National Bureau of Standards

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JUN 5 1961

NBS MONOGRAPH 29

Thermal Expansion of

Technical Solids at Low Temperatures

A Compilation From the Literature

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Thermal Expansion of

Technical Solids at Low Temperatures

A Compilation From the Literature

Robert J. Corruccini and John J. Gniewek

National Bureau of Standards Monograph 29

Issued May 19, 1961

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 20 cents

I

Thermal Expansion of Technical Solids at Low Temperatures * A Compilation From the Literature

Robert J. Corruccini and John J. Gniewek

Tables are given of the linear contraction relative to 293 °K, (Lin —Lt) I L293, and the linear expansion coefficient, dLIL^ndT, of thirty elements, forty-five alloys, twenty-two

other inorganic substances and twenty plastics and elas- tomers in the temperature range, 0 to 300 °K.

Introduction

This publication was intended to fill a need

among designers of cryogenic equipment for a compilation of thermal expansion data on cryogenic materials. The literature search relied

primarily on Physics Abstracts and is believed to provide complete coverage of the published liter- ature through 1958. It was found that very few

additional references were derived from subsequently searchijig other sources. Wherever possible, data have been presented

throughout the range, 0 to 300 °K. However,

the region below 100° K is of predominant

importance in cryogenic engineering, and, hence,

many substances of interest have been omitted

because data were not available below 100 °K.

Certain substances which are usually used as

fluids in cryogenics have been omitted. These

are helium, hydrogen, deuterium, neon, nitrogen,

carbon monoxide, fluorine, argon, oxygen, air, and

methane. Various properties of aU phases of

these substances are being compiled separately at

this laboratory.

The published data usually consisted of mismoothed values of length change. It was

necessary to adjust these to our adopted reference

temperature of 293 °K, to smooth and interpolate

at rounded values of temperatm-e, and to differ- entiate. Most of the results are given in table 2. The references on which the resulting data were

based are indicated in each table as "Sources of

above data". All other sources of low temperature data for each substance are listed as "Other

references". The selection of best sources will not be justified in detail. In general it was based on the precision of the data, the original authors'

estimates of accuracy, and the quality of the

samples. The bibliography gives complete refer- ences to the sources associated with the tables of

data. In addition, it contains selected references on theory, experimental techniques, and measure- ments of other substances which were outside our

scope but which were thought to be of more than

average interest. The bibliography attempts to be complete only with regard to the substances

listed in table 1.

•This work was partly supported by Wright Air Development Center, Air Research and Development Command U.S. Air Force.

Table 3 gives data on some miscellaneous substances that did not fit into the format of table 2. It was not practical to extend these data in any

way, and so they are quoted almost verbatim

from the original sources. Materials of construction often are anisotropic as a result of forming operations. This is especially noticeable with metals having highly anisotropic crystal lattices, such as zinc, and with

plastics based on chain polymers. The degree of

preferred orientation in such materials may be uncontrolled and, consequently, measurements of

the linear thermal expansion may vary greatly

with sample history and orientation. Measurements that are made in only one direction of such

a material can be given little weight. Wherever

a complete set of linear expansions along mutually

perpendicular directions were available, we cal- culated the mean linear expansion for presentation

in table 2. This quantity is to a very good

approximation one-third the volume expansion and

is the linear expansion that would be observed in

the absence of preferred orientation. Although

such a condition may not often be perfectly realiz- able, it represents average behavior and is a

precisely defined physical quantity. In order to show the maximum possible variation in the linear

expansion with orientation we have given in table

4 representative values along the principal crys- tallographic axes for some of the more anisotropic

elements. These data were taken directly from

the literature without smoothing.

Thermal cycling of polycrystalline materials in

which the crystallites are anisotropic produces in- ternal stresses. In extreme cases plastic deformation can result. This has been observed in tin,

cadmium, and zinc by Boas and Honeycombe

[1947] and in graphite by Hidnert [1934] and

Baskin and Meyer [1955].

There are two main classes of experiniental

methods using macroscopic and X-ray lattice parameter techniques, respectively. In a few cases

[Glover, 1954; Gott, 1942; Smith, 1954] appreciable

differences in thermal expansion by the two

methods have been found, amounting to over 10

percent at the worst. However, others have found no difference exceeding experimental error except near the melting point [Austin, Saini, Weigle, and

Pierce, 1940; Berry, 1953; Connell and Martin,

1951; van Duijn and van Galen, 1957; Feder and

Nowick, 1958; Hume-Rothery and Andrews, 1942;

Hume-Rothery and Boultbee, 1949; Hume-Rothery and Strawbridge, 1947; Simmons and Baluffi,

1
1959, 1960; Wagner and Beyer, 1936]. Such

differences, if real, would require high concentrations of vacancies or nonuniform distribution of

lattice defects. The dimensional effects produced

by lattice defects have been analyzed by Eshelby

[1953, 1954, 1956], Miller and Russell [1952, 1953],

and Toupin and Rivlin [I960]. The effect of impurities in metals is illustrated by measurements

due to Hume-Rothery and Boultbee [1949]. The

efl'ect of elastic strain has been examined by

Rosenfield and Averbach [1956] and the effect of

plastic deformation has been examined by Hordon,

Lement, and Averbach [1958].

Smoothing and interpolation were necessary

with many substances in order to obtain tables

that were sufficiently detailed to be useful. It was a common situation fo find published values

of length change at fairly small intervals from

ambient temperature to about liquid air temperature, then a single value (often from a different

source) of the length change between 78, 83, or 90 °K and 20 °K. By adjusting these length

changes to a common starting temperature, Tref,

such as 293 °K, the data could have been correlated

by finding a best fit to one of the Gruneisen equations, which we write in the form,

Xref

Lt Uref Ut

Lref ~a[l-b{Ur-Uo)]

Here U is internal energy, and a and b are constants to be evaluated by fitting the equation to the data. However this is a laborious procedure

due to the necessity of constructing in advance a complete table of tl versus T for each substance.

Consequently a quicker procedure was adopted in

many cases, which consisted of smoothing and in- terpolating graphically down to about 90 °K and

using the Gruneisen relation only at lower temperatures. Here the term, hillT—U^), is negligible, and internal energy can be replaced by

enthalpy. The latter quantity had already been

tabulated by us as part of another compilation.

The constant, a, can then be determined from any

single value of length change below about 90 °K,

such as, from 90 to 20 °K. By differentiation, a

is also the constant of proportionality between

dLjLdT and Cp. The error resulting from these

simplifications of the formula is appreciable only

for soft substances of high atomic weight, e.g., lead, indium, mercury. A more serious error is indicated by recent experiments and refinements

of theory showing that some variation in the constant, a, will generally occur at temperatures lower

than about one thhd of the Debye temperature.

See, for example, Barron [1955], Bijl and Pullan

[1954, 1955], Dheer and Surange [1958], Figgins,

Jones, and Riley [1956], Gibbons [1958], Rubin,

Altman, and Johnston [1954], Simmons and

Balluffi [1957]. Because of this effect, the values

interpolated by means of the formula are accurate

only to one or two figures. Also there is a lower

limit to the applicability of the formula. This is the temperature below which the linear term in

the specific heat due to electrons is appreciable.

Mikura [1941] and Visvanathan [1951] have shown

that a corresponding linear term in dLjLdT should

appear, but the coefficient of this term has been

calculated only for the free-electron case. Anomalies in the thermal expansion may occur

for various reasons. In fact, dilatometry is a

useful tool for exploring solid-state transformations. Some examples of substances showing low

temperature anomalies are Dy (ferromagnetic

Curie point), KH2PO4 (ferroelectric Curie point),

MnO (anti-ferromagnetic transformation or Neel

point), N2 (fii'st order phase change), CH4 (rotational transition) and soft rubbers ("glass"

transition)

.

Articles by Bijl [1957], Gruneisen [1926], and

Hume-Rothery [1945] may be consulted for general background on the representation of thermal

expansion.

Published thermal expansion data vary greatly

in precision. Some papers show as many as five significant figures in Ai/Z and four in the derivative. However, comparisons between careful in- vestigations on the same pure materials indicate

that absolute accuracies better than one percent

are seldom attained.

Descriptions of dilatometric techniques will be

found in many of the articles selected as "Sources

of Data." In addition the bibliography contains

selected articles prefixed (T) which are devoted

solely to techniques.

The assistance of Vincent D. Ai'p, Mrs. Marjorie Fewlass, and W. R. Slinkman is gratefully

acknowledged.

Tahle 1. List of substances Elements Alloys Other inorganics

{See table S.l) {See tablf 2.S) {See table tS) Aluminum Aluminum 2024-T4a Carbolloy •> Antimony Aluminum 7075-T6 » Carbon dioxide Beryllium Aluminum 25 i> Glasses: Bismuth Aluminum bronze Optical (misc.)" Cadmium Beryllium copper Pyrex Carbon (diamond) Brass Silica Carbon (graphite) Bronze •> Ice Chromium Cast aUoys (misc.)'> Indium antimonide Copper Cast iron ^ Quartz Germanium Constantan Magnesium oxide Gold Contracid Indium German silver Plastics and elastomers Iron Inconel {See table 24) Lead Inconel-X » Araldite Magnesium Invar Catalin Manganese Magnesium AN-M-29 » Dynakon

Mercury Monel Fluorothene Molybdenum K-Monel » Kel-F

Nickel Soft solder (50 Pb 50 Sn) Laminae Niobium d Steels: Lucite Palladium SAE 1010 a Nylon

Platinum SAE 1020 Panelyte Rhodium SAE 1095 Ple.xiglas Silicon SAE 6150 b Polystyrene

Silver SAE 52100 Polythene Sodium AISI 301 Rubber: Tantalum AISI 302 Hard

Tin AISI 304 Silastic 160 Titanium AISI 310 Selectron Tungsten AISI 316 Teflon

Zinc AISI 322 Tenite AISI 330 Vinylite AISI 347 AISI 410 Miscellaneous •> Titanium RC-130-B

Titanium Ti-150-A

» See table 3.2. b See table 3.1. > See table 3.3. <i Also termed Columbium.

2
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion

Elements

Aluminuin Antimony t Beryllium t Bismuth Cadmium b T

10« dL jg.,£293-iT 106 di jg,£293— £7" 106 dL ^^.Liiz—Lt 10' dL ,„,£293 —£t 108 dL

£293 X293 dT £293 £293 dT £293 Lm dT Lm £293 dT TA293 £293 dT

deg K deg-' K deg-^ K deg-i K deg-^ K deg-^ K

0 a Q a 250 Q a 131 0

a / 00 0

10 »415 »0.05 ^ 250 a 0.1 a 323 a 1. 1

a 733 a 1.1 20 415 .2 a 250 a. 8

a 131 ». 01 321 a 3.4 729 a 6.2 30 414 .9 a 248 a 2.4 a 131 a. 03 316 a 6. 1 a 720 a 11.6 40 413 2.2 a 245 a 4.1 a 131 a. 07 309 7.8 '706 a 15.8

rri OU 410 3.

a 240 a 5. 6a 13]^ a 13 300 9 1

a 689 a 19 0

fin 405 5^5 a 234 a 7!0 a 131 a! 2 291 10! 0

a 669 a 21! 4 70 399 7.4 a 226 a 7.9 a 130 a. 4 280 10.7 a 646 a 23.2 80 391 9.1 218 8.5 a ]30 a. 6 269 11.2 a 622 a 24.6

90 381 10.7 209 8.9 129 a. 9 258 11.6 597 25.6

100 370 12.2 200 9.3 128 1.3 246 11.9 571 26.4 120 343 14.6 181 9.7 124 2.2 222 12.2 517 27.8

140 312 16.5 162 10.0 119 3.4 198 12.5 460 28.7

160 277 17.9 142 10.2 111 4.7 173 12.7 402 29.3 180 240 19.0 121 10.4 100 5.9 147 12.8 343 29.7

200 201 20.0 100 10.5 87.3 7.1 121 12.9 284 30.0

220 160 20.8 78.9 10.6 72.8. 2 95. 5 13.0 223 30. 2 240 lis 21.5 57.

10.7 54.6 9.2 69.4 1.3.

163 30.4

260 75 22.1 35.9 10.8 35.2 10.1 43.3 13.1 102 30.6

273 45 22.5 21.8 10.9 21.8 10.6 26.2 13.1 61.9 30.8

280 30 22.7 14.2 10.9 14.3 10.8 17.1 13.1 40.3 30.9

293 0 23.0 0.0 10.9 0.0 11.2 0.0 13.1 0.0 31.1 300 -16 23.2 -7.7 11.0 -7.9 11.4 -9.2 13.1 -21.8 31.2

_ . oourccs 01 Altman, Rubin, and Johns- Erfling 1939 Erfling 1939 Erfling 1939 Gruneisen and Goens 1924 ton 1954 Hidnert and Sweeney 1927 Utner reIs. Ayrcs 1905 Dorsey 1907 Head and Laquer 1952 Dorsey 1907 Borelius and Johansson 1924

Biji and Pullan 1955 Gruneisen 1910 Gruneisen 1910 Dorsey 1907 Buffineton and Latimer Jacobs and Goetz 1937 Gruneisen 1910 1926 Wunnenberg, Fischer, and McLennan and Monkman

Ebert 1928 Sapper 1930 1929 Figrins, Jones, and Riley

1956 Gibbons 1958 Hennins 1907 Hordon, Lement, and Aver- bach 1958 Humc-Rothery and Strawbridge 1947 Lindemann 1911 Nix and MaoNair 1941 Shearer 1905

a Estimated using Gruneisen correlation as explained in Introduction. parallel and perpendicular, respectively, to the trigonal (Sb, Bi) or hexagonal

^Anisotropic. The above values were calculated from the relation. Mean (Be, Cd) axis. See table 4 for representative values of the {||) and (X) Value = H(ID+?3(i.), where (U) and (X) signify the same property measured expansions.

3
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Elements

Carbon i: (diamond Chromium d Copper Germanium Gold T

10» dL ^^^Lm-Lr 10« dL W dL £293—^7' 10» dL jQ,L293-£r 106 rfi

i293 dT Lm Lm dT Lm Lm dT i293 Lm dT £-293 i2«3 dT

degK deg-^ K deg-^ K deg-'^ K deg-i K deg-^ K

0

a 24.3 0 »98. 5 0 "326 0 "92 0 »324 0

10 a 24.

a 0. 00004 0 326 a 0. 04

20 a 24.

a_ 0003 a 9g. 5 a_03 326 .3 323 a 2. 4 30 a 24^3 a . 0008 a 98^4 09 325 1! 0 a 319 a 4_ g 40 8 24.

002 a 98^3 a. 2 324 2.92.

. 07 a 313 * 6. 7

50 a 24.3 ».0O4 "97.9 «. 5 321 3.8 92.1 .20 >306 »8.2

60 " 24. 3 a 007 97.3 . 84 316 5. 5 91. 9 .39 a 297 a 9 2

70 a 24. 2 a 01 96! 2 1. 27 310 7. 0 91. 4 . 67 a 288 a 10. 0

80 a 24. 2 a 02 94.

1. 75 302 8 4 90. 5 1. 05 278 a 10, 6

90 a24!l »]03 92^7 2. 19 293 9.5 89] 3 L54 267 11! 1

100 a 24.0 a. 04 90.3 2. 59 283 10. 5 87.2. 20 256 11. 5 120 a 23! 7 a' 08 84. 5 3. 25 260 12.0 81.

3. 25 233 12.

140 23.

. 14 77. 4 3 8 235 13.

74 9 3 91 208 12. 5

160 22.1 !21 6913 4.3 208 14! 1 67! 0 4^29 182 12.8

180 20.6 .30 60.3 4.7 179 14.7 58.3 4.58 156 13.1

200 18.6 .40 50.5 5.1 149 15,2 48.7 4. 82 129 13.3 220 16.0 .52 40.0 5.4 118 15.6 39.0 5.03 102 13.5

240 12.6 .65 29.1 6.5 87 15.9 28 9 5 23 74.4 13.7 260 8.5 .78 18.0 5.6 55 16.2 18^3 5! 42 47.0 13.9

273 6.9 .87 10.7 5.6 33 16.4 11.3 5.53 27.8 14.0 280 3.7 .92 6.9 5.5 22 16.5 7.4 5.59 18.7 14.0

293 0.0 1.0 0.0 5.1 0 16.7 0.0 5. 67 0.0 14.1 300 -2.

