I I I I I 0<m<M^-''-HOO'-«000

) q:0.0000000000

W

o

uo

COCOCOCOCOCOCOCOCOCO

isl oooooooooo zooooooooooo UJ - I I I I I I I I I I

i rn ci d ci fi

0.0000000000

ICICOClCDCICCflH M^r-ocN-fl-r-o
OOEOCOtECOCOaDCOCOCO'EJCO M ooooooocoocc zoooooooooooo o

UJ — i I I I J I I I I I I I

Q-000030000000

cocococococococococococo M oooooocooooo ZOOOOOOOCOOOOO

Q-000000000000

o

ooCO

I

*- >-* o o o

— o o o o

-J > o o o o

_i i— co r- r- r- < — o c c o u > o o o o

— — I I I I

fvj occooooocc 200000000000 UJ —> I I I I t I I I I I

a 0000000000 £:>••••••••• L-imCOOOOOOOO

COCOCOCQCOCOCOCOaDCDCO

inJ OOOOOOOOOOO ZOOOOOOOOOO DD

UJ — I t I I ( I I ( I I I cth-u-tfnr^-Om—iou^O'-'in 0<fiOindM(NtM[MinNaj

OOCDCOfflCDQDmCOCOCO

rsl OOOOOOOOOO ZOOOOOOOOOOO UJ >

I I I I I I I I

J a:

t\| 1 0.00000000000

1 O •£> iTi Is- OO O<ocor-*omir\inmir\ir\ jq: • • • • • <\ir\jr\jr\jf\j(\jr\jr\jr\jCN aoooooooooo £••••••••••

U '10 c vO L CO

a o o o o

X • * • • UJ o o o o

CD CD CO CO

IM OOOO Z O O O O O

UJ — I I I I en t- r» o O cm O < <T f\i m m

rsl OOOOOOOOOO ZOOOOOOOOOOO LJ-I — 1 1 I I 1 I I I 1 I

_i a:

COCOCOCOCOCDCDCDCOCDCO

NJ OOOOOOOOOOO ZOOOOOOOOOOOO UJ -- I I I I I t I I I I I

j. x, ai ai '.11 (C d co ff) vD

is) OOOOOOOOOO ZOOOOOOOOOOO LU~ I I I I I I I I I I

(VI (

a o o o a 0000000000 a. 00000000000 a 0000000000

1 <t ufl •£> t~~ O -H (
r-r^-r^r-r^-coeococD

|SJ ooooooooo zoooooooooo i i t i i i i i i

i oooooooooo :ooooooooooo

a o <f i X • • o e-i r- -j- o

«. i^-r--f*-h-f^-cooocooo ^ ooooooooo ZOOOOOOOOOO <si oooooooooo zooooooooooo

f- -" r-t f\J CM rH .

a o -r < s: • • UJ-t O I

<T O vO M tNj vO

ei r- rsi -j j- o

COo

O

CO

I

isi o o o

Z O Q-O O

IS) OOOOOOOOOO ZOOOOOOO OOOO LU — I I I t I I I I I I CCl-OOOOOO OOOO O<r-r\jmor-j3or-mco

jte •••• * m *o m if* en m *o m <t ir\

i o -* r- o o JWN N * .

isj oooooooo ZOOOOOOOO D

j- >o t> .-< r- r- i £••••••

fsl OOOOOOOOO ZOOOOOOOOOO I I I I I I I I I CI h- in r- o o o O o o o

O a o r- ii O C«l n

rr CM OJ en m m m m m ^n

n NO r- c\j ,_, >T %o m tn o

i

i <* O O O r

NJ O O O

Z O

CD CD CO CD CO CO CO CO CO CO NJ OOOOOOOOOO ZOOOOOOO OOOO LU — I I I I I I I I t I QT I— OOOOOO OOOO o< t— rsj tn o f— «o or^-mco

_jct •••••••••• m •£ m in m ir\ om <t m

COCOCDMDCDCOCD N OOOOOOOO zooooooooo LLJ —• I I I | 1 I I I M ooooooooo zoooooooooo I I I I I I

j(\jmf<"»ir\ininiri*o

t (M o -tf c- o o O-Ocnomor-^o

s: • 1UM rg* OO Of
r~^l^r-r^r^^^r^r^r^i^r^r^l^f^i^l^r^i^r^cocoaDcoaDaDcococoaDaoaD(DaDcocoQ3aDco

iNl ooooooooooooooocoooooooooooooooooooooooo Z000000000000000000 3.3000000000000000000000 LJ " I I I i I I I I I I I I I I I I I I I I I I I I I I t I I I I I I t I I I I I I 0<f^r-^-coa3a3coa3mi^NO^D^-3-t^fn(Nir-i^HOOa3-j^-«h-j-i>j-o>OcnocD >o-*rgovr*infn

