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Table 145. Cubical Expansion of Liquids

Table 145. Cubical Expansion of Liquids

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O F T H E E L E M E N T S (continued)



T A B L E 142.-EXPANSION



146



Element

Niobium



Temperature

or

temperature

r y e



.... . -212

-100



C



...... 40

Palladium . . . . -191 to 16

+ 1 6 t o 100



Potassium

Rhodium



.. ...



Rubidium



4



<



6.6



14,23,

24



10.3

12.4

12.8

13.8



226,

54.55



-191 to 16

- 90toO

0 to 100

0 to 300

0 to 500

0 to 1000



8.0

8.7

9.0

9.2

9.6

10.2



226,

30,32,

54,56



85.



57



.... O t o 5 n

, . . . . -174

- 92



5.0

7.4

7.9

8.4

0 to 100

9.7

0 to 500

0 to 1000 10.8

0 to 1500 12.1



71

-"



... . . - 98 to 19

... + 40

13 t o 3 2

50



66.

6.8

9.6

9.9



... . .. -+ 78

to 19

20 to 100

205

Amorphous.. - 78 to 0

to 21

0



19.58,

59.60



100

500

1000



Silver



.. ...... -191

-250toO

to 16



Oto 100

20 to 300

20 to 500

0 to 900



Tellurium

Thallium



40

0 to 100

0 to 200



..... +-21620 toto 20

100

20 to 300

20 to 600



Tin



... . . . ... . +-18318 toto 20

100



61



.... . +-19520 toto 200

20

20 to 400



20 to 600

20 to 800



.



Tungsten . . . . -190 to 0

(Wolfram)

-100 to 0

0 to 100

0 to 300

0 to 650

27 to 1000

27 to 1750

27 to 2400

Vanadium

Zinct



. . ..



.



......



14.58,

64



-183 t o 0

0 to 40

-183 to 18



+ 20 to 100

2 0 t o 200

20to300



Zirconium

2.30,

39

26,65,

66,67



(continued)



SMlTHSONlAN PHYSICAL TABLES



.. . .

.....



7,62



2.0

3.0

3.3



14.9

17.0

19.4

20.2

20.7

22.4



.... -190

0

+ 2 0 tt oo 2100



20 to 300

20 to 500

27 to 1400

27 to 2400



Titanium



Amorphous,

melted &

cast

Silicon



Coefficient

Temperature of linear

or

thermal

temperature expansion

ryge

xlyper

C

C

-193 t o 0

59.8

0 to 17

68.2

0 to 50

70.

Oto95

71.



25 to 200



20.3

22.9

45.2

42.7

48.7



. .... -160toO

37.3

0

43.9

. . .... . -172

+-0.42.4.9

- 87

+ 20 to 50



. .....



Thorium



63,37



Selenium :

Polycrystalline



Element

Sodium



Tantalum



7



16 to 500

16 to 1000



-



Ruthenium



,G



C



to0

5.8

to 0

6.9

7.2

0 to 100

0 to300

7.5

20 to 1500 10.0



Osmium



Platinum



Coefficient

of linear

thermal

expansion

x 1 y per



. . ..



-183 t o 0

0 to 20

20to200

20 to400

20 to 700



+



6.2

6.6

6.6

6.6

7.3

7.8



,=

2

4

k



44,68

69



2.46,

51.70



16.8



7



29.4

30.0



64



9.8

11.3

12.1

13.7



14,71,

72



15.8 to 22.6

23.8 to 27.0

24.



4,5.

73,74



6.8

8.9

9.4

9.9

10.1



14,72,

75,76,

77



3.8

4.2

4.4

4.6

4.6

4.7

5.2

5.8



2 46

7b.7'9,

80,81



6.6

7.8



14



9.

17.

30.

34.



to 10.

to 40.

to 40.

to39.



4.0 to 5.1

4.6 to 5.9

5.4

6.1

7.1



5.13.

32,38.

47,82

83

14,19,

72



T A B L E 142.-EXPANSION

P a r t 2.-Coefficients



Temperature

or

temperature

range



"C



Element



Coeffiicent of linear

thermal expansion

per "C

'Parallel to

axis

16.0~10-0

15.6

16.8



...