1.

-3.5 5.0 -11 16.8 -4.0 5.75 -10.2 14.1

Sources of Thewlis and Davey 1956 Erfling 1939 Rubin, Altman, and John- Gibbons 1958 Ebert 1928 above data ston 1954 Nix and MacNair 1941 Other refs. Cohen and Olie 1910 Disch 1921 Adenstedt 1933 Fine 1953 Dorsey 1907, 1908 RontRen 1912 Fine, Greiner and Ellis 1951 Aoyama and Ito 1939 MeSkimin 1953 Gruneisen 1910 Hidnert 1941 Beenakker and Swenson Nitka 1937

1955.

Bijl and Pullan 1955 BoreUus and Johansson

1924 Bufflngton and Latimer

1926 Dorsey 1907 Fraser and Hollis-Hallet

1955 Henning 1907 Keesom, van Agt, and

Jansen 1926 Keyston, MacPherson,

and Guptill 1959 Krupkowski and de Haas

1928 Lindemann 1911 Nix and MacNair 1941 Simmons and Balluffl 1957 Simon and Bergmann 1930

1 Estimated using Gruneisen correlation as explained in Introduction.

1= The above values are for "gem quality" diamond. Thewlis and Davey

also measured industrial diamond but obtained an anomalous minimum near

0° C. Following are some selected values of 10^(dL/LdT) for their industrial diamond: 175° K 0.7, 200° K 0.6, 260° K -0.1 (min), 300° K +0.3.

" Graphite lattice parameters have been measured at low temperatures by

Basbin and Meyer [1955] and by Walker, McKinstry, and Wright [1953]. The largest value reported for any of the expansion coefficients was 29X10"'

deg-i K and was for the translaminar direction at 77° K and above. Expansions parallel to the laminae were too small to detect. In addition frag- mentary and discordant macroscopic measurements lying within the above

limits have been reported by Cohen and Olie [1910], Dewar [1902], and Erfling

[1939]. Hidnert [1934] systematically measured the macroscopic expansions of

several polycrystalline artificial graphites and obtained values of W^idLf Ld T) at room temperature ranging from 0.6 to 4. The latter values define the probable range of commercial bonded graphites. These values would be

expected to trend toward zero with decreasing temperature.

<i Hidnert found that the density and expansion coefficient of new elec- trolytic chromium were unstable. This was attributed to the large initial hydrogen content. The metal is stabilized by annealing. The table is based on the more pure of two vacuum-annealed samples measured by Erfling. The results with the less pure sample were about 10% higher. There was

a minimum in the expansion coefficient at room temperature. This anomaly

has been confirmed by Fine et al., and coincides with the antiferromagnetie

transition (Neel point) found by Corliss, Hastings, and Weiss [1959].

4
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Elements

Indium ' Iron Lead ^ Magnesium " a-Manganese d /3-Manganese • T J 7"TM, ina lU" ATULi 10° ah

105 Lm-Lr 10' dL ^^^Lm-Lr dL Lm dT X293 d T £293 X293 .Lf293 u 1 Z>!93 T J/p

jL'203 fl i

degK deg-^ K K deg-i K rfeff-i K deg-i K

0 »706 0 »198 0 «708 0 "490 0

5 768 0.3

10 a 706 a2 707 3. 2 "490 " 0. 05

20 701 7 198 "0.1 700 "11 490 "]4 30 691 13 « 198 ".3 "686 " 17 "489 "1.4

40 676 17 » 197 Kl "667 "20 "486 "3.3

50 658 19.

» 196 a 1.3 "646 "22 "482 "5.7

60 638 20.4 » 195 »2.

"624 " 23 "475 "8.

70 617 21.5 »192 «2.8 "601 "24 "466 "10.3

80 595 22.4 » 189 »3. 5 "577 "24 454 12.2 380

90 572 23.2 185 4. 2 552 25 441 13.9 372 9.8 420

100 549 23.9 181 4.9 528 25 427 15 4 361 11.

406 14.

120 500 25.2 170 6.3 477 25.6 393 17^6 334 14! 4 375 17! 0

140 448 26.3 156 7.6 425 26.3 356 19.4 304 16.0 339 18.5

160 394 27.2 140 8.6 372 26.8 316 21.0 271 17.3 301 19.7

180 339 27.9 122 9.4 318 27.2 273 22.2 235 18.4 260 20.7

200 282 28.

102 10.

263 27. 5 227 23. 2 197 19.4 218 21.6

220 224 29.3 82 10.5 208 27.8 180 23.9 158 20.3 174 22.4

240 165 30.1 60 10.9 152 28.2 132 24.4 116 21.0 128 23.2

260 104 30.8 38 11.3 96 28.5 82.9 24.8 73.5 21.8 81.3 24.0

273 63 31.3 23 11.4 58 28.8 50.4 25.1 44.9 22.2 49.9 24.5

280 42 31.5 15 11.5 38 28.9 32.9 25.2 29.3 22.4 32.6 24.8

293 0 32.0 0 11.6 0 29 0.0 25.4 0.0 22.7 0.0 25.4 300 -22 32.2 -8 11.7 -20 29 -17.8 25.5 -16.0 22.9 -17.9 25.7

Sources of Swenson 1955 Ebert 1928 Dheer and Surange Ebert 1928 Erfling 1940 Erfling 1939 &bove Nix and MacNair 1958 Goens and Schmid

data 1941 Ebert 1928 1936 Xix and MacNair Head and Laquer

1942 1952 Olsen and Eohrer

1957

Other rets. Graham, Moore, & Adenstedt 1936 Dorsey 1908 Gruneisen 1910 Disch 1921 Raynor 1955 Dorsey 1907 Gruneisen 1910 Hidnert and Sweeney

Hidnert and Blair Owen and WiUiams Head and Laquer 1928

1943 1954 1952 Simon and Bergmaim Lindemann 1911 1930 McLeiman, Allen, and Wilhelm 1931

"Estimated using Gruneisen correlation as explained in Introduction.

•> Superconducting lead has a slightly greater volume and a slightly smaller expansion coefficient than normal lead according to data by Olsen and

Eohrer covering the region from 1 to the transition temperature, 7.2 °K.

For example, the difference in expansion coefficients at 5 °K is about 10%.

"Anisotropic. The above values were calculated from the relation. Mean

Value = ]/3(||)+2/3(±), where (\\) and (X) signify the same property measured

parallel and perpendicular, respectively, to the hexagonal axis. See table 4

for representative values of the and (X) expansions.

d a-Mn is the form that is stable at low temperatures. It has an antifer- romagnetic tran.sition at about 95 °K which would make extrapolation of the above values uncertain.

«i8-Mn is stable between 730 and about 1100 °C. Erfling's sample was

prepared by quenching from 1100 °C in vacuum. There were insufficient

specific heat data to make a reliable extrapolation below 90 "K.

'Anisotropic, tetragonal. Graham, Moore, and Raynor gave values of the lattice parameters down to 90 °K that show great anisotropy in the thermal expansion. Their low temperature data are not sufficiently accurate or detailed to serve as the basis of an extended table of values, so the more extensive data of Swenson on a polycrystalline sample were used. The

contractions tabulated above are about 8% smaller than the average linear contractions derivable from the data of Graham, Moore, and Raynor. The

data of Hidnert and Blair, also on a polycrystalline sample, are still smaller.

.5
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Elements

T

7-Manganese ii Mercury " Molybdenum Nickel Niobium « PaDadium

i-'m

10' dL

L^n dT -L'234

10' dL

T ^. /I T Lin

10' dL

x^293 u ± ^293

70' dL

/j293 fl i ^Q,i293-Lr Lin

10' dL

X/293 u 1 ^^^Lm-Lr

Liiz

10' dL

ij293 u J

deg K d€g ^ K Q€Q ^ iV dcQ~^ JC (leg ' J\. 0 "257 0

a 844 0

a 95 0

a 224 0a 143 0

a 241 0

10 a 841 a7 a 94. 9 aO. 01 20 a 257 a 0. 3 830 a 15 a nfi

. UD 224 a 143 a 241 a" A K U. 0 30 "256 a 0. 7 ^ 812 a 21 a 0/1 7 a 2 a 224 ^ . 5

a 143 a 0 9 a 240 a" 1 ^* 1. o 40 »255 a 1. 4

a" 7QQ iOO a 94 4a 223 a 1 0 a 141 a 1 7 a 238 a 2 5

50 6 253 a 2.4 a 760 a 29 a 93.

a.

a 221 a 1.9 a 139 a 2. 4 a 235 "3.8

60 |>250 a 3. 5

a 730 a 31 a 92. 7 a 1.2 a 219 a 2. 8

a 137 a 3.1 a 231 a 4.

70 " 246 * 4. 5

a» RQ7 oy/ » oo a 91 3 a 2 ya 216 a 3 8 133 3 6 a 225 a Q 80 a 241 ^ 5. 5 663 a 34. 5

a 2 1 211 a 4 7 129 ua 219 a ft 7 SO >235 * 6- 3 628 35.

Q7 1 o/. 1 Z. ZUD 5. 5 125 A A 211 7 i

100 > 228 ^ 7. <i oy^i o / . u Z. OU ZUl R 1 D. A 121 204 ft 1 120 a 213 a 8.

516 38.8 78.2 3.39 187 7.5 111 5.2 187 9.0

140 a 194 a 9. 7 437 40.2 71.1 3. 77 171 8.8 99. 4 6.6 168 9.7

160 a 174 a lU. D 355 Do. Z 4 13 152 y. o 87. 7 0. y 148 180 a 152 a 11. 5 Zoo 44.

64.10. 5 75 5 D. ^ 127 in 7

200 128 12.3 176 47.8 45.6 4.63 111 11.0 63 0 6.4 105 10.9 220 103 13.

76 52. 2 36.

4. 78 88 11. 5 50 0 6.83. 3 11.

230 22 55^3 d234 0 57.2 240 76. 2 13.7 26.5 4.89 65 11.9 36 7 6.7 60. 8 11.3 260 48. 3 14.2 16.6 4.98 41 12.2 23 1 6.8 38. 0 11.4

273 29. 6 14.6 10.1 5. 02 25 . 12.3 14 1 6.9 23. 1 11.5 280 19. 3 14.7 6.6 5.04 16 12.4 9 2 6.9 15. 0 11.5 293 0. 0 15.0 0.0 5. 07 0 12.6 0. 0 7.0 0. 0 11.6 300 -10. 6 15.1 -3.6 5.09 -9 12.6 -5 0 7.0 -8. 1 11.6

Sources of Erning 1940 Carpenter and Erfling 1939 Krupkowski and Erflins' 1942 Nix and MacNair

above Oakley 1931 Nix and MacNair dellaas 1928 1942 data HiU 1935 1942 Nix and MacNair

1941 Other rels. Dewar 1902 Gruneisen and Sckell

1934 Sapper and Biltz 1931

Disch 1921 Schad and Hidnert

1919

Adenstedt 1936 Altman, Rubin, and

Johnston 1954 Aoyama and Ito 1939 Chevenard 1926 Disch 1921 Henning 1907 Simon and Bergmann

1930

Hidnert and Krider

1933 Henning 1907 Scheel 1907

a Estimated using Gruneisen correlation as explained in Introduction. Value= W(II)+?4(J-)) where and (±) signify the same property measured

b 7-Mn is a ductile form that is stable between about 1100 and 1135 °C parallel and perpendicular, respectively, to the trigonal a.xis. See table 4 when pure. It is often found as a separate phase in manganese alloys. for representative values of the (1|) and (1.) expansions.

Erfling's sample was produced by electrolytic deposition. ^ Melting point of mercury.

" Anisotropic. The above values were calculated from the relation, Mean « Also termed columbium.

6
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Elements

Platinum Rhodium Silicon Silver Sodium i> T 10» dL 10? -^293-£t 106 dL 108 dL Lm-LT 10« dL Lm-Lr 108 dL

£293 Lm dT Lm i293 d T Z/293 t293 dT X>293 Lin dT 10° —=

^-293 Lm d f

deg K deg * it deg~^ A deg~^ K deg-^ K deg-i K

0 * 195 a 160 0

a 22 0 a 413 0

a 1430 0

10 « 195 aO. OS a 413 a 0.

a 1430 a 0.7

20 " 195 »0.5 > 160 "0.09 412 a 1 a 1130 a 5 30 a 194 a 1. 5

a 160 a. 4 a 410 a 3 a 1420 a 11 40 a 192 * 2.

a 159 a. 9 21. 6 —0. 05 a 405 a 6

a 1400 a 17

50 a 189 a 3.

a 158 a 1. 7 21. 7 — .20 a 398 a 8

a 1380 a 23

60 "185 •4.7 156 = 2.5 22.0 -.41 a 389 a 10 a 13liO a 29

70 «180 "5.4 153 3.2 22.5 -.59 a 378 a 12 a 1330 a 33

80 a 174 a 6.

149 3.23. 2 — . 77 366 a 13 1290 a 38

90 168 6. 5 145 4. 5 24. 0 — . 51 353 13. 6 1250 42. 4

100 161 6.8 140 5.0 24.3 -.31 339 14.6 1210 46.3

120 147 7.3 129 5.9 24. 7 +.01 308 15.9 1110 52.4

140 132 7.

117 6. 5 24. 3 . 31 276 16. 5 998 56.9 160 116 8.

104 6. 9 23. 4 . 65 242 16. 9 881 60. 4 180 99.

8.

89. 3 7. 3 21. 7 1. 05 208 17. 3 757 63.

200 82. 4 S 5 74.7 6 19 1 1 49 173 17 7 6*^9 00. - 220 65! 0 59! 1 7^8 15^9 1^83 137 18.1 497 60.7 240 47.5 8.7 43. 4 8. 0 11. 8 2. 07 100 18.

363 67.8 260 29.6 8.8 27.2 8.1 7. 8 2. 22 63 18.8 227 68.4

273 18.0 8.8 16.6 8.2 4.8 2.28 38 19.0 137 68.6

280 11.6 8.9 10.8 8.3 3. 3 2. 30 25 19.1 89.4 68.7 293 0.0 8.9 0.0 8.4 0.

2. 32 0 19.2 0.0 68.8

300 -6.4 8.9 -5.9 8.4 -1.4 2. 33 -13 19.3 -48.2 68.8

Sources Nix and MacXalr 1942 Erfling 1939 Gibbons 1958 Ebert 1928 Sieeel and Ouimby 1938

of above Valentlner and Wallot 1915 Ni.\ and MacNair 1942 data Other refs. Dorsey 1907 Head and Laquer 1952 ErmnR 1942 Ayres 1905 Barrett 1956 Hennlng 1907 Fine 1953 Buflflngton and Latimer Dewar 1902 Onnes and Clay 1906 Simon and Bergmann 1930 1926 Swenson 1955 Scheel 1907 Valentiner and Wallot 1915 Dorsey 1907 Scheel and Heuse 1907 Henning 1907 Valentinerand Wallotl915 Keesom and Jansen 1927 Keesom and Kohler 1933 Lindemann 1911 Owen and Williams 1954 Shearer 1905

a Estimated using Gruneisen correlation as explained in Introduction.

•> It has recently been shown (Barrett 1956, Hull and Rosenberg 1959) that sodium partially transforms at low temperatures from the normal bodycentered cubic structure to close-packed hexagonal. The transformation is of the marteasitic type and is promoted by cold-working at the low temperatures. The above values include an extrapolation downwards from the

region where the bee structure is stable. The effect of the transformation on the thermal expansion is not known, but is small, inasmuch as Barrett found the densities of the two forms at 5 °K. to be the same within his experi- mental uncertainty. The fit of the Gruneisen relation to the data was not very satisfactory, and hence there is not much confidence in the extrapolated

values above.