,•»"*«*•* aooooooo >oooooooooooooooooooooooooooooooo

ID C O M >J >C t

r^r~-r~- h- r- r- f— f^~ r— r— r

-— r— r^~ r— r*~f^r^r^p^r^r~-oocorococococococococococDcocococoaoco M oooooooooooooooooooooooooooooooooooooooo 200000000000000000000000000000000000000000 LJ •-* I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0<r^r^h-oooocoa3Comr~-v0^iri4-n-imt\j^-i-HOOco^'^Hr-^-a>j'0*Ocnooo^o-s-rsiC^r^fcricn

CO I*- I iin-t-j0.OOOOOOOOOOOOOOOOOOOO1 ooooooooooooooooooo

i aON 4 >OCDOi )u-\oir»o^ooooooooooo oooo f^-coeoc>0^0'-«fMrfi>d- iri\Ofk-eoo* o <\i -l no co r-(Hi-lHrtr-lr-liHHr-l(\JN(\Jf\JIM

cou

COo

o

I

X

y

r-r-r-r-r-cococoeo

^i oooooocoo oooooooooo 3

UJ — I I I I I I I , I ^ oooooooooo zoooooooooco UJ*-- I I I I t I I I I I ca*— omooomoooo 0<Q>-«00'-<f--ir\NDvr^-

cor-i^r-r^-r-r-r-r-r— N oooooooooo 200000000000 UJ--III I 1111,1 cct-omooou-ioooo 0< Oho- o ft t*» in o & <t

Q. O -* I s: • • lu -J O (

-* O O rvj M !0 m 1^- (\J ^ 4 ^

a *o en o in . X • • • •

UJ (M * * O I
r— r^— r— r— r^- r^- r— ^*- r

-— r~— i— r

1— r— ^— r~— r— i— odcdco3}iccdcd<i]g3ii}(ococococo<ox3)(Cq}<d<d

NJ ooooooooooooooocoooooooooooooooooooo ooo ZOOO oooooooooooooooooooooooooooooooooo ooo tu — I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I QiKn<DC\J>flfM<00D0, (>CDlflHr«-mffi(n'-ii^Ha3fw (7l tV^(T\OClOf*J^'flfs-Oifl(NC0C>'-"4' 0<OOrH^f\jr\irvjrgr\irg(Nrg-^rHOOOr-'*Ol*-H}-f\iCT-r*-ma*NDmoco*Oii^fnfNjo,'r-iO-3- r-^J3<Oi©ir>uitnt «n •*.*.* .* Q.0000000000000000000000000 ooooooooooo ooo

h-r-r-r^h-Nrs-r-h-h-i^i^h-r-r^r~-t,~iDcocococococoiicDcDiD<DcocDcDiDoocococDcotD

«si ooooooooooooooooooooooooooooooooooooooo 200000000000000 000000000000 ooooooooooo 000 I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I t I I t I

1 O- ffi (Ji CO CO CD I «0 sO ^O \G 1 1 »n .» * «* -tf

a. 000000000000000000000000000000000000 00

5:iuNco^oN^\DiDOinoirOiroinOino omoooooooooooo 000

HrtHHHHHHHHf\JWI\J (Mf\)

aou

CDo

©X

u

r~ r- r-i^h-r-i,-i*-Nr*f^f*-r-r^^f^'ocococococococococococococococococo cdcocdcocdco

ISI OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ZOOOOOOOOOOOOOOOOOOOOOOOOOOO DOOOOOOOOOOOOO llJ -- I t I 1 I I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Q;K-i^i^ma^r^v0^^cD^cooo^mcocncn^rsi^(>jrgrir^mc>rsjom^o>rH^(\ioc>wa3^'^ 0<<tininina^ir\irii^^^(^rg^^ooco^O^Of^oi^^rsjr^^^coa^rir^OCT'COin-J-r«j r-tO