...



. .. . .. ......... . , . .



Arsenic



..... .. . .. . ... ...



Bismuth



.... . . . . . . . . .. . . . .



Cadmium

Carbon

Graphite



Cobalt

Indium



.......... .. . . . .

. ..... . . .. . . .......



.. . . . . .. . . ..... . . .

................



Tellurium



. . . . .. ... .........

.................



Thallium



..................



Selenium



Tin



Zinc



. . . . . . . . . . .. . . .. . . . . . . .



......................



....... . .........



8.4

8.1



.. .



62



15.9

16.2

16.5



10.5

11.6



19,86,87



20 to 240



...



...

12.0



-190 to 18

20 to 100



48.2

50.4



18.5

18.9



13,88,89,90



+-14020

30

to 260

+



...

...



4.8



19.9 1,92



to 0

0 to 40

0 to 500

0 to 1000

0 to 1500

0 to 2300

20 to 870



17.2

18.8

20.7

23.1

26.7



...



33 to 100



16.1



12.6



89



56.

45.0



13.

11.7



93

94



26.4

27.7



25.6

26.6



95



42.6

47.0

49.6



33.4

37.5

37.5



96.97



5.8

6.6

8.3



4.0

4.6

5.8



98



20 to 1917



12.4



4.7



99



50



8.8

9.8

11.7



5.9

6.4

7.6



98



- 17 t o 9

23 to 87



+



20 to 100

20 to 200

-190 to -160

-188 to -79

-120



250

559



15 t o 55

20 to 60



-17.9



20

20 to 60



-



32 t o 91



+72.



6.6

1.3

1.8

2.0

2.4



...



...



74.1



1.6

1.7



27.2

27.0

9.



100

100,101

94



-195 to 20

0 to 20

14 to 25

34 to 194



14.1

15.8

16.8

25.7



19,94,102



+



25.9

29.0

32.2

45.8



18

+-190200 tototo 250

100



49.5

64.0

56.

59.



11.3

14.1

15.

16.



13,32,88,103,104



4.



13.



89,105



20 to 400



Zirconium



6,7,19,84



19.85



5 00



Ruthenium



Authority



7.0x10-0



...

...

2.8

11.7

15.0

15.7



. . ........... ...... +250

50



Rhenium



Perpendicular

to axis



1.6

8.6

10.4

13.1



Magnesium



Osmium



3.2 to 6.8



30 to 75



... ..... . . . .. . . .. -195



. . .. .. . .. .... . .. . . . .

. . . . . . . . . . .. .. .. .. ..



Mercury



147



OF T H E E L E M E N T S (continued)



of linear 1 thermal expansion of chemical elements (crystals)



0 to 100



1If there is random orientation of the crystals in a polycrystalline element such as antimony or cadmium, the



coefficient of linear expansion of the polycrystalline element may be computed from the following equation:

1

a = 7 (all

2al)



+



where all is the coefficient of linear expansion of the crystal parallel to its axis, and a l is the coefficient of

linear expansion of the crystal in the direction perpendicular to its axis. (See Part 1 for determined coefficients

of linear expansion of polycrystalline elements.)



(continued)

SMITHSONIAN PHYSICAL TABLES



TABLE 142.-EXPANSION



148



Element

Cadmium



....



Carbon:

Diamond

Cesium

Cobalt

Gallium

Iodine



Lithium

Nickel



...



......

.......



Coefficient

Temperature of cubical

OK

thermal

temperature expansion

range

xlyper

"C

C

100

91.

210

105.

250

110.

27

25 to650



3.2

9.1



0 to 23



291.



100

300



...... - 780 toto 29.6

18

....... -195

to25

+ 10 t o 4 0

.....



.......



Phosphorus



0 to 100

Oto 178

100



200

300



.. -273

-195



to 19

to 19



- 79 to 19



0 to44



O F T H E ELEMENTS (concluded)



of cubical thermal expanrlon of chemical elements



Part 3.-Coefficlents



.-x

6



9



4



106



107

108



35.6

39.4



106



53.