583018—61 2 7
Table 2.1. Linear thermal contraction and coefficients of linear thermal expansion—Concluded

Elements

Tantalum Tin" (white)'' Titanium<i Tungsten Zinc* T 108 ^Jj

105 Lm-Lr 108 dL 10! Lin-LT 108 dL

108

108 dL Lm—Lr 108 dL

-t- 263 £203 iv293 W ^ -^203 T.nnt H 7* if 293 iU' y£293 r J 7T

deg K deg 1 K deg-^K deg~ * .K^ 0 « 143 0

a 447 0 a 151 0 »85.8 0 "683 0

10 " 143 "0.05 " 447 "0.7 aS5.8 a 0. 007 " 683 "0.3

20 a 143 a 0 4

a 445 a 3 151 ^ 0 08 * 86 8 a flR UD a Q 30 a 142 all a 441 a 5 151

* 3 a g5 7 a 2 * 677 a ft A(\ a a 2 0 " 433 " 9 150 . 6 * 85 3 B 6 * 667 a 1 ^

50 "138 "2.8 " 423 " 11 149 1.2 " 84.5 a 1.0 • 652 "17

60 a 135 "3.5 " 412 " 12 148 2.0 "83.3 a 1.5 "633 "21

70 a 131 "41 399 a 13 145 2 7 * 81 7 a 2 8 * 611 " 22

80 a 127 "45 385 14 2 142 3 4 79 7 a 2 2

a 9^

90 122 " 4. 9 371 15 0 139 4 0 a 77 4 a 2 4 565 23 6

100 117 5.2 356 15.6 134 4.5 • 74.8 "2.7 541 24.

120 106 5 5 324 16 4 125 5 3 69 1 3 06 492 25 3

140 95 1 5 i( 290 17.113 6 0 62. 7 3 38 440 "^6 3

1 PC\ 83 5 5 9 255 17 7 101 6 5 55 6 3 66 386 27 3

180 7L6 6^0 219 18^2 87.4 6.9 48^1 3! 89 331 28! 1

200 59.3 6.1 183 18. 7 73.2 7.3 40.1 4.07 274 28.7

220 47.0 6.2 145 19.58.3 7.6 31.9 4.20 216 29.1 240 34.4 6.3 106 19. 5 42.9 7.8 23.4 4.30 157 29.4

200 21.6 6.5 66.7 19^9 27.0 8.0 14.7 4.39 98 29.6

273 13.1 6.5 40.7 20.1 16.5 8.2 8.9 4.44 60 29.7 280 8.5 6.6 26.5 20.3 10.8 8.2 5.8 4. 46 39 29.8

293 0.0 6.6 0.0 20. 5 0.0 8.3 0.0 4.49 0 29.9

300 -4.6 6.6 -14.4 20.6 -5.9 8.4 -3.2 4.52 -21 30.0

Sources of Ni.\ and MacNair 1942 Erfling 1939 Altman, Rubin, and John- Nix and McNair 1942 Gruneisen and Goens 1924 above ston 1954 data Erfling 1942 Other refs. Disch 1921 Cohen and Olie 1910 Head and Laquer 1952 Disch 1921 Borelius and Johansson 1924 Hidnert 1929 Dorsey 1907 Hidnert 1943 Hidnert and Sweeney 1925 Dorsey 1908 Qruneisen 1910 Gruneisen 1910 Head and Laquer 1952 Lindemaim 1911 McLennan and Monljman.

1929

" Estimated using Gruneisen correlation as explained in Introduction.

i> Anisotropic. The above values were calculated from the relation, Mean

Value = !4(|I)+5^(X), where (||) and (X) signify the same property meas- ured parallel and perpendicular, respectively, to the tetragonal axis. See

table 4 for representative values of the and (±) expansions.

« ThewUs and Davey (1954) measured the lattice parameter of grey tin, a

brittle form with diamond-type lattice that is stable below 18° C. Their

data cover the range, —130 to +20 °C, and are represented by a constant expansion coefficient, dLjLdT =4.7X10-8 deg-! C. See also Cohen and Olie

(1910). The ordinary ductile variety (white tin) if pure may transform to grey tin at low ambient temperatures but is stabilized by impurities.

<< Titanium, having hexagonal crystal structure, should expand anisotropi- caUy. However, no lattice parameter or single crystal measurements are available to indicate the magnitude of this effect at low temperatures. The

above data at 100 °K or higher are based on an average of two strips cut by

Erfling perpendicular to one another from a rolled sheet. Although Altman

et al., and Head and Laquer both measured samples from bar stock of unknown history, their results were within 3% of Erfling's average values, thus

indicating that effects due to preferred orientation are small. The largest

effect of this kind was shown by a wire measured by Erfilng. Its axial expansion was as much as 13% greater than the above values. The table values below 100 °K are based on Altman et al.

0 Anisotropic. The aljove values were calculated from the relation. Mean

Value =i^(||)+?^(J.), where (||) and (±) signify the same property measured

parallel and perpendicular, respectively to the hexagonal axis. See table

4 for representative values of the (||) and (J.) expansions. The data on

polycrystalline zinc are discordant. Thus the expansion coefficient5 . of Dorsey and of Head and Laquer are as much as 20% lower than values above,

while those of Gruneisen and of Lindemann are less than one-third as great. These differences are attributable to the exceptional anisotropy of zinc combined with uncontrolled preferred orientation of the crystallites. It is evidently difficult to prevent such preferred orientation, and the expansions

of various samples of polycrystalline zinc could conceivably cover a wide

range of values between the limits set by the (|!) and (±) values.

8
Table 2.2. Linear thermal contraction and coefficients of linear thermal expansion

Alloys

Aluminum bronze ^ Beryllium copper " Brass, yellow ^ Constantan • Contracld ' German silver e T Lm

10' dL

L^idf

10' dL LmdT10' dL Lmdf

^^^Lm-Lr 10' dL T^zdf X29310' dL

'Utidf Lin-Lr

Lim

10' dL

LmdT

degK

0

1020

30

40

deg-^K

«3I6

316 316

316

315

deg-^K

0 »0.04

« .09

.5

1.4

"384

»384

383

382

380

der' K

0 •0.1

.5 1.8

3.7

269

deg-i K

» 232

a 232 232

232

231

deg-> K

0

0 0. 01 ».06

.3

.9

"376

» 376 »376

375

373

deg-^ K

0 «0.2 ».5

1.3 3.2

5060

70

80

90 265 9

313

309 304

296

287

2.7

4.3

6.5 8.4 9.6

375 368

360

350

339

5.8

7.6 9.2

10.6

11.8

258

253 247

240

4.6

5.6

6.6

7.5

230

228

224

220

214

1.8 2.8

3.9

5.0

5.9

369 362 354

345 335

5.1 6.8 8.4

9.7

10.8

100 120

140

160

180

255 235

213

189

164

10

11

1112

13

277

255

231 206

179

10.4

11.6 12.4

13.2 13.8

326

299

269

237 204

12.9

14.4

15.4

16.3 16.9

232

214

194

172

148

8.3 9.6

10.6

11.4

12.1

208

193 176

156

135

6.8

8.2

9.3

10.2 10.8

323

298 269

238

205

11.8

13.6

14.9

15.9

16.7

200

220

240 260

137

110

81

51

14

14

15

15

151

12190

57

14.5

15.2

16.0

16.7

169 13498.4

61.8

17.4

17.8

18.1 18.5

124

98.

71.8

45.0

12.6

13.0

13.3

13.5

11390.2

66.4

41.9

11.3

11.7

12.1 12.4

170

13599

62

17.3 17.8

18.1 18.3

273

280

293

300

«32

= 21 «0

a _11

• 16

' 16

« 16

« 16

35

23

0 -13

17.2

17.4

17.9

18.1

37.3

24.6 0.0 -13.3

18.7

18.8

19.0

19.1

27.3

17.8 0.0 -9.6

13.6

13.7 13.7 13.8

25.4

16.9

0.0 -9.1

12.6 12.8

13.0

13.1

3724

0 -13

18.5

18.5 18.6

18.6

Sources of above

data

Fontana 1948 Beenakker and

Swenson 1955 Altman, Rubin, and Johnston 1954 Aoyama and Ito 1939 Krupkowski and

deHaas 1928

Altman, Rubin, and Johnston 1952 Beenakker and

Swenson 1955

Other refs. Jaffee and Ramsey

1948 Beenakker and

Swenson 1955 Fraser and Hollis- Hallet 1955 Henning 1907 Keyston, MacPherson, and

Guptill 1959

Henning 1907 Krupkowski 1929

• Estimated

i> 9 Al, =s 1 Fe, 0.5 Xi, 0.5 Sn, bal. Cu. The accuracy of the original data

is e.stimated as not better than ±10%. Jaffee and Ramsey give data above 170 °K for three compositions in various physical conditions.

= 2 Be, 0.3 Co, bal. Cu (BERYLCO 25). Originally half-hard, then heat

treated for 2 hours at 200 °C. No observable difference was found in the thermal expansions for the two states of hardness.

d 65 Cu, 35 Zn.

" 50 Cu, 50 Ni. The name Constantan is applied to binary alloys in the

range, 60 to 45 Cu, 40 to 55 Ni. The most common composition is 55 Cu,

45 Ni. The above expansion data should represent all Constantans within a few percent. Small expansion anomalies of magnetic origin occur in this system. The ferromagnetic Curie points range from about 0 °K for 40% Ni

to roughly 150 °K for 55% Ni.

' 60 Ni, 15 Cr, 16 Fe, 7 Mo.

e Composition unknown. The compositions of alloys known by this name

usually lie within the limits, 45 to 62 Cu, 10 to 30 Ni, 20 to 35 Zn.

9
Table 2.2. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Alloys

Inconel ^

. Lm—Li

Lm

'229

'229 229

229

228

227 224

221

217

211

205

191 174 154

134

112

89.

65.6 41.4

25.2

16.6

0.0 -9.0

108 dL

Lm (IT

deg-' K

0

"0. 03

.3

1.0

1.9 2.8

3.8 4.8

5.7

6.5

7.9

9.1 10.0

10.7

11.2

11.6

12.0

12.3

12.5 12.6

12.9

13.0

Invar "

, Lm—Lr

'52

5252

62

52

52

52

5150

49

47

4339

34

29

23

1814

5.2

3.4

0-1.8

Monel <i

105

. X293— ir

Lm '

'251 '251

251

251 250

248

245

241 236

230

223

206

187 167

144

12196.4

70.9

44. 7

27.

15.

0. 0 -9.7

W_dL

Lin dT

deg-^K

0 »0.03

".2.6

1.4

2.3

3.4

4.6

5.7

6.7

7.5

10.8

11.5

12.0

12.5

12.9

13.3

13.5 13.6 13.8

13.9

Soft solder

10* Lm—Li

467

447

407

365

321 276

229

182 13383

5133

0 -18

10' dL Lm dT

deg-i K

19.6

20.0 20.7

21.4

22,2 22.9

23.5

24.

24.6

25.0

25.2

25.3

25.4

25.5

Steel, SAE 1020 '

£233

202

201

201

200

198

195

192

187

182

170

155 138

120

10180.7 59.6

37.7

22.9

15. 1 0.0 -8.3

£293 dT

der^K

0

'0.1

.3

1.4 2.3

3.1

4.0 4.8

5.5 6.8

7.8 8.7

9.4

10.4 10.8

11.

11. 4 11.5 11.7

11.9

Steel, SAE 1095 e

105 Lm—Lt

£293

213 6.7 206 6.9

199 7.2

184 7.8

168 8.3

151 8.9

132 9.8

112 10.4 90.5 11.3

67.1 12.0 42.5 12.6

26.0 12.8

17.0 12.9 0.0 13.2 -9.3 13.3

Altman, Rubin, and

Johnston 1952 Beenakker and Swenson 1955 Altman, Rubin, andJohnston 1952 Dorsey 1907 Altman, Rubin, andJohnston 1952 Werner 1924

Lucks and Deem 1958 Chevenard 1914 Gregg 1954 Masumoto 1934 Molby 1912 Scheel 1921Ackerman 1936 Aoyama and Ito 1939 Eraser and HoUisHallet 1955 Krupkowski and de Haas 1928Beenakker and Swenson 1955 Dorsey 1910 Gregg 1954

» Estimated.

b 80 Ni, 14 Cr, 6 Fe.

" The expansions of the Invar alloys are sensitive to composition and heat treatment [see Metals Handbook, ASM, 1948, pp. 601-5]. The above data

are for an alloy beUeved to be 42 Ni, 0.8 Mn, bal. Fe, annealed [Lloyd B.

Nesbitt, private communication]. Although Beenakker and Swenson re- ferred to this as "Invar", this composition appro.ximates the alloy, Dumet,

used for sealing to glass. In the iron-nickel alloy system, the minimum value

of room temperature expansion coefficient occurs at about 36% Ni.

"'67 Ni, 30 Gu, 1.5 Fe, "cold-roUed".

» 50 Pb, 50 Sn.

' 0.18 0 , 0.33 Mn, 0.01 Si, bal. Fe. According to Beenakker and Swenson,

cast iron had the same thermal expansion as 1020 steel viithin their experi- mental uncertainty of ±3X10-= in AL/L.

E The above data are the average of two German steels that appro.ximated

the specification of SAE 1095. The steels were both "hard" and could be

represented by the approximate composition: 1.1 C, 0.2 Si, 0.3 Mn, 0.02 S, 0.03 P. Their expansion coefficients differed from each other by about 10%. The expansion coefficients in the "soft" condition were also measured and

were lower than the above values by 10% at 80 °K to 16% at 300 °K.

10
Table 2.2. Linear thermal contraction and coefficients of linear thermal expansion—Continued

Alloys

T

Steel, SAE 52100 b Steel, AISI 301 <= Steel, AISI 302 d Steel, AISI 304 « Steel, AISI 310 ' Steel, AISI 316 e —Tt X5 df

J. J 10* dL

ijM df

10° dL Lm df L^ dT

7"J- 10^

L2^l

W T Ul/ df

105 dL

L^z L^ ~df

degK

n

deg-i K deg-i K deg-i ^ dcg-^ deg-i K

U >316 0 a296 0 "297 0

10 316 »0.04 296 »0. 01 297 •0.04

3) 316 • .09 296 . 02 297 s 09 316 296 . 62 297 . 0 40 315 l.i 296 1.

296 1 4

rnOU 313 2.7 294 2.3 294 2.7 50 309 4.3 291 4.3 290 4.3

< U 304 6.285 6.

285 6.

198 6.2 296 8.3 279 7. 5 277 8.

90 192 6.6 267 9.6 287 9.6 271 8.

246 g g 269 9.

lUU 185 6.9 257 10.1 277 10.4 261 9.6 237 9 1 259 10.2 120 171 7.3 236 11.0 255 11.

241 10. 9 218 g g 237 11 3 140 156 7.6 213 U.8 231 1Z4 218 12. 0 198 10 7 214 12.

160 140 8 2 188 12 5 206 13.2 193 12'176 11 4 189 12 7 180 123 8.9 163 13.1 179 13.8 167 13; 4 152 12 1 163 13.2

oivt ^JU 105 9.7 136 13.6 151 14.5 139 14.0 127 12 7 136 13.6 oon —zu 84.4 10.6 109 14.1 121 15.2 111 14.5 101 13 2 109 14.1 240 62.4 11.3 80.1 14.5 89.6 16.0 81.7 14.9 74.5 13 6 SO.l 14.5 260 39.4 11.7 50.5 15.0 57.0 16.7 51.4 15.3 46.9 14 0 50.6 15.0

273 24.0 11.9 30.9 15.3 35.0 17.2 31.4 15. 5 28.6 14 2 30.9 15.3 280 15.6 12.0 20.2 15.4 22.9 17.4 20.5 15.6 18.7 14 3 20.2 15.4 293 0.0 12.1 0.0 15.7 0.0 17.9 0.0 15.9 0.0 14 5 0.0 15.7 300 -8.5 12.1 -11.0 15.8 -12.7 18.1 -11.1 16.0 -10.2 14 6 -11.0 15.8

Sources of above

data

Werner 1924 Forman 1950 Beenakker and

Swenson 1955 Altman, Rubin, and

Johnston 1954 Beenakker and Swenson 1955

Ftmnan 1950 Beenakker and Swenson 1955

Other refc. Lucks and Deem 1958 Fontana 1948 Fontana, Bishop, and Spretnak 1953 Furman 1950

Furman 1950 Lucks and Deem

195S

» Estimated.