1 f> Q> O^ CO CO ( h- vO ^ >o 1 1 •* * -a- J- * <r -a- 0.0000000 lOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

r-i>.f*.fw.r*r.p*r-r~r-f,-r-h-r~r^r^cocococococococococococococococococo cococococo co

rsl OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I I I I I I I I I I I I I I I I I I I I I I I I III III

I s &• O ff) (

Q. 00000000000000000000000000< X • ••••••

Ujr-cooow^^ocooirvOLnoirioinOt

* 4- * *a- >*•*-* *

0000000000000
fficuimaj'Dccstoajia;'

I oooooooooooo :ooooooooooooo J — I I I I t I I I I j i r

aoooooooooooo

S

•i-H

i—

i

i—

i

nj

cococoajaiaDcoaDcococDco

I oooooooooooo rooooooooooooo

CL oooooooooooo

CL O O O

(---•-HOOOOOOO •— COOOOCOOO _J>00 DOOOOOO

SIt-OCOOOOOOOO KUMiM-I^OinoOO

UJD •• • IQ,_._ia>-J (\JMHHH

I- z

o

— COOOOOOOOOO O _l>OOO0OO0OOOOO < — t I I I I I I I I I I I Si-^on>oh^ ^ m n -J 4 i^ aiumt^cNj'-H-HOOOOOOO

I r- i r- r- r- i • r- r- r- ri i i i i i i i

r- r- r- r-- r^ r

coajcocx>r-r^r-»o»£) OCOOCOCOO ooooooooo I I I I I I I I I

\£) \0 *£i *G & "£> *C) *C *£> *G if\ if^

• oooooooooooo oooooooooooo * — I I I 1 i i i i I I <— oooooooooooo u>oooooooooooo

UJ if) F _l LU

uj tr: kOiOMDO-h.

a) r—

I

PL,

CL ooooooooo aoooooooooooo a oooooooooooo

INI o o o

z o o o o

UJ — I I I cr h- to rg &

o < *-< -o o

jo: • • •

(NJ <\l <\l

coaDaococococDCoa>

J ooooooooo :o

I I I I I ; t— fsi o r- o to t O < -o Oinm Mr

_j cr • • • • •

COS)COCOCO(DCOa}COIS(SIS M oooooooooooo zooooooooooooo NJ OOOOOOOOOOOO Z O OOOOOOOOOOOO UJ — I I I I I I I I I I I I Qir-h-»0i-tocOE«ir-r-i.} >Oflo<-i O<(>orgm*<"i.3, «tf-n"\ir»a">ir\\0

j cr jf\if\jrsjf\j(Njrsif\jfMt (NJ

CL O O O CL OOOOOOOOO a oooooooooooo z • • • • ••• LUOOOOOOOOOOOO r-CO<N-J>OtD OIN^OOOO -1 -( ^H i-i i-h l\J fNJ (\J IM <\l m

a oooooooooooo
Appendix III - Bibliography

1. Alers, P. B. , Spohr, D. A., and Webber, R. T., "The Thermal

Conductivity of Metals", Conf. de Phys. des basses temps. , Paris,

453-455 (Sept. 2-8, 1955).

2. Aliyev, N. G. and Volkenshteyn, N. V. , "Low-Temperature

Thermal Conductivity of Scandium and Yttrium", Fiz. Metal.

Metalloved, _19, 793(1965).

3. Allen, J. F.,and Mendoza, E. , "Thermal Conductivity of Copper

and German Silver at Liquid Helium Temperature", Proc. Camb.

Phil. Soc, 44, 280-288(1947).

4. Amundsen, T. , Myhre, A. , and Salter, J. A. M. , "The WiedemannFranz Ratio of Aluminum at Liquid Helium Temperatures", Phil.

Mag. , _25, 513-517 (1972).

5. Andrews, F. A., Webber, R. T. , and Spohr, D. A., "Thermal

Conductivities of Pure Metals at Low Temperatures I. Aluminum",

54, 994-996 (1951).

6. Aoyama, S. , and Ito, T. , "Thermal and Electrical Conductivities

of Metals and Alloys at Low Temperature, Part I on Nickel-Copper

Alloys", Nihon Kinzoku Gakkai-Shi (Journal of the Japan Institute

of Metals), 4, 3-7 (1940).