55.



109,

110

111,

112,

113



162.

170.



114



38.2

41.9

46.5



106



112,

115



....



....

.



Rubidium



Selenium :

Compressed

Not compressed

Sodium



204. to251.

264.



317.

398.

362.

372.



Element

Potassium



Coefficient

Temperature of cubical

or

thermal

temperature expansion

range

xlpper

"C

C

Oto 5 5

240



0 to 38

0 to 100



.. 0 to 100

...... - 1 8 6Oto53

to17

Oto79

20to95



Sulfur

Rhombic



...



Tin



.....

..........



Zinc



.........



Crystallized

Sicilian



-273 t o 1 8

-195to 18

- 7 9 t o 18

0 to 100

0 to 100



-



."0x

L.



B



i

57,

108,

114



270



108



175



116



198



186

207

208

226



111,

69.

114,



139

164



112

116



180



108.



117



354

260



80

140

190



68

78

89



106



50

200

300



a9

104

110



32,

106



Authorities



1. Nix and MacNair, 1941; 2. Nix and MacNair, 1942; 3. Hidnert, 1923; 4. Dorsey, 1907;

5. Griineisen, 1910; 6. Hidnert, 1935; 7. Fizeau, 1869; 8. Cath and Steenis, 1936; 9. Hidnert

and Sweeney, 1927; 10. Losana, 1939; 11. Jacobs and Goetz, 1937; 12. Dupuy & Hackspill, 1933;

13. Griineisen & Goens, 1924 ; 14. Erfling, 1942 ; 15. Bastien, 1934; 16. Rontgen, 1912 ; 17. Joly,

1898; 18. Hidnert, 1934; 19. Erfling, 1939; 20. Hidnert, 1941; 21. Schulze, 1927; 22. Masumoto,

1931; 23. Hidnert and Krider, 1933; 24. Matthies, 1936; 25. Krupkowski, 1929; 26. Henning,

1907; 27. Aoyama and Ito, 1939; 28. Hidnert, 1922; 29. Dittenberger, 1902; 30. Esser and

Eusterbrock, 1941; 31. Nitka, 1937; 32. Austin, 1932; 33. Hidnert and Blair, 1943; 34. Holborn

and Valentiner, 1907; 35. Hidnert, 1942; 36. Souder and Hidnert, 1922; 37. Dorsey, 1908;

38. Lindemann, 1911; 39. Ebert, 1928; 40. Rauramo and Saarialho, 1911; 41. Friend and

Vallance, 1924; 42. Hidnert and Sweeney, 1932; 43. Simon and Bergman, 1930; 44. Bridgman,

1936; 45. Hidnert and Sweeney, 1928; 46. Disch, 1921; 47. Schulze, 1921; 48. Erfling, 1940;

49. Schad and Hidnert, 1919; 50. Hidnert and Gero, 1924; 51. Worthing, 1926; 52. Jaeger,

Bottema, and Rosenbohm, 1938; 53. Souder and Hidnert, 1922; 53a. Hidnert, 1930; 54. Scheel.

1907; 55. Holzmann, 1931 ; 56. Scheel and Heuse, 1907; 57. Hagan, 1911 ; 58. Valentiner and

Wallot, 1915; 59. Sweeney, 1929; 60. Ebert, 1938; 61. Hume-Rothery and Lonsdale, 1945;

62. Bridgman, 1933; 63. Borelius and Paulson, 1946; 64. Schulze, 1930; 65. Keesom and

Jansen, 1927; 66. Scheel, 1921; 67. Owen and Roberts, 1939; 68. Siege1 and Quimby, 1938;

69. Hagan, 1883; 70. Hidnert, 1929; 71. Hidnert and Sweeney, 1933; 72. Kroll, 1939; 73. Grube

and Vosskiihler, 1934; 74. Bochvar and Maurakh, 1930; 75. Hidnert, 1943; 76. Greiner and

Ellis, 1948 ; 77. Adenstedt, 1949 ; 78. Hidnert and Sweeney, 1924 ; 79. Dodge, 1918 ; 80. Forsythe,