>> The measurements were made on a German steel that approximated the

specifications of SAE 52100. Its composition was 0.94 C, 0.27 Si, 0.34 Mn,

0.95 Cr, bal. Fe. The above data adequat«ly represent two "hard" samples, one of which was "heated at 780 °C", the other "quenched from 850 °C in

oil and tempered at 630 °C". The e.tpansion coefficients in the "soft" condition were also measured and were about 8% lower than the above

values at SO "K, about the same from 125 to 200 °K, and about 10% lower at

300 ^ K

'0.13'C, 0.80 Mn, 0.54 Si, 16.9 Cr, 7.25 Xi, bal. Fe. Annealed 30 min at

1950 "^F and water quenched. After c-ooling to SO °K and rewarming to room

temperature a small permanent expansion was fovmd to have occurred due

to irreversible formation of ferrite.

d Composition and heat treatment of sample not stated. Composition

limits for this alloy are: 0.08-0.20 C, 2 (max.) iln, 1 (max.) Si, 17-19 Cr, 8-10 Xi, bal. Fe.

« Compositionlimits for this alloy are: 0.08 (max.) C, 2 (max.) iln, 1 (max.)

Si, 18-20 Cr, 8-11 Xi. Altman et al., found small irreversible effects and, below

35 °K, small negative values of expansion coefficient. While we have given

their restilts inferior weight in this region, the effects were undoubtedly

real and attributable to martensitic transformation on cooling [Reed and

-SlikeseU, 1958]. In this alloy the extent of transformation that is produced

by cooling is sensitive to compo.^ition and has been found to vary from zero

to about sO^c [R- R- Reed, private communication]. Complete transformation would be accompanied by a mean increase in linear dimension of roughly 1% [Ward, Jepson, and Rait, 1952; and Fiedler, Averbaeh, and Cohen,

1955].

' 0.11 C, 1.51 Mn, 0.42 Si, 0.01 S, 0.02 P, 27.2 Cr, 21.6 Xi, bal. Fe. Annealed

30 min at 1950 °F and water quenched.

5 Composition and heat treatment of sample not stated. Composition

limits for this alloy are: 0.10 (max.) C, 2 (max.) Mn, 1 (mas.) Si, 16-18 Cr,

10-14 Xi, 2-3 Mo, bal. Fe.
Table 2.2. Linear thermal contraction and coefficients of linear thermal expansion—Concluded

Alloys

Steel, AISI 322 t. Steel, AISI 330 « Steel, AISI 347 a Steel, AISI 410 = Titanium, RC-130-B ' Titanium, Ti-150-A e T

108 dL 106 10' dL 105-^293 l^T 106 dL

105 106 dL

105 TM ^ 106 dL

//293 L2n dT 1/293 dT Lm Lisi dT i293 L291 dT Li'a Lm dT Lm Lm dT

d€Q K deo-i K der^ K deg-i K deg-i K deg-i K deg-i K

u » 176 0 20 176 » 0. 06

30 176 . 2

40 176 . 4

50 175 .9 60 174 1.6

70 172 2. 4 21s 5.

168 3.

80 169 3. 2 213 5. 4 164 4. 3

90 208 5.

262 9.165 4. 0 208 5.

159 4.

100 146 5 202 6.3 253 9.8 161 4.7 202 6.3 154 5.0

120 136 5 188 7. 5 233 10. 5 1.50 6. 0 187 7.143 5. 7 140 124 6 172 8. 5 211 11. 3 138 7.0 172 8.

131 6. 4 160 112 7 154 9. 3 187 12.

123 7. 7 1.55 8. 8 118 7.0 180 98 7 135 10.1 163 12.8 107 8.3 137 9.7 103 7.6

200 83 8 114 10,8 136 13.4 89.4 8.8 117 10.6 87 8.2 220 67 8 91.6 11.5 109 14.0 71.4 9.2 95 11.4 71 8.7

240 50 9 68.0 12.1 80.2 14.6 52.6 9. 5 71 12.3 53 9.2

260 32 9 43 3 12.7 50.6 15.0 33.2 9.8 40 13.1 34 9.7

27o 20 10 26.6 13.0 30.9 15.3 20. 3 10.0 28 13.7 21 10.1 280 13 10 17.4 13.2 20.2 15. 4 13.2 10. 1 19 14.0 14 10.2 293 0 10 0.0 13.6 0.0 15.6 0.0 10.3 0 14.5 0 10.5 300 -7 10 -9.6 13.8 -11.0 15.7 -7.2 . 10.4 -10 14.8 -7 10.7

Sources oi Fontana 1948 Furman 1950 Furman 1950 Altman, Euhin, and Bishop, Spretnak, Bishop, Spretnak, above Johnston 1952 and Fontana 1953 i> and Fontana 1953 t data

Other refs. Lucks and Deem 1958

» Estimated.

b 0.07 C, 0.43 Mn, 0.53 Si, 17.0 Cr, 6.5 Ni, 0.12 Al, 0.37 Ti, bal. Fe. "Air

cooled from 1900 °F and aged at 1000 °F for 40 min." These data are of a lower order of accuracy than the other data on steels in table 2.2. "0.05 C, 1.81 Mn, 0.62 Si, 0.006 S, 0.006 P, 15.3 Cr, 35.2 Ni, bal. Fe. Annealed 30 min at 1950 °F and water quenched.

<i 0.07 C, 1.74 Mn, 0..56 Si, 0.006 S, 0.019 P, 18.65 Cr, 11.3 Ni, 0.77 Nb, bal. Fe. Annealed 30 min at 1950 °F and water quenched.

= 0.09 C, 0.32 Mn, 0.36 Si, 0.01 S, 0.01 P, 12.6 Cr, 0.12 NI, 0.06 Cu, 0.03 N,

bal. Fe.

' 0.24 C, 3.8 Mn, 3.8 Al, bal. Ti. Annealed one hr at 1300 °F and air cooled.

8 0.05 (max.) C, 2.7 Cr, 1.3 Fe, 0.08 (max.) N, bal. Ti. Annealed 6 hr at

1200 °F.

h Comparison of measurements in this paper on a commercially pure

titanium with data from other sources (see Ti, table 2.1) suggests that the above data on titanium alloys may be grossly inaccurate.

12
Table 2.3. Linear thermal contractions and coefficients of linear thermal expansion

Other inorganic substances «

Carbon dioxide Pyrex Silica glass •> Ice c Indium antimonide Quartz (crystalline, ||) Magnesium oxide T 106 |j£

105 -^"r

10^ dL 10^ dL

Z'293 ~Lm dT i293 Tno, 'fpr ^293

deg K deg-^ K

• 54. 7 deg~i K deg-^ K

0 > —

8

'139 0

10 83.7 -0. 06 '139

20 266 32 55. 7 -6.60 84. 4 —0. 10 ' 139 ' 0 02

30 262 49 86.

2

—1. 72 f I3g ' 06

40 256 67 56. 7 —4. 90 87.

2

—0. 82 ' 139 '14

50 249 83 88.0 -0. 33 '1.39 '. 27 60 240 98 .56.2 -3. 02 88.2 -^0.28 '138 '.45 70 229 116 87. 6 0. 89 '138 '. 8 80 216 132 53. 7 -1.41 612 7.7 86. 4 1. 50 f ' 1. 2 90 203 147 603 10. 2 84. 6 2. 18 107 2. 7 135 ' 1 7 100 187 160 50.2 -0.12 592 12.7 82.2 2. 76 104 3.1 ' 133 '2.3

110 171 170

120 153 177 46.2 -1-0. 87 502 17.7 75. 7 3. 48 97. 7 3. 7 1 127 ' 3.

4

130 135 184

140 117 190 41. 7 1. 01 522 22. 7 68. 6 3. 83 89.

8

4. 2 ' 119 ' 4. 6

150 97 197

160 77 207 37.2 2.08 471 27.7 60.

8

4. 08 80.

9

4.

7

109 5.

6

170 56 230

180 31 272 32.

2

2. 32 411 32. 7 52.

6

4. 27 71.

2

5.

1

97 6. 6 190 0 351

200 27. 2 2. 36 341 37.6 43.9 4.43 60.5 5.5 83 7.4 220 21. 7 2.18 261 42.6 34.8 4.58 49.1 5.9 67 8.1 240 15.7 1..S1 171 47.6 25.6 4. 71 36.7 6.4 61 8.8

260 10. 2 1. 26 70 52. 6 16.2 4.83 23.6 6.8 33 9.4

273 6.2 0. 81 0 55.8 9.8 4. 91 14.6 7.1 20 9.7

280 4. 2 0. 54 6.5 4.95 9.6 7.2 13 9.9

293 0.0 0.0 0.0 5.01 0.0 7.5 0 10.2 300 -2.3 -0. 29 -3.5 5. 04 -5.3 7.6 -7 10.3

Sources of Keesom and Kohler Head and Keesom and Powell 1958 Gibbons 1958 BufEngton and Durand 1936 above 1933-4 Laquer Doborzyn- Latimer 1926 data Maass and Barnes 1952 ski 1934

1926 Scheel and

Heuse 1914 Other Keesom and KoMer BuflBngton Beattie et al. Dennison 1921 Potter 1956 Dorsey 1908

refs. 1933 and Lati- 1941 Dewar 1902 Lindemann 1912 mer 1926 Dorsey 1907 Jakob and Erk 1928 Nix and MacNair

Tool and Head and Konie 1944 1941 Saunders Laquer 19.52 Lisgarten and Black- Scheel 1907

1948 Henning 1907 man 1956 Sosman 1927 Winter- Scheel 1907 Lonsdale 1958 Klein Scott 1933 Shallcross and

1950 Sosman 1927 Carpenter 1957 Souder and

Hidnert

1926 Valentiner and Wallot

1915

" Estimated.

>> The thermal expansion of siUca glass (fused silica, vitreous siUca, quartz

glass), though small, is variable from sample to sample. The aljove values

are thought to be fairly representative of average behavior. The temperature of minimum length can vary from 180 to 230° K. Variations from the above values as large as 2X10-5 below 180 °K and 50% from 180 to 300 °K

are possible.

= According to Powell, ice is slightly anisotropic, the expansion coeflBcients

parallel and normal to the optic axis ditfering by about IXIO"' deg-i K. The above values are an average over all directions. The only other extended investigation [Jakob and Erk] is not in good agreement with Powell and found negative expansion coelBcients below about 70 °K. Measured parallel to the optic axis. Nix and MacNair measured expansions perpendicular to the optic axis but presented only a coarse graph of the results, from which the following values of W{dLjLd T) were taken: 7 at

100 °K, 10 at 1.50°, 12 at 200°, 13 at 250°, 14 at 300 "K.

« Ebert [1928] has given two isolated data for ruby mica measured in the lamination plane. These are as follows: 105(^273— i83)/il^273=120 and 10H£!73

-X20)/i273 =135.

' Extrapolated using Gruneisen correlation as explained in Introduction.

13
Table 2.4. Linear thermal contractions

Plastics and elastomers "

T

Av^ilrHi'ii b 1 ^.1, i.ii, 1 1 1 1 " J. imJUJLuciic -L-JdMllIJcH-. ^ T -f h ijUCllG M 1 Pn yion ' i aneiyteji

Jr a,iieiytG _L 501 rod F 4129 942 942

Q 1061 849 282 428 1135 1202 1134 1389 364 cWO 20 1051 835 279 422 1114 1188 1123 1379 362 824

40 1022 811 271 407 1070 1154 1092 1352 355 cm

60 983 779 261 388 1019 1104 1048 1308 344 770 80 935 740 248 366 9G2 1042 995 1247 329 733

100 880 695 233 342 900 971 936 1172 310 689

120 819 644 215 315 834 893 869 1088 288 639

140 ^ 751 588 194 286 763 811 796 996 263 584

160 676 528 172 255 686 724 717 896 236 524

180 594 464 148 222 604 G32 632 789 207 459

200 505 397 123 187 517 535 540 673 176 389

220 410 325 98 150 424 432 441 648 143 314

240 308 247 72 111 324 323 335 412 108 235

260 199 161 45 70 214 207 220 265 70 151

273 122 100 27 42 134 120 130 161 43 93 280 81 67 18 28 90 84 91 107 29 62

293 0 0 0 0 0 0 0 0 0 0 300 -46 -40 -9 -15 -52 -47 -53 -61 -15 -32

« Data from Laquer and Head [1952].

b Epoxy casting resin made by Ciba Co. 40 g of the material was catalyzed with 2 ml triethanolamlne. Cured 8 hr at 120 ° C and then 24 hr at 180 ° C.

0 Phenolic plastic made by Catalin Corp. of Am. in. diameter rod.

d Glass fiber reinforced, molded polyester rod, 0.146 in. diameter, made hy

Dynakon Corp., Cleveland, Ohio.

e Same except H in. thick sheet.

' Polychlorotrifluoroethylene. The samples were, respectively, from a 5

in. diameter rod of Fluorothene made by Union Carbon and Carbide and

from a He in. thick sheet of Kel-F made by M. W. Kellog and Co.

e An unsaturated polyester made by American Cyanamide Co. Catalyzed

with 0.5 wt. % of tert. butyl hvdroperoxide. Cured 48 hr at room temperature followed by 1 hr at 100 ° C.

> Polymethylmethacrylate. "Probably Du Pont Lucite". Average of two samples from rod stock.

' From H in. diameter rod. "Probably E. I. Du Pont de Nemours and

Co., grade FM-1".

> From a 1 in. diameter rod, grade 942. This is a molded, cloth-base, lami- nated phenolic made by Panelyte Div., St. Regis Paper Co. Measured parallel to the lamination and normal to the rod axis. Same except measured normal to both the lamination and the rod axis.

Plastics and elastomers »

10Hi293- ir)/X203 T

Plexiglas ^ Polystyrene " Polythene ^ Rubber,

hard

Rubber,'

Silastic 160 Selectron e 5026 Teflon i> Tenite I

i Tenite II i Vinylite ^

deg K

020

4060

80

1220 1210

1160

1110

1050

1550

1522 1466

1394

1308

2449

2439

2404 2349

2279

1272

1263

1240 1213

1174

2301 2296

2276

2231 2161

1319

1305 1270

1217

1150

2140

2110

2060 2000

1930

18.50 1830

1785 1730

1070

2304

2284

2244

2189 2114

1303 1288

1249

1193 1125

100

120 140

160 180

990

930

860

780 690

1211

1105 992

874

752

2194

2089

1964 1814

1639

1128

1069

1001 942

834

2066

1951 1816

1656 1466

1075 994

907 815

718

1850

1760

1660

1540 1400

1600

1520 1425 1315

1190

2019 1904

1764

1604 1424

1050 969

882

789

691

200 220

240

260

590 490

370 240

626

499

368

232

1439

1199 919

594

736

625

501 364

1246

996

721

441

615

505 380

256

1240

1050 855

645

1045

880

690

465

1219

994

749

484

587 475

354

225

273

280

293

298 300

150

99

0 -55

14193

0 -51

359

239

0 -131

256

1810 -117

256

165

0 -119

164

112

0 -69

500

0

290

195

0 -115

299

199

0 -111

136

90

0 -50

a Data from Laquer and Head [1952] except as otherwise noted. (In addition to the substances listed in the table, data have been given for 16 specially compounded rubbers by Dunsmoor et al. [1958] and Trepus et al. [1959]. These data consist mainly of values of (L2n—Ln)ILm. See also Wood, Bekkedahl, and Peters [1939].) Polymethylmethacrylate made by Rohm and Haas Co. Data from

Giauque, Geballe, Lyon, and Fritz [1952].

" Average of two samples from rod stock, both "probably American Phenolic Corp. grade 912A".

d Polyethylene made by E. I. Du Pont de Nemours and Co. Molded

under 2000 psi pressme at 150 °C for 10 mln. Directional variations were

negligible. See also Hunter and Oakes [1945]. Five filled polythenes were measured by Head and Laquer [1952].