7. Arajs, A., and Colvin, R. V. , "Thermal Conductivity of Scandium

Between 5 and 320°K", 4th Conference on Rare Earth Research,

261-267 (1964).

8. Backlund, N. G. , "An Experimental Investigation of the Electrical

and Thermal Conductivity of Iron and Some Dilute Iron Alloys at Temperatures Above 100°K", J. Phys. Chem. Solids £0, 1-16

(1961).

9. Backlund, N. G. , "Measurements and Analysis of the Thermal

Conductivity of Tungsten and Molybdenum at 100-400° K", J. Phys.

Chem. Solids 28, 2219-2223(1967).

10. Beitchman, J. G. , Trussel, C. W. , and Coleman, R. V. , "Electron

Transport and Lorenz Number in Iron", Phys. Rev. Letters 25,

1291-1294 (1970).

11. Berman, R. , "The Thermal Conductivity of Some Alloys at Low

Temperatures", Phil. Mag. 42, 642-650(1951).

Ill- 1
12. de Haas, W. J., and de Nobel, J. , "The Thermal and Electrical

Resistance of a Tungsten Single Crystal at Low Temperatures

and in Magnetic Fields", Physica 5, 449-463 (1938).

13. Estermann, I., and Zimmerman, J. E. , "Heat Conduction in

Alloys at Low Temperature", J. Appl. Phys. 2_3, 572-588(1952).

14. Eucken, A., and Dittrich, K., "Zur Kenntnis des WiedemannFranzschen Gesetzes, II", Z. Physik, Chem. 129 , 211-228(1927).

15. Farrell, T.,and Greig, D. , "Thermal Conductivity of Nickel and

Its Alloys", J. Phys. C (Solid State Phys. ) 2, 1465-1473(1969).

16. Fenton, E. W. , Rogers, J. S. , and Woods, S. B. , "Lorenz Number

of Pure Aluminum, Silver, and Gold at Low Temperatures", Can.

J. Phys. 41, 2026-2033(1963).

17. Flynn, D. R. , Private Communication, (1971).

18. Goff, J. F. , "Lorenz Number of Chromium", Phys. Rev. IB , 1351-1362 (1970).

19. Goens, E . , and Gruneisen, E. , "Electrical and Thermal Conductivity in Zinc and Cadmium Crystals", Ann. Physik 14, 164-180

(1932).

20. Gruneisen, E.,and Goens, E. , "Investigations on Metal Crystals.

V. Electrical and Thermal Conductivity of Single and Poly-crystal

Metals", Z. Physik 44, 615-642(1927).

21. Harper, A.F. A., Kemp, W. R. G. , Klemens, P. G. , Tainsh,

R. J., and White, G. K., "The Thermal and Electrical Conductivity of Chromium at Low Temperatures", Phil. Mag. 2, 577-

583 (1957). ~

22. Hust, J. G. , "Thermal Conductivity Standard Reference Materials

from 4 to 300 K. I- Armco Iron", 9th Thermal Conductivity Conference, Ames Lab. , USAEC; U.S. Office of Naval Research, Iowa

State University (Conf. 691002), March 1970, p. ?17-233, Oct 6-8

(1969).

23. Hust, J. G. , "Thermal Conductivity Standard Reference Materials

from 4 to 300 K. I. Armco Iron", unpublished NBS Report.

24. Hust J. G. , "Thermal Conductivity, Electrical Resistiviey, and

Thermopower of Aerospace Alloys from 4 to 300 K. II. AISI 347

Stainless Steel", unpublished NBS Report.

Ill2
25. Hust, J. G.,and Powell, R. L. , "Thermal Conductivity of Aerospace Alloys at Crvogenic Temperatures", 8th Thermal Conductivity Conference, Oct 7-10 ( 1968), Purdue University, West Lafayette

Indiana, Plenum Press, New York (1969).

26. Hust, J. G. , Powell, R. L. , and Weitzel, D. H. , "Thermal

Conductivity, Electrical Resistivity, and Thermopower of Aerospace Alloys from 4 to 300 K", unpublished NBS Report27. Hust, J. G. , Powell, R. L. , and Weitzel, D. H. , "Thermal

Conductivity Standard Reference Materials from 4 to 300 K. I. Armco Iron: Including Apparatus Description and Error Analysis",

J. Res. Nat. Bur. Stand. (U.S.), 74A, 673-690(1970).

28. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity, Electrical

Resistivity, and Thermopower of Aerospace Alloys from 4 to 300 K.