1927; 81. Worthing , 1917; 82. Souder and Hidnert, 1924; 83. Bauer and Sieglcrsehmidt, 1929;

84. Bridqman, 1924; 85. Kossolapow and Trapesnikow, 1936: 86. Roberts, 1924; 87, Goetz and

Hergenrother, 1932; 88. McLennan and Monkman, 1929; 89. Shinoda, 1934; 90. Kossolapow

and Trapesnikow, 1935; 91. Pierry, 1946; 92. Backhurst, 1922; 93. Frevel and Ott, 1935;

94. Shinoda, 1933; 95. Goens and Schmid, 1931 ; 96. Hill, 1935; 97. Griineisen and Sckell,

1934; 98. Owen and Roberts, 1937; 99. Becker, 1931; 100. Straumanis, 1940; 101. Bridgman,

1925; 102. Ievens, Straumanis, and Karlsons, 1938; 103. Staker, 1942; 104. Owen and Iball,

1933: 105. Pfaff. 1859; 106. Uffelmann, 1930: 107. Krishnan, 1944; 108. Hackspill, 1913;

109. Klemm, 1931; 110. Richards and Boyer, 1921; 111. Dewar, 1902; 112. Sapper and Biltz,

1931; 113. Straumanis and Sauka, 1942; 114. Bernini and Cantoni, 1914; 115. Leduc, 1891;

116. Spring, 1881; 117. Griffiths and Griffiths, 1915; 118. Schad, 1927.



SMITHSONIAN PHYSICAL TABLES



149

TABLE'143.-COEFFICIENTS

OF LINEAR THERMAL EXPANSION OF

SOME ALLOYS *



C



Coefficient X

of linear

thermal expansion X 1W

per "C



20 to 100

20 to 500



22.4 to 17.8

26.6 to 22.2



1 **



20 to 100

20 to 300

20 to 100

20 to 300



22.0

23.8

19.7

20.8



2



..................

..................



20 to 100

20 to 300

20 to 100

20 to 300



21.9

23.7

18.2

19.5



2



Aluminum-silicon, 4.2 to 12.6 Si..



..........

19.7 Si ..................

40 Si ...................



20 to 100

20 to 300

20 to 100

20 to 300

20 to 100

20 to 300



22.2 to 19.4

24.8 to 22.1

18.5

19.0

14.7

17.1



3,2



Aluminum-zinc, 0 to 50 Zn ................



20 to 100



23.6 to 26.5



4



.......................



25 to 100

25 to 300



16.9 to 19.7

17.7 to 21.2



5



Bronze, 4.2 to 10.1 Sn. ....................



25 to 100

25 to 300



17.1 to 17.8

17.8 to 19.0



5



...............................



20 to 100

20 to 400



8.7 to 11.1

11.5 to 12.7



6



20 to 60



-1.1 to +1.7



7



20 to 100

20 to 300



15.9 to 17.3

16.4 to 17.4



8



13.0

14.7

11.8

13.7



9



Alloy



Temperature

or temperatureorange



t



Aluminum-beryllium, 4.2 to 32.7 Be. .......

Aluminum-copper, 9.9 Cu



.................



33.2 Cu



.................



Aluminum-nickel, 3.4 Ni

19.5 Ni



Brass, 3 to 40 Zn..



Cast iron



Cobalt-iron-chromium, 53.0 to 55.5 Co, 35.0

to 37.5 Fe, 9.0 to 10.5 Cr.. .............

Copper-beryllium, 3.0 Cu..



................



Copper-nickel, 19.5 Ni



....................



49.8 Ni



....................



-182 to 0

0 to 40

-182 to 0

0 to 40



Authority



Copper-tin (see Bronze)

Copper-zinc (see Brass)

Dumet :

Axial

Radial



.................................

.................................

Duralumin ...............................



6.1 to 6.8

8.0 to 10.0



20 to 100

20 to 500



21.9 to 23.8

25.4 to 27.6



10

3



.............



25 to 300



5.0



11



......................

.5 to 10.5 Al. ..............