' Measured normal to a 1 in. thick slab made by W. H. Salisbury and

Co. Shore hardness was 90 on the A2 scale. See also Dorsey [1908].

' A silicone rubber, hardness 77, made by Dow Corning Corp. Molded

under 200 psi at 120 °C for 10 min. Cured 15 hr at 150 °C, 7 hr at 200 °C, and 17 hr at 250 °C. A similar sample that was uncured had a hardness of 48 on the Shore A2 scale. It was too soft to measure closer than ±25%.

Within these limits it was the same as the harder sample.

B An unsaturated polyester made by Columbia Resins Div., Pittsburgh

Plate Glass Co. Catalyzed with 0.5 wt % tert. butyl hydroperoxide. Cured

48 hr at room temperature, then 1 hr at 100 °C.

h Polytetrafluoroethylene. Extruded and annealed sample measured by

Kirby [1950]. He found that strained samples could have expansions larger or smaller than those of annealed Teflon, the differences being as large as 20%. Laquer and Head [1952] measured two samples of Du Pont Teflon rod taken normal and parallel to the extrusion direction. The expansions parallel were roughly 15%, larger than those normal, and the average is 10 to 15%

larger than the above data by Kirby. The data of Laquer and Head were

used only to guide the extrapolation of Kirby's values below 80 "K. Teflon has a first order transition at 20 °C. Therefore we use 25 °C as a reference temperature and tabulate W^l^Lim— Lt)I Lm above.

' Formula 0072-MS. A cellulose acetate made by Tennessee Eastman

Corp. Molded under 6000 psi pressm-e at 150 °C for 20 min.

i Formula 205A-MS. Otherwise same as above.

^ Average of two types with nearly identical expansions made by Bakelite

Corp.: (D'VYDR. 95% vinyl chloride, 5% vinyl acetate. Stabilized with

5 wt % dibutyl tin maleate and molded under 6500 psi pressure at 150 °C for

5 min. (2) VMCH. 86% vinyl chloride, 13% vinyl acetate, M% dicarboxylic

acid. Stabilized with 5 wt % dibutyl tin maleate and molded under 5000

psi pressure at 130 °C for 30 min.

14
Table 3. Miscellaneous substances

3.1. Mostly alloys. Data from Gregg [1954]

Substance

High speed steel (18 W, 4 Cr, 1 V) High speed steel (6 W, 5 Mo, 4 Cr, 2 V) High speed steel (18 W, 4 Cr, 2 V, 9 Co) High speed steel (5 W, 4 Cr, 4 V, 4 Mo)

High speed steel (4 W, 5 Mo, 4 Cr, 1 V, 12 Co) Tool steel (1.10 C) Tool steel (0.90 C, 1.20 Mn, 0.50 Cr, 0.50 W)

Tool steel (0.50 C, 0.90 Cr, 1.25 VT) Tool steel (2.25 C, 12.00 Cr, 1.00 Mo)

Chrome vanadium steel (SAE 6150) Aluminum (25) Cast aUoy (20 Co, 8 W, 7 Mo, 5 Cr, 2 V, 0.7 C, .7 B, bal. Ee) Cast aUoy (44 Co, 17 W, 33 Cr, 2.25 C, 2 Fe) Carboloy (Grade 44 A)

Bronze > (SAE 660) Cast iron t ^

Rockwell Hardness

C 63 C 64 C 65 C 64 C 67 C 66 C 63 C 66 C 64 C 58 H 64 C 69 C 58 A 91 F 78 B 85

10* (i294 —iT)/£294

7"= 194 °K

111110

1310

12

12

12

13

1322

9

10

2

19

11

r=166 °K

14

13

1316

12

14

14

15

14

1528

1113

322

13

T=77 °K

20

20

1823

16

20

20

18

20

22

31

1518

33

19

" See also Henning [1907]. •> See also Beenakker and Swenson [1955], Chevenard [1926].

3.2. Various alloys. Data from Lucks and Deem [1958]

Substance * Condition

10' (£293— ir)/i283

r=200 °K r=144 °K T=116 °K

Aluminum, 2024 » (4.5 Cu, 1.5 Mg, 0.6 Mn)..

Aluminum, 7075 » (5.5 Zn, 2.5 Mg, 1.5 Cu,

0.3 Cr, 0.2 Mn).

Inconel-X (73 Ni, 15 Cr, 7 Fe, 2.5 Ti, 1 Cb,

0.7 Al, 0.4 Si, 0.5 Mn).

Magnesium, .\X-M-29 (3 Al, 1 Zn, 0.3 Mn).. "K" Monel = (66 Xi, 29 Cu, 2.75 Al, 0.9 Fe,

0.75 Mn, 0.5 Si, 0.15 C, 0.005 S). Steel, SAE 1010 (0.10 C, 0.5 Mn)

T 4 «. 194

185

113

'-231 115

98

294

276

176

i>353 176

148

345 314

206

b 408 206

172

T 6 « Hot rolled. Solution treated 3 hr at 2100 °F, air cooled. Double

aged 24 hr at 1550 °F, air cooled; 20 hr at 1300 °r, air cooled. Hot rolled. Annealed 1 hr at 600 °F. Furnace cooled Hot rolled. Aimealed 1 hr at 1650 "F. Water quenched Hot rolled

« See also Fontana [1948, 1953].

t" Average of three mutually perpendicular orientations. Values in the

rolling direction were 2% lower; values in the rolling plane but transverse

to the rolling direction were 5% lower; values normal to the rolling plane were 7% higher.

= K-Monel has a Curie point at about 160 °K. The above data are too sparse to indicate if there is an appreciable anomaly in the expansion at the Curie point.

<i The compositions given are nominal or average ones for these alloys. They were taken from the ASM Metals Handbook, 1948 edition, in which

alloy 2024 is listed as alloy 24S, alloy 7075 is listed as alloy 75S and magnesium

AN-M-29 is listed as alloy AZ31X.

' Solution treatment and precipitation. See ASM Metals Handbook for

details.

3.3. Optical glasses. Data from Molby [1949] "

10=^ T

Crown

C-1 »

Borosilicate crown BSC-1 »Borosilicate crown BSC-2 »Light barium crown LBC-2 »Dense

barium crown DBC-1 a

Dense

barium

crown DBC-3 »

Dense

flint DF2 »

Extra

dense

flint EDF-3 «

Barium

flint BF-1 »

Crown

flint CF-1 » Glass

#11 b Glass

#32 b Glass

#33 b Glass#45 b

deg K

80 134 133 112 137 110 105 136 139 142 110 100 102 92 96

90 130 128 109 132 107 101 131 135 137 107 97 99 90 94

100 126 124 105 128 104 98 126 130 133 104 94 96 87 91

120 116 114 97 117 95 90 115 118 122 95 88 89 83 85 140 106 104 88 106 87 82 104 106 111 87 80 81 74 78 160 95 92 77 95 77 73 92 94 98 77 72 72 66 70

180 82 80 66 82 67 63 79 81 85 67 63 63 58 62 200 69 67 57 68 56 53 66 67 71 56 53 53 49 52 220 55 53 45 54 44 42 52 53 56 44 42 42 39 42

240 41 39 33 40 33 31 38 39 41 33 31 31 29 31 260 26 25 21 25 21 20 24 25 26 21 20 20 18 20 273 16 15 13 15 13 12 15 15 16 13 12 12 11 12

280 10 10 8 10 8 8 9 10 10 8 8 8 7 8 293 0 0 0 0 0 0 0 0 0 0 0 0 0 0 300 -6 -6 -5 -5 —5 -4 -5 -5 -5 -5 -4 -4 -4 -4

» Bausch and Lomb Co. designation. Composition was not given. ° Dorsey [1907] also gives data on a crown glass. Composition not stated,

b Eastman Kodak Co. designation. Composition was not given.

15
Table 4. Anisotropy of single crystals

i.l.^ Antimony, beryllium, bismuth, tin (white)

10« L2-L\

L7n T2—.T1

T2 Antimony Beryllium Bismuth Tin (white)

II ± H X II X n X

deo K deg K rfcg-i K deg-i K deg-i K deg-' K deg-' K deg-' K deg-' K deg-' K

293 273 16. 18 8.24 8. 59 11.70 16. 20 11. 00 28. 99 15. 83 273 ZOO 16. 17 8.11 7. 58 10. 73 16. 20 11. 53 27. 98 15.60

193 16. 15 7. 84 5. 81 8. 65 10. 20 11.38 26. 67 15. 00

193 163 16. 11 7. 43 3. 97 6. 09 16. 08 11. 04 26. 69 14. 22

153 113 16. 09 6. 78 2. 07 3. 45 15. 94 10. 59 24.44 13. 08

113 90 15. 81 6. 04 0. 73 1.58 15. 86 9. 89 23. 23 11.79

90 78 15. 48 6. 27 0. 79 15. 56 9. 25 22. 45 10.66 90 67 0. 13

78 58 14.7 4.2 14.9 8.5 26. 57 8. 58

58 20 13.3 5.1

» The tabulated values are average expansion coefficients in the intervals, mony, bismuth), hexagonal (beryUium), or tetragonal (tin) axis. The data

Ti to T2, measured parallel and normal, respectively, to the trigonal (antl- are from Erfling [1939].

4.2. » Cadmium, zinc

Ti

108 Lm

Cadmium Zinc

II X II X

degK deg K deg-' K deg-' K deg-' K deg-' K

293 253 54.3 19.1 64. 3 +12.5

253 213 55.4 17.8 6.5.1 11.3 213 173 56.7 16.4 65.4 10.

1

173 133 58.0 14.6 65.6 8.3

133 93 58.9 11.7 64.4 +5.0

86 20 54.5 3.6 52.6 -2.1

"The tabulated values are average expansion coefficients in the intervals, T\ to T2, measured parallel and normal, respectively, to the hexagonal axis. The data are from Gruneisen and Goens [1924].

4.3. » Magnesium

T2

109 ^293

II

L2—L\

T2-T1

X

degK degK deg-' K deg-' K

293 193 25.7 24.3

193 90 20.3 18.8

90 78 13.8 13.0

78 20 5. 88 5. 38

^The tabulated values are average expansion coefficients in the intervals, Ti to T2, measured parallel and normal, respectively to the hexagonal axis. The data are from Goens and Schmid [1936].

4.4. Mercury

T

lOSXEx

coefl Musion

cient" Source

II X

degK

168 113 83 to 113

86 to 194

deg-' K

49.8

44.9

42.6

47.0

deg-' K

37.7

35.2

33.4 37.5

Hill [1935] Hill [1935) Hill [1935] Gruneisen and SckeU [1934]

»The first two lines give instantaneous expan.sion coefficients, Wi^idLjLdT),

while the last two lines give average expansion coefficients, {W^IL)[(L2—Ia)I (T2— Ti)], in the indicated temperature intervals. The directions of measure- ment were parallel and normal, respectively, to the trigonal axis.

References ^

Ackerman, D. E., Properties of Monel at low temperatures,

Metal Progr. 30, No. 5, 56-60 (1936). [105 to 300 °K.]

Adenstedt, H., Thermal expansion of solids at low temperatures (Cu, Ni, Fe, zincblende, LiF, calcite, aragonite,

NH4C1), Ann. Physik 26, 69-96 (1936). [20 to 273 °K.

In German.]

*van Agt, F. P. G., and H. K. Onnes, On the measurement

of very low temperatures. XXXII. The thermal

expansion of Jena glass 16 III, Leiden Comm. No. 176a

(1925). [20 to 371 °K.]

Altman, H. W., T. Rubin, and H. L. Johnston, Coefficients

of thermal expansion of solids at low temperatures.

II. The thermal expansion of Monel, Inconel, Contracid, SAE 1020 low carbon steel and type 410 stainless

steel. Report TR 264-19 (1952). Cryogenic Laboratory, The Ohio State University. ASTIA Document

ATI 158988. [20 to 300 °K.]

Altman, H. W., T. Rubin, and H. L. Johnston, Coefficientof thermal expansion of solids at low temperatures.

III. The thermal expansion of pure metals, with the data for aluminum, nickel, titanium and zirconium,

Ohio State U. Tech. Report 264-27 (1954). ASTIA

Document AD 26970. [15 to 300 °K.]

Altman, H. W., T. Rubin, and H. L. Johnston, Coefficient

of thermal expansion of solids at low temperatures. IV. The thermal expansion of type 304 stainless steel and

yellow brass. Report TR 264-28 (1954). Cryogenic

Laboratory, The Ohio State University. ASTIA

Document AD 31268. [14 to 300 °K.]

Aoyama, S., and T. Ito, Thermal expansion of nickel- copper allovs at low temperatures (Part I), Sci. Repts.

Tohoku Uiiiv. 27, 348-364 (1939). [Ni, Cu, 13 Ni-Cu

alloys. 77 to 273 °K. In English.]

Armstrong, P. E., O. N. Carlson, and J. F. Smith,

Elastic constants of thorium single crystals in the range

77 — 400 "K, J. Appl. Phys. 30, 36-41 (1959) . [Includes

thermal expansion, 80 to 400 °K.]

Austin, J. B., H. Saini, J. Weigle, and R. H. H. Pierce, A

direct comparison on a crystal of calcite of the X-ray

and optical interferometer methods of determining

linear thermal expansion. Phj^s. Rev. 57, 931 (1940).

[Room temperature.]

Ayres, H. D., Coefficients of linear expansion at low

temperatures, Phvs. Rev. 20, 38-51 (1905). [Al, Ag. 86 to 372 °K.]

1 References are arranged alphabetically by authors. The prefix (*) in- dicates selected references not referred to in the text or tables. The prefix (I') indicates references devoted primarily to experimental techniques. Titles

in foreign languages have been freely translated in order to indicate content and have been supplemented where necessary by additional indications of content placed in brackets.

16
*Banister, J. R., S. Legvold, and F. H. Spedding, Structure

of Gd, Dv, Er at low temperatures, Phys. Rev. 94, 1140-2 (1954). [XaCl, Gd, Dy, Er. 42 to 300 °K.]

*Barrett, C. S., Crystal structure of barium and europium

at 293, 78, and 5°K, J. Chem. Phys. 25, 1123 (1956). Barrett, C. S., X-ray study of the alkali metals at low

temperature, Acta'Crvst. 9, 671-7 (1956). [Na, Li, K,

Rb, Cs. 5 to 78 °K.]

Barron, T. H. K., On the thermal exnansion of solids at low temperatures, Phil. Mag. 46, 720-734 (1955). [Theoret.]

Barron, T. H. K., Low temperature deviations from

Gruneisen's theory of the thermal expansion of solids. Conf. Phvs. Basses Temps., Paris (1955), Annexe

1955-3, Suppl. Bull. inst. intern, froid, pp. 448-452.

[Theoret. In English.]

*Barron, T. H. K., Gruniesen parameters for the equation

of state of solids, Ann. Phys. 1, 77-90 (1957). [Theoret.]

*Barson, F., S. Legvold, and F. H. Spedding, A low

temperature dilatometric study of some rare-earth

metals, AEG Publ. No. ISC-424 (1953). Tech. Inform.

Serv., Oak Rid-e, Tenn. [La, Pr, Nd, Gd, Dy, Er. 100 to 350 °K.]

*Barson, F., S. Legvold, and F. H. Spedding, Thermal

expansion of rare earth metals, Phvs. Rev. 105, 418-

424 (1957). [Gd, Tb, Dy: 120 °K and up. La, Ce,

Pr, Nd, Er, Yb; 300 °K and up.]

Baskin, Y., and L. Meyer, Lattice constants of graphite

at low temperatures, Phys. Rev. 100, 544 (1955). [4 to 297 °K.]

Beattie, J. A., B. E. Blaisdell, J. Kaye, H. T. Gerry, and

C. A. Johnson, An experimental study of absolute temperature scale. VIII. The thermal expansion and compressibility of vitreous silica and the thermal dilatation

of mercurv, Proc. Am. Acad. Arts Sci., 74, 371 ('1941).

[Silica glass. -200 to 4-450 °C.] Beenakker, J. J. M., and C. A. Swenson, Total thermal

contractions of some technical metals to 4.2 °K, Rev.