III. Annealed Inconel 718", unpublished NBS Report.

29. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity Standard

Reference Materials from 4 to 300 K. II. OSRM Iron 1265",

unpublished NBS Report.

30. Hust, J. G. > and Sparks, L. L. , "Thermal Conductivity Standard

Reference Materials from 4 to 300 K: IV. AGARD Gold", unpublished NBS Report.

31. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity Standard

Reference Materials from 4 to 300 K. III. AGARD Stainless Steel",

unpublished NBS Report.

32. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity, Electrical

Resistivity, and Thermopower of Aerospace Alloys from 4 to 300 K:

IV. A286 Stainless Steel", unpublished NBS Report.

33. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity, Electrical

Resistivity, and Thermopower of Aerospace Alloys from 4 to 300

K: V. Aluminum 2024", unpublished NBS Report.

34. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity, Electrical

Resistivity, and Thermopower of Aerospace Alloys from 4 to 300

K: VI. Fe - 22Cr - 13Ni - 5Mr Stainless Steel", unpublished NBS

Report •

35. Hust, J. G. , and Sparks, L. L. , "Thermal Conductivity Standard

Reference Materials from 4 to 300 K: V. AGARD Stainless Steel",

unpublished NBS Report.

Ill36. Hust, J. G., and Sparks, L. L. , "Standard Reference Materials:

Thermal Conductivity of Electrolytic Iron, SRM 734, from 4 to 300 K", Nat. Bur. Stand. (U.S,), Spec. Publ. 260-31 (197 If).

37. Hust, J. G., and Sparks, L. L. , "Standard Reference Materials:

Thermal Conductivity of Austenitic Stainless Steel, SRM 735,

from 5 to 280 K", Nat. Bur. Stand. (U.S.), Spec. Publ. 260-35

(1972).

38. Hust, J. G. , Weitzel, D. H. , and Powell, R. L. , "Thermal

Conductivity of Aerospace Alloys at Cryogenic Temperatures",

7th Thermal Conductivity Conference, Nov. 13-16, 1967,

Gaithersburg, Md. (Nat. Bur. Stand., Spec. Publ. 302, pp. 271-

278 (1968).

39. Hust, J. G. , Weitzel, D. H. , and Powell, R. L. , "Thermal

Conductivity, Electrical Resistivity, and Thermopower of Aerospace Alloys from 4 to 300 K", J. Res. Nat. Bur. Stand. (U.S.),

75A , 269-277 (1971).

40. Kannuluik, W. G. , "On the Thermal Conductivity of Some Metal

Wires", Proc. Roy. Soc. A131 , 320-335(1931).

41. Kannuluik, W. G. , "The Thermal and Electrical Conductivities

of Several Metals Between 183° C and 100° C, Proc. Roy. Soc.

A141 , 159-168 (1933).

42. Karweil, J. , and Schafer, K. , "The Thermal Conductivity of

Poorly Conducting Alloys Between 3 and 20°K", Ann. Physik

36, 567-577 (1939).

43. Kemp, W. R. G. , Klemens, P. G. , Sreedhar, A. K. , and White,

G. K. , "The Thermal and Electrical Conductivity of Palladium at Low Temperatures", Phil. Mag. 46, 811-814(1955).

44. Kemp, W. R. G. , Klemens, P. G. , and Tainsh, R. J., "Lattice

Thermal Conductivity of Some Copper Alloys", Aust. J. Phys.

K), 454-461 (1957).

45. Kemp, W. R. G. , Klemens, P. G. , Tainsh, R. J., "Thermal and

Electrical Conductivities of Rhodium and Iron", Ann. Phys. (Ger.)

5, 35-41 (1959).

46. Kemp, W. R. G. , Klemens, P. G. , Tainsh, R. J., "The Lattice

Thermal Conductivity of Copper Alloys: Effect of Plastic Deformation

and Annealing", Phil. Mag. 4, 845-857 ( 1959b).

III-4
47. Kemp, W. R. G. , Klemens, P. G. , White, G. K. , "Thermal and

Electrical Conductivities of Iron, Nickel, Titanium, and Zirconium

at Low Temperatures", Aust. J. Phys . 9, 180-188(1956).