1 to 40 Cr.. ...............



0 to 100



0 to 2



12



20 to 100



11.6 to 12.2



13



20 to 100



12.4 to 9.4



12



Fernico, 54 Fe, 31 Ni, 15 Co..

Invar, 64 Fe, 36 Ni..

Iron-aluminum,

Iron-chromium,



20 to 300

20 to 300



*Compiled by Peter Hidnert and H. S. Krider National Bureau of Standards.

t.Chemica1 composition is given in percent by keight.

$Coefficient of expansion varies with composition and treatment.

** Numbers refer to authorities given at end of table.



(continued)



SMITHWNIAN PHYSICAL TABLES



150

T A B L E 143.-COEFFICIENTS OF L I N E A R T H E R M A L E X P A N S I O N OF

SOME A L L O Y S (continued)



Alloy



Iron-cobalt 9.9 to 49.4 Co. .................



Temperature

or temperaturqrange

C



30 to 100



Coefficient

of linear

thermal expansion X 106

per "C



Authority



11.2to 9.3



14



Iron-manganese, 2.8 to 14.4 Mn ............



20 to 100



12.7 to 16.9



13



Iron-nickel, 3.6 Ni .......................

34.5 N; .......................

36 Ni ........................

40 to 50 N i . . ..................



20 to

20 to

0 to

30 to



10.9

3.7

0 to 2

4.1 to 9.7



15,12,

14



8.7 to 18.4

13.1 to 20.6



16



Iron-nickel-chromium, 6.6 to 74.7 Fe, 1.3 to

70.1 Ni, 4.9 to 26.7 Cr .................

Iron-nickel-cobalt, 62.5 to 64.0 Fe, 30.5 to

34.0 Ni, 3.5 to 6.0 Co.. ................

61.3 Fe, 31.8 Ni, 6.0 Co.. ................

58.7 Fe, 32.4 Ni, 8.2 Co ..................



100



100

100

100



20 to 100

20 to 1000

20

20 to 100

20 to 240

20 to 200

20 to 295



.o to



.5



14,17



.9

2.4

1.7

2.6



Iron-silicon, 1.0 to 8.4 S i . . .................



20 to 100



12.2 to 11.3



13



Kanthal (A, A-1, and D) 5



20 to 100

20 to 900



11.4 to 11.7

13.9 to 15.1



18



Lead-antimony, 2.9 to 39.6 S b . . ............



20 to 100



28.2 to 20.4



8



Magnesium-aluminum, 10.4 Al..



...........

30 A1 ..............



20 to 100

20 to 200

0 to 100

0 to 200



25.9

27.2

23.7

25.1



19,20



Magnesium-tin, 20.4 Sn.. ..................



24.3

24.7

21.1

21.3



21



...................



30 to 100

30 to 300

30 to 100

30 to 300



Magnesium-zinc, 20 Z n . . ..................

50 Zn ...................



40 to 100

40 to 100



29.5

30.2



22



20 to 100

0 to 400

0 to 800



18.1

18.9

21.1



23,a



25 to 100

25 to 600



13.5 to 1425

15.9 to 16.7



15,13



20 to 100

20 to lo00

20 to 100

20 to 1000



13.0

17.2

13.5

17.7



16,25



14.8 to 15.4

16.8 to 17.4



26



................



Kovar (see Fernico)



46.3 Sn



Manganin



...............................



Monel Metal



.............................



Nickel-chromium, 20.4 Cr..



................



47.7 Cr..



................



Nickel silver, 62.0 to 63.2 Cu, 10.0 to 20.2 Ni,

17.4 to 27.1 Zn ........................



0 to loo

0 to 400



I Composition of Kanthal: A : 68.5 Fe, 23.4 Cr, 6.2 Al, 1.9 Co, 0.06 C ; A-1: 69.0 Fe, 23.4 Cr, 5.7 Al,

1.9 CO, 0.06 C ; D: 70.9 Fe, 22.6 Cr, 4.5 Al, 2.0 Co, 0.09 C.



(continued)



SMITHSbNIAN PHYSICAL TABLES



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