Sci. Instr. 26, 1204-5 (1955). [Brass, german silver, Cu, beryllium-copper, stainless steels 302-304-316, 70 Cu-30 Ni, cast iron, cold-rolled steel, 1020 steel. Invar.]

*Bekkedahl, N., Forms of rubber as indicated by temperature-volume relationship, J. Research NBS 13, 411-431

(1934). [Natural rubber hydrocarbon. 83 to 330 °K.]

Berry, C. R., Effect of internal strains on linear expansion,

x-ray lattice constant, and densitv of crystals, J. Appl.

Phys. 24, 658 (1953). [Review.]"

*Bijl, D., The thermal expansion of some simple solids at low temperatures. Conf. Phys. Basses Temps., Paris

(1955), Annexe 1955-3, Suppl. Bull. inst. interr. froid, pp. 445-7. [Variation of the Gruneisen constant with

temperature for Ag, Al, Cu, Fe, KBr. In English.]

Bijl, D., The representation of specific heat and thermal

expansion data of simple solids. Progress in Low

Temperature Physics, Vol. II (1957), pp. 395-430.

[Review.]

Bijl, D., and H. Pullan, Thermal expansion of simple

solids at low temperatures and Gruneisen's law, Phil.

ISIag. 45, 290-4 (19.54). [Cu, Al, Fe. Theoret.]

Bijl, D., and H. Pullan, A new method for measuring the thermal expansion of sohds at low temperatures; The

thermal e.xpansion of copper and aluminum and the Gruneisen rule, Phvsica 21, 285-298 (1955). [Cu, Al. 20 to 273 °K.]

*Biltz, W., W. Fischer, and E. Wunnenberg, Molecular

and atomic volumes. 25. Volumes of organic crystals

at low temperatures, Z. physik. Chem. 151, 13-55

(1930). [Two score organic substances. 78° and up. in German.]

*Biltz, W., and A. Sapper, Molecular and atomic volumes.

34. Low temperature densities of some hahdes of elements of the fourth through the sixth group, Z. anorg. u. allgem. Chem. 203, 277-306 (1932). [78 and

194 °K. In German.]

Bishop, S. M., J. W. Spretnak, and M. G. Fontana,

Mechanical properties, including fatigue of titaniumbase alloys RC-130-B and Ti-150-A at verj low

temperatures. Trans. Am. Soc. Metals 45, 993-1007

(1953). [77 to 293 °K.]

T Black, I. A., L. H. Bolz, F. P. Brooks, F. A. Mauer, and

H. S. Peiser, A liquid-hehum cold cell for use with an

x-ray diffractometer, J. Research NBS 61, 367-371

(1958). *Blackman, M., On the thermal expansion of solids, Proc. Phys. Soc. B70, 827 (1957). [Theoret.] ^^Blackman, M., On negative volume expansion coefficients, Phil. Mag. 3, 831-8 (1958). [Theoret.] Boas, W., and R. W. K. Honeycombe, The anisotropy of thermal expansion as a cause of deformation in metals and alloys, Proc. Roy. Soc. A188, 427 (1947). [Sn, Cd, Zn, and alloys. 83 °K and up.]

Borelius, G., and C. H. Johansson, Expansion measure- ments at low temperatures with double mirror dila- tometer, Ann. Physik 75, 23-36 (1924). [Cu, Zn, Cd.

103 to 273 °K. In German.]

Buffington, R. M., and W. M. Latimer, The measurement

of coefficients of expansion at low temperatures; Some

thermodynamic applications of expansion data, J. Am.

Chem. Soc. 48, 2305-19 (1926). [Al, Ag, Cu, Pyrex,

NaCl, quartz. 85 to 300 °K.]

Calhoun, B. A., and S. C. Abrahams, A low temperature

adaptor for the Norelco High Angle Spectrometer, Rev. Sci. Instr. 24, 397 (1953). [78 °K and up].

Carpenter, L. G., and F. H. Oakley, Thermal expansion

and atomic heat of solid mercurv, Phil. Mag. 12, 511

(1931). [183 to 231 °K.]

*Cheesman, G. II., and C. M. Soane, The lattice constants of the inert elements, Proc. Phys. Soc. B70,

700-2 (1957). [Xe, Kr. 58 to 89 °K.]

Chevenard, P., Nickel steels. Rev. m^t. 11, 841-862 (1914)

[Fe-Ni alloys. 20 °K and up. In French.]

Chevenard, P., Thermal anomalies of certain solid solutions, J. Inst. Metals 36, 39-62 (1926). [Cast iron, Ni, Ni-Cr alloys. 120 °K and up.]

TChilds, B. G., The preparation of metal single crystals

for expansion measurements, J. Sci. Instr. 27, 102

(1950). *Childs, B. G., The thermal expansion of anisotropic

metals. Revs. Modern Phys. 25, 665-70 (1953V

[Review.]

Cohen, E., and J. Olie, Atomic volumes of allotropic modifications at very low temperatures. I., Z. physik.

Chem. 71, 385-400 (1910) or Leiden Comm. No. 113. [Diamond, graphite, white tin, gray tin. 110 to 291 '^K. Latter ref. in English.]

Connell, L. F., and H. C. Martin, Concerning reported

discrepancies between x-ray and macroscopic measure- ments of thermal expansion of some alkali halides, Acta

Cryst. 4, 75-6 (1951). [KI, KBr. 293 to 473 °K.]

Corliss, L. M., J. M. Hastings, and R. J. Weiss, Antiphase

antiferromagnetic structure of chromium, Phys. Rev.

Letters 3, 211-2 (1959). Corruccini, R. J., and J. J. Gniewek, Specific heats and

enthalpies of technical solids at low temperatures: a

compilation from the literature. NBS Mono. 21 (1960). *Cruikshank, D. W. J., E. Mendoza, and J. H. Robertson,

Summarized proceedings of a conference on low temperature crystallography—Oxford, April 1956. Brit. J. Appl. Phys. 7, 425 (1956). [Includes unpubl. data by

Dobbs on Kr at 75 to 105 °K.]

*Davies, R. 0., and G. 0. Jones, Thermodynamic and

kinetic properties of glasses. Advances in Phys. 2, 370

C1953). [Review. Illustrates the eff'ect of glass transi- tions on dilatation.! *Dayal, B., The theory of the thermal expansion ot dia- mond, Proc. Indian Acad. Sci. A20, 187-191 (1944). *Dayal, B., The thermal expansion of metals at low

temperatures, Proc. Indian Acad. Sci. A20, 192-9 (1944). [Theoret.)

*Dayal, B., Theory of the thermal expansion of the alkali halides, Proc. Indian Acad. Sci. A20, 145-154 (1944). [NaCl, KCl, KBr.]

Dennison, D. M., The crystal structure of ice, Phys. Rev.

17, 20 (1921). [83 "K.]

Dewar, J., Coefficients of the cubical expansion of ice, hydrated salts, solid carbonic acid and other substances

at low temperatures, Proc. Roy. Soc. 70, 237-246 (1902).

[27 miscellaneous substances. 84 to 289 °K.]

17
Dheer, P. N., and S. L. Surange, Thermal expansion of lead at low temperatures, Phil. Mag. 3, 665-74 (1958).

[4.5 to 10 "K.]

Disch, J., Thermal expansion of several substances. II., Z. Phvsik 5, 173-5 (1921). [Cr, Mn, Mo, Ni, Ta, W.

83 to 773 °K. In German.]

*Dobbs, E. R., and G. 0. Jones, Theory and properties of

solid argon, Repts. Progr. in Phvs. 30, 516-564 1,1957). [20 to 80 °K.]

*Dobbs, E. R., and K. Luszczynski, The lattice constant

of solid krypton. Conf. Phys. IBasses Temps., Paris

(1955), Annexe 1955-3, Supp'l. Bull. inst. intern, froid, pp. 439-440. [91° K. In English.]

*Domb, C., and J. S. Dugdale, Solid helium, Progress in Low Temperature Fhvsics, Vol. II, Interscience Publ.

1957, pp. 338-367. [Review].

Dorsev, H. G., Coefficient ot linear expansion at low temperatures, Phys. Rev. 25, 88-102 (1907). [Cd, Ag, Sn, Cu, Au, Bi, Sb, Pt, crown glass, Fe, soft solder, silica glass. 93 to 293 °K.]

Dorsey, H. G., Further measurements of the coefficient of linear expansion at low temperatures, Phys. Rev. 27, 1-10 (1908). [Au, Pb, Se, Zn, quartz, hard rubber, hard

fiberboard. 93 to 293 °K.]

Dorsey, H. G., Coefficients of linear expansion at low temperatures, Phys, Rev. 30, 271-2 (1910). [Abstract. 8 carbon steels, fused silica. 93 to 293 °K.]

*Druyvesteyn, M. J., Some remarks on the thermal ex- pansion and the Poisson contraction of the cubic metals.

Philips Research Repts. 1, 77-80 (1946). [Review.]

*Dugdale, J. S., and D. K. C. MacDonald, The thermal

expansion of solids, Phys. Rev. 89, 832-4 (1953). [Theoret.] van Duijn, J., and J. van Galen, Influence of vacancies on

the thermal expansion of lead near the melting point,

Phvsica 23, 822 (1957). Dunsmoor, R. J., F. W. Tipton, G. E. Trepus, J. J. Hill, and H. A. Mahle, Design criteria for "0"-rings and

similar elastic seals, Boeing Airplane Co., Document

No. D2-2964, July, 1958. [Rubbers. 78 to 293 °K.]

Durand, M. A., The coefficient ot thermal expansion of magnesium oxide. Physics 7, 297-8 (1936). [85 to 480 °K.]

Ebert, H., Expansion measurements at low temperatures

Z. Physik 47, 712-722 (1928). [Al, Ag, Au, Fe, Mg, Pb, Jena glasses 16 III and 59 III, 3 Berlin porcelains, mica. 20 to 373 °K. In German.]

T Ebert, H., Measurement of thermal expansion. Review

of methods for solids. Arch. tech. Messen, Issue 158

(V9211-1), pp. 121-3, Dec. 1948. [In German.]

''Eeles, E. G., A precision low temperature X-ray camera, Advances in Cryogenic Eng. 3, 248-53, (1957). Plenum Press. [Liquid He region.]

*Ellefson, B. S., and N. W. Taylor, Crystal structures and

expansion anomalies of MnO, MnS, FeO, Fe304 between

100 °K and 200 °K, J. Chem. Phys. 2, 58-64 (1934).

Erfling, H. D., Thermal expansion of solids at low temperatures. II. (Cr, /3-Mn, Mo, Rh, Be, graphite, Tl, Zr, Bi, Sb, Sn, and bervD, Ann. Physik 34, 136-60 (1939).

[57 to 293 °K. In German.]

Erfling, H. D., Change in thermal expansion and electrical resistance of 7-manganese upon transformation to «-phase, Ann. Physik 37, 162-8 (1940). [78 to 293 °K.

In German.]

Erfling, H. D., Thermal expansion of solids at low temperatures. III. (Ca, Nb, Th, V, Si, Ti, Zr), Ann. Physik

41, 467-475 (1942). [57 to 300 °K. In German.]

Eshelby, J. D., Geometrical and apparent x-ray expansions

of a crystal containing lattice defects, J. Appl. Phys.

24, 1249 (1953). [Letter. Theoret.]

Eshelby, J. D., Distortion of a crvstal bv point imperfections, J. Appl. Phys. 25, 255 (1954). "[Theoret.] Eshelby, J. D., The continuum theory of lattice defects. Solid State Physics 3, 79-144 (1956). [Theoret.]

Feder, R., and A. S. Nowick, Use of thermal expansion measurements to detect lattice vacancies near the melting point of pure lead and aluminum, Phys. Rev.

109, 1959-1963 (1958).

Fiedler, H. C, B. L. Averbach, and M. Cohen, The effect

of deformation on the martensitic transformation in austenitic stainless steels, Trans. ASM 47, 269 (1955). Figgins, B. F., G. O. Jones, and D. P. Riley, The thermal

expansion of aluminium at low temperatures as measured

by an x-ray diffraction method, Phil. Mag. 1, 747-758

(1956). [20 to 299 °K.]

*Figgins, B. F., and B. L. Smith, Density and expansivity

of solid krypton, Phil. Mag. 5, 186-8 (1960). [20 to 90 °K.]

Fine, M. E., Elasticity and thermal expansion of ger- manium between -195 and 275 °C, J. Appl. Phys. 24,

338-340 (1953). [100 to 550 °K.]

Fine, M. E., Cp-Cv in silicon and germanium, J. Chem.

Phys. 21, 1427 (1953). [Letter. Si. 95 to 425 °K.]

Fine, M. E., E. S. Greiner, and W. C. Ellis, Transitions in chromium. Trans. A.I.M.E. (J. Metals), 189, 56-8

(1951). [78 to 673 °K.]

*Foex, M., A transformation common to the monoxides of manganese, iron, cobalt and nickel, Compt. rend. 227,

193-4 (1948). [MnO, FeO, CoO, NiO. 78 to 673 °K.

Illustrates anomaly at Neel point. In French]

Fontana, M. G., Investigation of mechanical properties

and physical metallurgy of aircraft alloys at very low

temperatures. Part II. Strength properties and hardness, Air Force Tech. Report No. 5662 Part II. (1948). [Aluminums 2S, 24S, 6 IS, 75S, and 125S, magnesium FS-1,

aluminum bronze, SAE 2330 and 8630 steels, stainless

steels 304 and 322, 8V2% nickel steel. 80 to 300 °K.]

Fontana, M. G., S. M. Bishop, and J. W. Spretnak,

Mechanical properties of metals at low temperatures.

Air Force Tech. Report No. 5662-V (1953). [Aluminum

alloys 24S-T4 and 75S-T6, SAE 8630 steel, Ti, type 304

stainless steel. 20 to 290 °K.]

Eraser, D. B., and A. C. Hollis-Hallett, Total contractions

of some metals on cooling from room temperature to 4° K, Proc. 9th Intern. Congr. Refrig. (1955). Vol. 1, pp. 1064-6. [Brass, Cu, Duralumin, Monel, "stainless

steel".] Furman, D. E., Thermal expansion characteristics of

stainless steels between -300° and 1000 °F, Trans. A.I.M.E. (J. Metals) 188, 688-691 (1950). [Types 301,

304, 316, 347, 310, 330 stainless steel. 90 to 810 °K.]

Giauque, W. F., T. H. Geballe, D. N. Lyon, and J. J. Fritz, Some properties of plastics and the use of plastic

apparatus at low temperatures, Rev. Sci. Instr. 23,

169-173 (1952). [Plexiglas. 20 to 300 °K.]

Gibbons, D. F., Thermal expansion of some crystals with

the diamond structure, Phys. Rev. 112, 136-40 (1958).

[Si, Ge, InSb. 4 to 300 °K.]

Glover, R. E., Lattice expansion of KCl single crystals

between 20 °C and 600 °C, Z. Physik 138, 222-236

(1954). [In German.]

Goens, E., and E. Schmid, Elastic constants, resistivity

and thermal expansion of magnesium crystal, Phvs. Z. 37, 385-391 (1936). [21 to 473 °K. In German.]

Gott, A., Thermal lattice expansion and macroscopic

expansion of alkali halides crystallized from the melt, Ann. Physik 41, 520 (1942). [290 °K and up. In German.]

Graham, J., A. Moore, and G. V. Raynor, The effect of temperature on the lattice spacings of indium, J. Inst. Metals 84, 86-7 (1955). [90 to 408 °K.]

Gregg, H. T., Sub-zero treatment of metals, G. E. Review,

July 1954, pp. 19-21. [23 miscellaneous materials. 77

to 294 °K.]

Gruneisen, E., Thermal expansion of metals, Ann. Physik

33, 33-64 (1910). [Ir, Mg, Zn, Cd, Sb, Au, Pb, Bi, Sn. 90 to 290 °K. In German.]

Gruneisen, E., Geiger-Scheel Handbuch der Physik (1926).