48. Kohlhaas, R. , and Kierspe, W. , "Thermal Conductivity of Pure

Iron and Some Ferritic and Austenitic Steels Between the Temperature of Liquid Air and Room Temperature", Arch. Eisenhiittenw 36, 301-309 (1965).

49- Lees, C. H. , "XI Bakerian Lecture - The Effects of Temperature

and Pressure on the Thermal Conductivities of Solids", Phil. Trans.

Roy. Soc. A208 , 381-443(1908).

50. Lewis, E. J. , "Some Thermal and Electrical Properties of Berythium", Phys. Rev. 34, 157-187 (1929).

51. Malm, H. L. , and Woods, S. B. , "The Low-Temperature Thermal

Conductivity Electrical Resistivity, and Thermoelectric Power

of Dilute Silver Alloys with Manganese", Can. J. Phys. 44,

2293-2309 (1966).

52. Mannchen, W., "Thermal, Electrical Conductivities, and Lorenz

Number of Light Metal Alloys", Z. Metal Kunde 23, 193-196(1931).

53. Moore, J. P. , McElroy, D. L. , Barisoni, M. , "Thermal Conductivity

Measurements Between 78 and 340° K on Aluminum, Iron, Platinum,

and Tungsten", 6th Thermal Conductivity Conference, Oct. 19-21

1966, Air Force Materials Laboratory, Dayton, Ohio, pp. 737-778

54. Moore, J. P., McElroy, D. L. , and Graves, R. S. , "Thermal

Conductivity and Electrical Resistivity of High-Purity Copper from

78to400°K", Can. J. Phys. 45, 3849-3865(19 67).

55. Moore, J. P., Williams, R. K. , and McElroy, D. L. , "Physical

Properties of Chromium from 77 to 400° K", 7th Thermal Conductivity

Conference, Nov. 13-16 (1967), National Bureau of Standards,

Gaithersburg, Md. , NBS, Spec. Publ. 302, pp. 297-310 (1968).

56. Moore, J. P., Williams, R. K. , and McElroy, D. L. , "Further

Comments on Transport Properties of Chromium", 8th Thermal

Conductivity Conference, Oct. 7-10(1968), Purdue University, West Lafayette, Indiana, Plenum Press, New York, pp. 303-

313 (1969).

57. Powell, R. L. , Bunch, M. D. , and Gibson, E. F. , "Low-Temperature Transport Properties of Commercial Metals and Alloys",

J. Appl. Phys. 31, 504-505(1960).

Ill -5
58. Powell, R. L. , Hall, W. J., and Rode r, H. M. , "Low- Temperature

Transport Properties of Commercial Metals and Alloys", J. Appl.

Phys. 3l_, 496-503 (I960).

59. Powell, R. L. , Harden, J. L. , and Gibson, E. F. , "Low Temperature Transport Properties of Commercial Metals and Alloys",

J. Appl. Phys. 3_1, 1221-1224(1961).

60. Powell, R. L. , Roder, H. M. , and Hall, W. J. , "Low Temperature Transport Properties of Copper and Its Dilute Alloys Pure

Copper Annealed and Cold-Drawn", Phys. Rev. 115 , 314-323 (1959).

61. Powell, R. W. , and Jolliffe, B. W. , "The Thermal Conductivities

of Scandium and Some Rare Earth Metals", Phys. Letters 14,

171-172 (1965).

62. Powell, R. W. , and T ye, R. P., "The Thermal and Electrical

Conductivity of Titanium and Its Alloys", J. Less-Common Metals

3_, 226-233 (1961).

63. Powell, R. W. , Tye, R. P., and Woodman, M. J., "Thermal

Conductivities and Electrical Resistivities of the Platinum Metals",

Platinum Metals Rev. _6, 138-143 (1962).

64. Powell, R. W. , Tye, R. P., and Woodman, M. J., "The Thermal

Conductivity and Electrical Resistivity of Polycrystalline Metals

of the Platinum Group and of Single Crystals of Ruthenium", J. Less-Common Metals 1_2, 1-10(1967).

65. Powell, R. W. , Tye, R. P. , and Woodman, M. J. , "The Thermal

Conductivity of Pure and Alloyed Aluminum I. Solid Aluminum as a Reference Material", Adv. in Thermophysical Properties at Extreme

Temperatures and Pressures, Proc. 3rd Symp. , Purdue, ASME

(1965) pp. 277-288.