Vol. X. Thermal properties of matter, Chapt. 1 The

solid state. Sec. d. Change of state of solids. [Review. In German.]

Gruneiisen, E., and E. Goens, Investigations on metallic

crystals III. Thermal expansion of zinc and cadmium,

Z. Physik 29, 141-156 (1924). [Zn, Cd, Jena glass. 20 to 373 °K. In German.]

Gruneisen, E., and O. Sckell, Mercury crystals: density,

resistivity, thermal expansion, elastic constants, Ann.

Physik 19, 387-408 (1934) . [83 to 195 °K. In German.]

18
THaynes, F. G., Automatic recording of dilatometer measurements, BiiU. Inst. Metals 2, 193-6 (1954). (Accomi panies J. Inst. Metals, Vol. 83).

'

' Head, E. L., and H. L. Laquer, Low temperature thermal

expansion of various materials, AECD-3706 (1952),

Office of Technical Services, Dept. Commerce, Washington 25, D.C. [B, Ti, Rh, JNIg, Zn, Li, U, Pyrex, LiH,

NaF, filled polvthenes. Includes unpublished data on Pb by Altman," Rubin, and Johnston. 20 to 300 °K.]

To be published.

*Henglein, Fr. A., Thermal expansion of some alkali metal

haUdes at low temperatures, Z. physik. Chem. 115,

91-120 (1925). [NaCl, KCl, NaBr, KBr, Nal, KI.

89 to 300 °K. In German.]

*Henglein, F. A., Thermal expansion of some alkali metal

halides at low temperatures. II., Z. phvsik. Chem.

- 117, 285-292 (1925). [LiF, LiCl, LiBr, Lil, NaF, KF,

RbCl, RbBr, Rbl. 89 to 273 °K. In German.]

*Henglein, F. A., Thermal expansion in crystals and

chemical constitution, Z. Elektrochem. 31, 424-8 (1925). [A summary based on the data on 15 alkali halides from

the preceding two references. In German.]

Henning, F., The expansion of solids at low temperatures, Ann. Physik 22, 631 (1907). [Jena glass 59 III, silica glass, porcelain, Pt, Pd, Pt-Ir, Ag, Cu, Ni, Al, constantan, bronze, brass, cast iron, ingot iron, -RTOught iron, soft steel. 82 to 289 °K. In German.]

*Heuse, W., Molar volumes of hydrocarbons and some

other substances at low temperature, Z. phvsik. Chem.

A147, 266-274 (1930). [A score of hydrocarbons,

NH3, CO2, acetone, Br,, CI2, NO, N2O, H,0. 20 °K

only. In German.]

*Heuse, W., Dilatometric observation of the transformation point of methane, Z. physik. Chem. A147, 282-7

(1930). [20.1 to 20.8 °K. In German.]

Hidnert, P., Thermal expansion of tantalum, BS J. Research 2, 887-896 (1929). [83 to 773 °K.]

Hidnert, P., Thermal expansion of artificial graphite and

carbon, J. Research NBS 13, 37-51 (1934). [293 to 1273 °K.]

Hidnert, P., Thermal expansion of electrolytic chromium,

J. Research NBS 26, 81-91 (1941). [168 to 990 °K.]

Hidnert, P., Thermal expansion of cast and of swaged

chromium, J. Research NBS 27, 113-124 (1941). [83 to 980 °K.]

•'• Hidnert, P., Thermal expansion of titanium, J. Research

NBS 30, 101-105 (1943). [83 to 973 °K.]

Hidnert, P., and M. G. Blair, Thermal expansivity and

density of indium, J. Research NBS 30, 427-33 (1943).

[83 to 373 °K.]

Hidnert, P., and H. S. Krider, Thermal expansion of columbium, BS J. Research 11, 279-284 (1933). [138

to 578 °K.]

THidnert, P., and W. Souder, Thermal expansion of solids, NBS Circular 486 (1950). Hidnert, P., and W. T. Sweeney, Thermal expansion of

tung.sten, BS Sci. Pap. 20, 483-7 (1925). [173 to 773 °K.]

Hidnert, P., and W. T. Sweeney, Thermal expansion of beryllium and aluminum-beryllium alloys, BS Sci. Pap.

22, 533-545 (1927). [153 to 973 °K.]

Hidnert, P., and W. T. Sweeney, Thermal expansion of magnesium and some of its alloys, BS J. Research 1, 771-792 (1928). [90 to 773 °K.]

Hill, D. M., The principal expansion coefficients of single

crystals of mercury, Phys. Rev. 48, 620-4 (1935). [83 to 158 °K.]

Hordon, M. J., B. S. Lement, and B. L. Averbach, Influ- ence of plastic deformation on expansivity and elastic modulus of aluminum, Acta Met. 6, 446-453 (1958).

Tie [77 to 300 °K.]

I Hull, D., and H. M. Rosenberg, Microscopy at liquid

helium temperatures: phase transition in sodium, Phys.

lie ' Rev. Letters 2, 20.5-6 (1959).

JH. Hume-Rothery, W., On Gruneisen's equation for thermal » expansion, Proc. Roy. Soc. 57, 209-222 (1945).

[Theoret.] Hume-Rothery, W., and K. W. Andrews, The lattice spacing and thermal expansion of copper, J. Inst.

Metals 68, Part 2, 19-26 (1942) Paper No. 915. [291 to 1144 °K.]

Hume-Rothery, W., and T. H. Boultbee, The coefficients of expansion of some solid solutions in aluminium, Phil. Mag. 40, 71 (1949). [223 to 473 °K.]

*Hume-Rothery, W., and K. Lonsdale, The lattice spacing

of rubidium between —183 °C and +19 °C, Phil. Mag.

36, 842-5 (1945). T Hume-Rothery, W., and D. J. Strawbridge, A general purpose Debye-Scherrer camera and its application to work at low temperatures, J. Sci. Instr. 24, 89-91

(1947). [Al. 175 °K arid up.]

Hunter, E., arid W. G. Oakes, The effect of temperature on the density of Polythene, Trans. Faraday Soc. 41,

49-56 (1945). [95 to 443 °K.]

Jacobs, R. B., and A. Goetz, The thermal expansion of the Bi lattice between 25° arid 530° Abs., Phys. Rev. 51,

159-164 (1937).

Jafifee, R. I., and R. H. Ramsey, Properties of aluminum

bronzes at subzero and high temperatures. Metal Progr.

54, 57 (1948). [172 °K and up.]

Jakob, M., and S. Erk, Thermal expansion of ice between

0° and -253°, Z. Kalteind. 35, 125-130 (1928). [20 to 273 °K. In German.]

*Johansson, C. H., Thermal expansion of some binary

solid-solution series, Ann. Physik 76, 445-454 (1925). [Ag-Pd. Cu-Pd. 83 to 300 °K. In German.]

*Justi, E., and H. Nitka, Transformations of solid H2S, Phvs. Z. 37, 435 (1936). [X-ray lattice parameters.

20 to 150 °K. In German.]

^Kan, L. S., and B. G. Lazarev, A low temperature X-ray

camera, Zhur. Tekh. Fiz. 21, 1542 (1951). [20 °K and

up. In Russian.]

Keesom, W. H., F. P. G. van Agt, and A. F. J. Jansen,

The thermal expansion of copper between -[-101° and

-253 °C, Leiden Comm. No. 182a (1926). *Keesom, W. H., and A. Bijl, The thermal expansion of Jena glass 16 III, Leiden Comm. No. 203a (1929). [20 to 373 °K.]

Keesom, W. H., and D. W. Doborzynski, Measurements

by the interferometric method on the thermal expansion

of Jena glass 2954 III down to 4°K, Physica 1, 1089-1102

(1934). [4 to 373 °K. Includes silica glass, 4 to 20 °K.]

*Keesom, W. H., and D. W. Doborzynski, Measurements

on the thermal expansion of Jena thermometer glass 2954

III by the method of the vertical comparator, Physica 1, 1085-8 (1934). [20 to 373 °K.]

Keesom, W. H., and A. F. J. Jansen, The thermal expansion

of silver between +101 °C and —253 °C, Leiden Comm.

No. 185c (1927). Keesom, W. H., and J. W. L. Kohler, New determination

of the lattice constant of carbon dioxide, Physica 1, 167

(1933). [Ag, CO2. 83 °K.]

Keesom, W. H., and J. W. L. Kohler, The lattice constant and expansion coefficient of solid carbon dioxide, Physica

1, 655 (1933-4). [20 to 114 °K.]

TKeith, H. D., An x-ray study in high-vacuum of the struc- ture of evaporated copper films, Proc. Phys. Soc. B69,

180 (1956). [90 °K and up.]

*Kelly, F. M., and W. B. Pearson, The rubidium transition

at -^180 °K, Can. J. Phys. 33, 17-24 (1955). [X-ray

lattice parameter, 77 to 297 °K.]

Keyston, J. R. G., J. D. MacPherson, and E. W. Guptill, Coefficient of thermal expansion of barium titanate. Rev.

Sci. Instr. 30, 246-8 (1959). [BaTiOs, brass, Cu. 81 to 373 °K.]

Kirby, R. K., Thermal expansion of polytetrafluoroethylene

(Teflon) from -190° to +300°C, J. Research NBS 57,

91-4 (1956).

*Kittel, C, Note on the correlation through anharmonic

force theory of the compressibility modulus and thermal

expansion coefficient of KBr at low temperatures, J. Chem. Phys. 16, 850 (1948). [Theoret.] *Kondo, K., On the properties of ferromagnetic alloy of manganese and bismuth at low temperature, I. Magnetic,

dilatometric and calorimetric studies, J. Phys. Soc. Japan

5, 26-30 (1950). [MnBi. 115 to 273 °K. In English.]

Konig, H., A cubic modification of ice, Z. Krist. 105, 279-

286 (1944). [~170 °K. In German.]

19
*Krishnan, R. S., and R. Srinivasan, Thermal expansion of cesium bromide, Proc. Phys. Soc. B69, 679-682 (1956).

[134 to 574 °K.]

Krupkowski, M. A., Nickel-copper alloys, Rev. met. 26,

193-208 (1929). [20 to 717 °K. In French.]

Krupkowski, A., and W. J. de Haas, Thermo-electric and

dilatation determinations with Ni-Cu alloys at low temperatures, Leiden Comm. No. 194b (1928). [Cu, Ni,

Cu-Ni alloys. 20 to 283 °K.]

*Kussmann, A., M. Auwarter, and G. Grfn. von Rittberg,

The iron-platinum Invars and their expansion anomalies, Ann. Physik 4, 174-182 (1948). [123 to 1000 °K. In German.]

Laquer, H. L., and E. L. Head, Low temperature thermal

expansion of plastics, AECU-2161 (1952). Tech. Inform.

Serv., A.E.C., Oak Rid'^e, Tenn. [20 Plastics. 20 to 300 °K.] To be published.

*Lazarev, B. G., and A. I. Sudovtsov, Change of volume of

tin in the superconductin^s; transition in a magnetic

field, Dokl. Akad. Nauk S.S.S.R. 69, 345 (1949). [In Russian.]

TLeibfried, G., A mechanical arrangement for measuring

small chanoes in length, Z. Physik 127, 580-7 (1950).

*Lifshitz, I. M., Thermal properties of chain and laminar

structures at low temperatures, Zhur. Eksp. i Teoret.

Fiz. 22, 475-486 (1952). [Theoret. In Russian.]

Lindemann, C. L., Temperature dependence of the thermal

coefficient of expansion, Phys. Z. 12, 1197-99 (1911).

[Al, Cu, Zn, Ag, Pb. 20 to 292 °K. In German.]

Lindemann, C. L., Temperature dependence of the thermal

coefficient of expansion. II., Phys. Z. 13, 737-9 (1912). [NaCl, quartz, glass, B2O3. 20 to 300 °K. In German.]

Lisgarten, N. D., and M. Blackman, The cubic form of ice, Nature 178, 39-40 (1956). [93 °K and up.]

Lonsdale, K., The structure of ice, Proc. Roy. Soc. 247,

424-434 (1958). [H2O, D2O. Review.]

*Lonsdale, K., and W. Hume-Rothery, The lattice spacings

of lithium at 20 °C and -183 °C, Phil. Mag. 36, 799-

801 (1945).

'''Lonsdale, K., and H. Smith, X-ray crystal photography

at low temperatures, J. Sci. Instr. 18, 133 (1941).

[90 °K region.]

Lucks, C. F., and H. W. Deem, Thermal properties of thirteen metals, ASTM Special Tech. Publ. No. 227

(1958). [Aluminum 2024-T4 and 7075-T6, Inconel,

Inconel-X, magnesium AN-M-29, K-Monel, SAE 1010

steel, stainless steels 301, 316, and 347. 116 °K and up.]

Maass, 0., and W. H. Barnes, Some thermal constants of

solid and liquid carbon dioxide, Proc. Roy. Soc. Alll,

224-244 (1926). [90 to 193 °K.]

*Mader, H., The mechanical and physical properties of pure aluminum and some aluminum alloys at the temperature of liquid oxygen, Metall 5, 1-5, Jan. 1951.

[Alloys with 3, 5, 7, and 9% Mg. 150 to 673 °Iv. In German.]

Masumoto, H., On the thermal expansion of alloys of cobalt, iron and chromium, and a new alloy "Stainless- Invar", Sci. Repts. Tohoku Univ. 23, 265-280 (1934).

[83 to 450 °K. In Enghsh.]

McLennan, J. C, J. F. Allen, and J. 0. Wilhelm, On the

dilatation of superconductors. Trans, Roy. Soc. Can.

(Ill) 25, 1-12 (1931). [Pb, Rose's metal. 4 to 20 °K.]

McLennan, J. C, and R. J. Monkman, On the thermal

expansion of zinc and cadium crystals and on the crystal structure of erbium and niobium. Trans, Roy. Soc. Can.

(Ill) 23, 255-67 (1929). [83 to 291 °K.]

McSkimin, H. J., Measurement of elastic constants at low

temperatures by means of ultrasonic waves—Data for

silicon and germanium single crystals, and for fused

silica, J. Appl. Phys. 34, 988-997 (1953). [Ge. 70

to 335 °K.]

TMichels, A., T. Wassenaar, and T. N. Swietering, A

method for the measurement of the thermal expansion

of solids between 0 and -180 °C, Physica 19, 371

(1953). [Optical lever.] Mikura, Z., Contribution of the conduction electrons in a metal to the thermal expansion, Proc. Phys.-Math.

Soc. Japan 23, 309-18 (1941). [Theoret. In English.]

Miller, P. H., and B. R. Russell, Effect of internal strains on linear expansion, X-ray lattice constant, and density

of crystals, J. Appl. Phys. 23, 1163 (1952). [Theoret.]

Miller, P. H., and B. R. Russell, Effect on distribution of

lattice defects within crystals of linear e.xpansion and

x-ray lattice constant, J. Appl. Phys. 24, 1248-9

(1953). [Letter. Theoret.]

Molby, F. A., The linear expansion of Invar steel between

100 °C and -190 °C, Phys. Rev. 35, 79-80 (1912). Molby, F. A., Index of refraction and coefficients of expansion of optical glasses at low temperatures, J. Opt. Soc. , Am 39, 600-611 (1949). [14 glasses. 79 to 373 °K.] * *Muller, A., The crystal structure of the normal paraffins

at temperatures ranging from that of liquid air to the

melting points, Proc. Roy. Soc. A137, 417-430 (1930). i [C5H12 to C3)H62. X-ray lattice parameters.] 1 Nitka, H., Debve-Scherrer patterns of germanium between | 20 ° and 1110 ° Abs., Phys. Z. 38, 896 (1937). [In i, German.]

*Nix, F. C, and D. MacNair, A dilatometric study of the

[ order-disorder transformation in Cu-Au alloys, Phys. ; Rev. 60, 320-9 (1941). [83 ° K and up.]

|j T Nix, F. C, and D. MacNair, An interferometric-dila- tometer with photographic recording. Rev. Sci. Instr. 12, j 66-70 (1941). [Quartz. 83 to 930 °K.] 1 Nix, F. C, and D. MacNair, The thermal expansion of ; pure metals: copper, gold, aluminum, nickel, and iron, Phys. Rev. 60, 597-605 (1941). [81 to 300 °K.]