66. Radhakrishna, P. , and Nielsen, M. , "Transport Properties of

Cobalt at Low Temperature", Phys. Stat. Sol. _H, 111-115(1965).

67. Reddemann, H. , "Wiedemann - Franz Number of 3 - Manganese at -190°C", Ann. Physik 2_2, 28-30(1935).

68. Staebler, J. , "Electrical and Thermal Conductivities and Wiedemann

Franz Number of Light Metals and Magnesium Alloys", Doctoral

Thesis Submitted to Techischen Hochshule, Beslau (1929).

69. Tamarin, P. V. , Chuprikov, G. E. , and Shalyt, S. S. , "Investigation of the Phenomena of Charge and Heat Transfer in Yttrium

Single Crystals at Low Temperatures", Sov. Phys. J.E.T.P. 28,

836-837 (1969).

Ill6
70. Tyler, W. W. , Nesbitt, L. B. , and Wilson, Jr., A. C. , "Some

Low Temperature Properties of Titanium Alloy RC-130-B and

Stainless Steel", J. Metals, 1104-1105 (1953).

71. Tyler, W. W. , and Wilson, Jr., A. C. , "Thermal Conductivity,

Electrical Resistivity, and Thermoelectric Power of Titanium

Alloy RC-130-B", General Electrical Co. , Knolls Atomic Power

Laboratory, Report No. KAPL - 803 ( 1952) Contr. No. W - 31 - 109

Eng 52, 41.

72. Wagner, D. K. , Garland, J. C. , and Bowers, R. , "Low-Temperature

Electrical and Thermal Resistivities of Tungsten", Phys. Rev. 3B,

3141-3149 (1971).

73. White, G. K. , "The Thermal and Electrical Conductivity of Copper

at Low Temperature", Aust. J. Phys. _6, 397-404(1953).

74. White, G. K. , and Tainsh, R. J. , "Electron Scattering in Nickel

at Low Temperatures", Phys. Rev. Letters 165(1967).

75. White, G. K., and Tainsh, R. J., "Lorenz Number for High-Purity

Copper", Phys. Rev. 119 , 1869-187 1(1960).

76. White, G. K. , and Woods, S. B. , "Thermal and Electrical Conductivities of Solids at Low Temperatures", Can. J. Phys. 33, 58-73

(1955).

77. White, G. K. , and Woods, S. B. , "Thermal and Electrical Conductivity of Rhodium, Iridium, and Platinum", Can. J. Phys. 35, 248-

257 (1957).

78. White, G. K. , and Woods, S. B. , "Low Temperature Resistivity of

Transition Elements: Vanadium, Niobium, and Hafnium", Can. J. Phys. 35, 892-900 (1957a).

79. White, G. K. , and Woods, S. B. , "Low Temperature Resistivity of

the Transition Elements: Cobalt, Tungsten, and Rhenium", Can. J. Phys. 35, 656-665 (1957).

80. White, G. K. , and Woods, S. B. , "Conductivity of a - Manganese",

Can. J. Phys. 35, 346-348 (1957c).

81. Wilkes, K. E., and Powell, R. W., "Thermal Conductivity of

Aluminum Between about 78 and 373K", 7th Thermal Conductivity

Conference, NBS, Gaithersburg, Md. Nov. 13-16, 1967,

Nat. Bur. Stand. (U.S.) Spec. Publ. 302, 29 3-296(1968).

Ill -7
12. Wilkes, K. E. , Powell, R. W. , and Dewitt, D. P., "Thermal

Conductivity Measurements on Cobalt and Zinc Between 78 and 37 3K'

8th Thermal Conductivity Conference, Oct. 7-10, 1968, Purdue

University, West Lafayette, Indiana, Plenum Press, New York,

pp. 3-8 (1969).

Ill8
form NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-634

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Lorenz Ratios of Technically Important Metals and Alloys

5. Publication Date February 1973

6. Performing Organization Code

7. AUTHOR(S)

J. G. Hust and L. L. Sparks

8. Performing Organization

10. Project/Task/Work Unit Nc 2750131

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulder Labs

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as Item 9.