Nix, F. C.,-and D. MacNair, The thermal expansion of pure

metals. II: molybdenum, palladium, silver, tantalum, ,1 tungsten, platinum, and lead, Phys. Rev. 61, 74-78 ' (1942). [85 to 300 °K.] : *Okamura, T., On the transformation of magnetite at a 1 low temperature, Sci. Repts. Tokoku Univ. 21, 231-241 i (1932). [89 to 173 ° K. In English.] ! Olsen, J. L., and H. Rohrer, The volume change at the superconducting transition, Helv. Phys. Acta 30, 49-66

(1957). [Sn, Pb, In, Tl, Ta. In English.]

Onnes, H. K., and J. Clay, On the measurement of very low temperatures. X. Coefficient of expansion of ; Jena glass and of platinum between +16° and —182°.

Leiden Comm. No. 95b (1906). [91 to 289 ° K.] ; *Onnes, H. K., and W. Heuse, On the measurement of very low temperatures. V. The expansion coefficient of Jena and Thuringer glass between +16° and —182°

C. Leiden Comm. No. 85 (1903). [Jena glass 16 III, , Thuringer glass No. 50.] T Owen, E. A., and G. I. Williams, A low-temperature ' x-ray camera, J. Sci. Instr. 31, 49-54 (1954). [Ag, Fe. 79 to 291 °K.] :| *Owen, E. A., and G. I. Williams, X-ray measurements on

lithium at low temperatures, Proc. Phys. Soc. A67, i 895-900 (1954). [79 to 293 °K.]

*Pearson, W. B., Thermal expansion of lithium, 77° to 1 300 °K, Can. J. Phys. 32, 708-713 (1954). *Pearson, W. B., A handbook of lattice spacings and struc- tures of metals and alloys, Pergamon Press (1958).

[Handbook and compilation.] T Post, B., R. S. Schwartz, and I. Fankuchen, An improved

device for x-ray diffraction studies at low temperatures, Rev. Sci. Instr. 22, 218 (1951). [80 °K and up.] [ Potter, R. F., Elastic moduli of indium antimonide, Phys. I Rev. 103, 47-50 (1956). [83 to 523 °K.] I Powell, R. W., Preliminary measurements of the thermal \. conductivity and expansion of ice, Proc. Roy. Soc. 247, ' ii 464-6 (1958). [78 to 273 °K.]

Reed, R. P., and R. P. Mikesell, The stability of austenitic

stainless steels at low temperatures as determined by IS magnetic measurements. Advances in Cryogenic Eng.

4, 84-100 (1958). Plenum Press. T Robertson, J. H., X-ray diffraction by single crystals at 8 low temperatures: a cryostat for use with liquid hydrogen, J. Sci. Inst. 37, 41-5 (1960). Rontgen, W. C, Linear thermal expansion coefficients of S cuprite and diamond, Sitzber. math.-physik. Kl. koni- ghch bayer. Akad. Wiss. Munich (1912) pp. 381-7.

[85 to 351 °K. In German.] 1

20
Rosenfield, A. R., and B. E. Averbach, The effect of stress on the expansion coefficient, J. Appl. Phys. 27, 154

(1956) . Rubin, T., H. W. Altman, and H. L. Johnston, Coefficients

of thermal expansion of soUds at low temperatures. I. The thermal expansion of copper from 15 to 300 °K, J. Am. Chem. Soc. 76, 5289-93 (1954). *Ruhemann, B., Temperature dependence of the lattice constants of MnO, Phvs. Z. Sowjetunion 7, 590-607

(1935). [77 to 300 °K. In German.]

T Ruhemann, B., X-ray cameras for low temperatures,

Phys. Z. Sowjetunion 7, 572-582 (1935). [20 °K and

up. In German.]

*Ruhemann, B., and F. Simon, Crystal structures of

krj-pton, xenon, h3'drogen iodide and hydrogen bromide

as functions of temperature, Z. physik. Chem. B15, 389

(1932) and B16, 408 (1932). [21 to 125 °K. In Ger- man.]

Sapper, A., and W. Biltz, Molecular and atomic volumes.

31. Low temperature densities of some elements, Z.

anora;. u. alla;em. Chem. 198, 184-190 (1931). [Hg,

CI2, Br., I2, Ca, S, P. 78 °K and up. In German.]

~ Saunders, J. B., Improved interferometric procedure

with application to expansion measurements, J. Research NBS 23, 179-195 (1939). T Saunders, J. B., Interferometer measurements on the expansion of iron, J. Research NBS 33, 75-85 (1944). [285 to 674 °K.]

Schad, L. W., and P. Hidnert, Preliminary determination

of the thermal expansion of molybdenum, BS Sci. Pap.

15, 31-40 (1919). [131 to 578 °K.]

*Schallamach, A., X-ray investigation of the structure

transition of methane at the X point, Proc. Roy. Soc. A171, 569-578 (19.39). [14 to 35 °K.]

I' Scheel, K., Apparatus for expansion determination by

the Fizeau method at the temperature of liquid air, Z. Instrumentenk. 24, 285 (1904). [In German.]

Scheel, K., The expansion of quartz glass, Verhandl deut. physik. Ges. 9, 718-721 (1907). [83 to 373 °K. In German.]

Scheel, K., Expansion of solids, especially of quartz in the direction of its principal axis, platinum, palladium,

and quartz-glass at the temperature of liquid air, Verhandl. deut. physik. Ges. 9, 3-23 (1907). [83 to 373 °K. In German.]

Scheel, K., Thermal expansion of several substances. I., Z. Physik 5, 167-172 (1921). [.lena glasses 16 III and

59 III, Berhn porcelain, 90 Pt 10 Ir, two Invars. 82 to 273 °K. In German.]

Scheel, K., and W. Heuse, Determination of the expansion

of platinum between —183° and room temperature with

the comparator and Fizeau apparatus, Verhandl. deut. physik. Ges. 9, 449-459 (1907). [In German.]

Scheel, K., and W. Heuse, The absolute expansion of quartzglass at the temperature of liquid hydrogen,

Verhandl. deut. physik. Ges. 16, 1-3 (1914). [20 to 373 °K. In German.]

*Schuch, A. F., and H. L. Laquer, Low temperature

thermal expansion of uranium, Phys. Rev. 86, 803

(1952). [Letter. 20 to 300 °K.]

Scott, R. B., (1933), private communication.

Shallcross, F. V., and G. B. Carpenter, X-ray diffraction study of the cubic phase of ice, J. Chem. Phys. 26,

782-4 (1957). [83 °K and up.]

Shearer, J. S., Note on coefficients of expansion at low

temperature, Phys. Rev. 20, 52-3 (1905). [Al, Ag. 93

to 273 °K.]

Siegel, S., and S. L. Quimby, The thermal expansion of crystaUine sodium between 80 °K and 290 °K, Phvs. Rev. 54, 76-8 (1938). Simmons, R. O., and R. W. BaUuffi, Low temperature

thermal expansion of copper, Phys. Rev. 108, 278-80

(1957) . [8 to 100 °K.]

Simmons, R. O., and R. W. Balluffi, X-ray and expansion

effects produced by imperfections in solids: Deuteronirradiated germanium, J. Appl. Phys. 30, 1249-1258

(1959). [Al. 595 to 930 °K.]

Simmons, R. 0., and R. W. Balluffi, Measurements of equihbrium vacancy concentrations in silver. Bull Am

Phys. Soc. 5, 181 (1960). [Abstract. 287 to 1229 "K.j

Simon, F., and R. Bergmann, Thermally excited quantum

jumps in solids. IV. Thermal expansion in the region

of the anomaly, Z. physik. Chem. B8, 255-280 (1930)

[Li, Si, Fe, steel, Ni, Cu, NH4CI, NH4 Br, (NH4)3POi.

85 to 300 °K. In German.]

T Simon, F., and C. von Simson, The crystal structure of hydrogen chloride, Z. Physik 21, 168 (1924). [81 to 107 °K. In German.]

*Simon, F., and E. Vohsen, Crystal structure determination of the alkali metals and strontium, Z. physik. Chem

133, 165 (1928). [X-ray lattice constant of Li, Na, K,

Rb, Cs, Sr at 100 °K. In German.]

Smith, R. C., Determination of the difference between

macroscopic and microscopic thermal coefficients of ex- pansion for ionic crystals. Thesis, North Carohna State College (1954). ASTIA Document No. AD 37750. [NaCl, KCl, KBr. 293 to 373 °K.]

Sosman, R. B., The properties of silica. The Chemical

Catalog Co. Inc., New York, N.Y. (1927) Ch. 20. [Review.]

Souder, W. and P. Hidnert, Measurements on the thermal

expansion of fused sihca, BS Sci. Pap. 21, 1-23 (1926). [148 to 1273 °K.]

^Steward, E. G., Ch. 10, Low-temperature methods, pp. 265-277 in "X-ray diffraction by polycrystalline materials", Eds. H. S. Peiser, H. P. Rooksby, and A. J. C. Wilson, The Institute of Physics, London (1955). *Stewart, J. W., and R. I. La Rock, Compression and

densities of four solidified hydrocarbons and carbon

tetrafluoride at 77 °K, J. Chem. Phys. 28, 425-7 (1958). [Ethane, ethylene, propane, propylene, CF.|.]

Swenson, C. A., Compression of the alkah metals to 10,000

atmospheres at low temperature, Phys. Rev. 99, 423-

430 (1955). [Li, Na, K, Rb, Cs. 4.2 and 77 °K.]

Swenson, C. A., Properties of indium and thallium at low

temperatures, Phys. Rev. 100, 1607-14 (1955). [4 to 300 °K.]

Thewlis, J., and A. R. Davey, Thermal expansion of grey

tin, Nature 174, 1011 (1954). [Letter. 143 to 293

°K.]

Thewlis, J., and A. R. Davey, Thermal expansion of diamond, Phil. Mag. 1, 409-14 (1956). [123 to 1200

°K.]

Tool, A. Q., and J. B. Saunders, Expansion effects shown

by some Pyrex glasses, J. Research NBS 40, 67-83

(1948). [293 °K and up.]

Toupin, R. A., and R. S. Rivlin, Dimensional changes in crystals caused by dislocations, J. Mathematical Phys.

1, 8-15 (1960). [Theoret.] Trepus, G. E., R. S. Roper, W. R. Hickman, and J. T.

Mitchell, Design data for "0"-rings and similar elastic

seals, WADC Tech. Report 56-272 Part IV (1959). [Rubbers. 78 to 293 °K.]

*Trombe, F., and M. Foex, Dilatometric study and deter- mination of the allotropic states of metallic lanthanum

and cerium, Compt. rend. 217, 501-3 (1943). [78 to 673 °K. In French.]

*Trombe, F., and M. Foex, Regions of existence and

properties of the allotropic states of metallic cerium, Ann. de Chim. 19, 417-445 (1944). [78 to 773 °K.

In French.]

*Trombe, F., and M. Foex, Dilatometric study of metallic neodymium, Compt. rend. 232, 63-5 (1951). [78 to 923 °K. In French.]

*Trombe, F., and M. Foex, Dilatometric study of metallic gadolinium, Compt. rend. 235, 42-4 (1952). [78 to 573 °K. In French.]

*Trombe, F., and M. Foex, Dilatometric study of metallic dysprosium, Compt, rend. 235, 163-5 (1952). [78 to 573 °K. In French.]

*Trombe, F., and M. Foex, Dilatation anomalies of the ferromagnetic rare earth metals gadolinium and dysprosium, J. recherches centre natl. recherche sci. 5, 71-5

(1953). [Gd, La, Nd, Dy. 78 °K and up. In French.]

21
*Ubbelohde, A. R., and I. Woodward, Structure and ther- mal properties associated with some hydrogen bonds in

crystals. VII. Behavior of KH2PO4 and KH2ASO4 on

cooHng, Proc. Roy. Soc. A188, 358-371 (1947). [80 to 293 °K. Illustrates expansion anomaly at the ferroelectric Curie point.]

Valentiner, S., and J. Wallot, Dependence of the expansion

coefficients of solids on the temperature, Ann. Physik

46, 837-867 (1915). [Pt, Ir, Rh, Si, fluorite, pyrite, Invar, fused quartz. 81 to 290 °K. In German.]

T Vanderman, E. J., Microformer dilatometer, Rev. Sci. Instr. 22, 757 (1951). *Varley, J. H. O., The thermal expansion of pure metals and the possibility of negative coefficients of volume ex- pansion, Proc. Roy. Soc. A237, 413 (1956). [Theoret.]

Visvanathan, S., Thermal expansion at low temperatures,

Phys. Rev. 81, 626 (1951). [Letter. Theoret.]

T Viswamitra, M. A., and S. Ramaseshan, Simple device

for growing crystals at low temperatures in x-ray cameras. Rev. Sci. Instr. 31, 456-7 (1960). Wagner, C, and J. Beyer, Electrical conductivity and the

unit cell in silver bromide, Z. physik. Chem. B32, 113

(1936). [293 to 673 °K. In German.]

Walker, P. L., H. A. McKinstry, and C. C. Wright, X-ray

diffraction studies of a graphitized carbon, Ind. Eng.

Chem. 45, 1711 (1953). [77 to 1400 °K.]

Ward, J. 0., M. D. Jepson, and J. R. Rait, Effect of alloying elements on the breakdown of austenite at sub-zero temperatures, J. Iron Steel Inst. 170, 1 (1952j.

Werner, A., Thermal expansion of mild and hardened steel, Z. Instrumentenk. 44, 315-320 (1924). [21 steels. 73

to 423 °K. In German.]

Winter-Klein, A., Variation of the expansion coefficient of

glass at low temperature, Compt. rend. 230, 1857-8

(1950). [BorosiHcate crown, light flint. 90 °K and up. In French.]

T Wood, L. A., N. Bekkedahl, and C. G. Peters, Application of the interferometer to the measurement of dimensional changes in rubber, J. Research NBS 23, 571-583

(1939). ["Stark" rubber. 88 to 320 °K.]

Work, R. N., A photoelectric recording interferometer

for measurement of dimensional changes, J. Research

NBS 47, 80 (1951). Wunnenberg, E., W. Fischer, and A. Sapper, Molecular

and Atomic Volumes. 24. Techniques of volumetric measurements of low temperature solids, Z. physik.

Chem. 151, 1-12 (1930). [Thuringian glass, Bi, calcite, KCl. 78 °K. In German.]

*Wyckoff, R. W. G., Crystal structures, Interscience Publ. Inc. [A loose-leaf compilation including lattice parameters, issuance of which began in 1948.] *Zollweg, R. J., X-ray lattice constant of barium oxide,

Phys. Rev. 100, 671-3 (1955). [8 to 435 °K.]

Boulder, Colo., December 8, 1960.

22 U.S. GOVERNMENT PRINTING OFFICE: 1961
THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colo., is suggested in the following listing of the divisions and sections engaged in technical work. In

general, each section carries out speciahzed research, development, and engineering in the field indicated by its

title. A brief description of the activities, and of the resultant publications, appears on the inside of the front

cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-Ray, Radioactivity. Radiation Theory. High Energy Radiation. Radiological

Equipment. Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Analytical

Chemistry. Inorganic Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion Controls.

, Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

II Structure. Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal Physics.

PHectrodeposition

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth.

Constitution and Microstructure.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials.

I Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. I I Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog

Systems. Applications Engineering.

Atomic Physics. Spectroscopy. Radiometry. Solid State Physics. Electron Physics. Atomic Physics. Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical

Instruments. Basic Instrumentation.

1 Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy.

' Molecular Kinetics. Mass Spectrometry. Molecular Structure and Radiation Chemistry.

• Office of Weights and Measures. BOULDER, COLO.

1

I Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas

|j Liquefaction.

1 Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere

Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Service.

I Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

j Tropospheric Analysis. Propagation-Terrain Effects. Radio- Meteorology. Lower Atomsphere Physics.

I Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

I Materials. Atomic Frequency and Time Interval Standards. Electronic Cahbration Center. Millimeter- Wave Research. Microwave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna

Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exposphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.