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significa bibliography or literature survey, mention it here.) A comprehensive review and compilation of the world literature on Lorenz ratio of technically important metals and alloys is presented. Lorenz

ratio, electrical resistivity, thermal conductivity and characterization data are compiled in tabular form and the Lorenz ratio data are presented in graphical form as well. Data are included here only if the research reported

both thermal conductivity and electrical resistivity of the specimens. No

attempt has been made to smooth data or present recommended values.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Alloys; compilation; cryogenic; electrical resistivity; Lorenz Ratio; metals;

thermal conductivity.

18. AVAILABILITY STATEMENT

fx] UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

133

22. Price

$1.25

*U.S. Government Printing Office: 1973-784-210/1124 USCOMM-DC 66244-P7I

NBS TECHNICAL PUBLICATIONS

PERIODICALS JOURNAL OF RESEARCH reports National Bureau of Standards research and development in

physics, mathematics, and chemistry. Comprehensive

scientific papers give complete details of the work,

including laboratory data, experimental procedures, and theoretical and mathematical analyses. Illustrated with photographs, drawings, and charts. Includes

listings of other NBS papers as issued.

Published in two sections, available separately:

• Physics and Chemistry (Section A)

Papers of interest primarily to scientists working in these fields. This section covers a broad range of

physical and chemical research, with major emphasis

on standards of physical measurement, fundamental

constants, and properties of matter. Issued six times

a year. Annual subscription: Domestic, $17.00; Foreign, $21.25.

• Mathematical Sciences (Section B)

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical analysis, theoretical physics and chemistry,

logical design and programming of computers and

computer systems. Short numerical tables. Issued quarterly. Annual subscription: Domestic, $9.00; Foreign,

$11.25.TECHNICAL NEWS BULLETIN

The best single source of information concerning the Bureau's measurement, research, developmental, cooperative, and publication activities, this monthly

publication is designed for the industry-oriented

individual whose daily work involves intimate contact with science and technology

for engineers, chemists,

physicists, research managers, product-development

managers, and company executives. Includes listing of

all NBS papers as issued. Annual subscription: Domestic, $6.50; Foreign, $8.25.

^PERIODICALS Applied Mathematics Series. Mathematical tables, manuals, and studies. Building Science Series. Research results, test methods, and performance criteria of building materials, components, systems, and structures. Handbooks. Recommended codes of engineering and industrial practice (including safety codes) de- veloped in cooperation with interested industries, professional organizations, and regulatory bodies. Special Publications. Proceedings of NBS conferences, bibliographies, annual reports, wall charts, pamphlets, etc. Monographs. Major contributions to the technical

literature on various subjects related to the Bureau's

scientific and technical activities. National Standard Reference Data Series. NSRDS provides quantitative data on the physical and chemical properties of materials, compiled from

the world's literature and critically evaluated. Product Standards. Provide requirements for sizes, types, quality, and methods for testing various industrial products. , These standards are developed co- operatively with interested Government and industry groups and provide the basis for common understanding of product characteristics for both buyers and

sellers. Their use is voluntary.

Technical Notes. This series consists of communications and reports (covering both other-agency and

NBS-sponsored work) of limited or transitory interest. Federal Information Processing Standards

Publications. This series is the official publication within the Federal Government for information on

standards adopted and promulgated under the Public Law 89-306, and Bureau of the Budget Circular A-86

entitled. Standardization of Data Elements and Codes

in Data Systems. Consumer Information Series. Practical information, based on NBS research and experience, cover- ing areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service (Publications and Reports of Interest in Cryogenics). A literature survey issued weekly. Annual subscription : Domestic, .$20.00; foreign, $25.00.

ciuueiied Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00. Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription: $20.00. Send subscription orders and remittances for the preceding bibliographic services to the U.S. Department

of Commerce, National Technical Information Service, Springfield, Va. 22151.

Electromagnetic Metrology Current Awareness Service (Abstracts of Selected Articles on Measurement

Techniques and Standards of Electromagnetic Quantities from D-C to Millimeter- Wave Frequencies). Issued monthly. Annual subscription: $100.00 (Special rates for multi-subscriptions). Send subscription order and

remittance to the Electromagnetic Metrology Information Center, Electromagnetics Division, National Bureau

of Standards, Boulder, Colo. 80302. Order NBS publications (except Bibliographic Subscription Services) from: Superintendent of Documents, Government Printing Office, Washington. D.C. 20402.
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. DC. 20234

OFFICIAL BUSINESS

Penalty for Private Use, $300

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

215