IX. THERMAL EXPANSIVITY OF SOLIDS

A.
23.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.
N.
0.
P.
Q.
Introduction
Aluni num
Be ry 11 i urn
Beryllium Copper
Brass (Yellow)
Cons tan tan
Copper
Glass
1. Crown C-1
IX. THERMAL EXPANSIVITY OF SOLIDS
CONTENTS
2. Borosilicate Crown BSC-1
3. 11
'I BSC-2
4. Light Barium Crown LBC-2
5. Dense Barium Crown DBC-1
11 11 DBC-3
6.
7. Dense Flint DF-2
8. Extra Dense Flint EDF-3
9. Barium Flint BF-1
10. Crown Flint CF-1
11. Eastman Kodak KO. 11
12. Eastman Kodak No. 32
13. Castman Rodak No. 33
14. Eastman Kodak No. ,45
15. Pyrex
16. Silica
17. Glass and Copper
>
Inconel -
Indium
I nvar
Iron
Le ad
Mag ne s i urn
Mo ne 1
Nickel
N io b i urn, Ni o b i urn-T i t an i urn
- __ . . _. -. , - . . . . . - . . IX-INDEX-1

R.
S.
m
I.
%Po
v.
W.
X.
Y.
Plastics
1. Xraldite No.501
2. Flurothsne
3. Lucite
4. Nylon
5. Plexiglas
6. Polystyrene
7. Polythene
8. Teflon
9. Kel-F
10. Plastics and Cop?er
P la t inum
Quartz
Silver
Soft Solder
Stainless Steels
I. AIS1 304
2. " 310
3, I' 316
4. I' 347
5. " 321
Steel SAE 1020, 9 xi Steel
Tantalum
2, Tin (White)
AA. Zinc
IX-INDEX-%
- . .
- - _
. .
.

INTRODUCTION TO THERMAL EXPANSIVITY OF SOLIDS
Values of thermal expansion are given in the form of
(a) total fractional expansion, L293 - LT : and (b) by coefficient
7
L 293
of expansion dL change per unit length per K. For example
L dT ’
the total fractional expansion (or contraction) for copper for
a temperature change from 293.15OK (2OoC) to 50°K is .00321
in./ine, i.e., a bar will be .00321 inches shorter at 50°K-.per
inch of length than it was at 293.15 OK. However, the co-
efficient of expansion for copper at 50 0 K is.0000038 in./in.- 0 K,
i.e. it will expand (or contract) .0000038 inches per inch per
0
0 K temperature change from 50 K.
Reprinted from WADD TECH. REPORT 60-56
. . . .. . . - _. .- . ....
IX-A-1
0
January 9, 1967

Temp I
0
K
0
10
20
30
40
50
60
70
80
90
100
THERMAL EXPANSION OF ALUMINUM
Source of Data: Altman, Rubin and Johnston 1954,
Other References: Ayres 1950, Bill and Pullan 1955, Buffington
and Latimer 1926, Ebert 1928, Gibbons 1958,
Henning 1907, Hume-Rothery and Strawbridge
1947, Lindemann 1911, Nix and MacNair 1941.
L293 - LT
415
4 15
415
414
413
410
405
3 99
391
381
370
L293
Taken from NBS 29
It
I1
tI
It
I1
It
It
It
It
It
Table of Selected Values
-- 0
1 dL
L dT
per K
0
-.005 x 16'
.02 '
.09
.22 It
.3a 11
.55 I'
.74 It
.91 I'
1.07 'I
1.22 I'
.. . .-
Temp.
0
K
120
140
160
180
200
220
240
2 60
273
280
293
300
IX-B- 1
L293 - LT
343
312
277
240
201
160
118
75
45
30
0
-16
L293
It
I1
II
It
I1
I1
It
It
It
I1
It
. - . . . . . - .
__ . . . -
-- 0
1 dL
L dT
per K
1.46
1.65
1.79
1.90
2 .oo
2.08
2.15
2.21
2.25
2.27
2.30
2.32
It
I1
It
It
I1
11
11
It
It
I1
I1
. . ... . - .

. - .. . -
w4
e
aa
- a
a
>
IX-B-2
_.. -- . . - . . . . ._ .

IX-B-3
.. .

Temp.
0
K
0
20
30
40
50
60
70
80
90
100
120
THERMAL EXPANSION OF BERYLLIUM
Sources of Data: Erfling 1939
Hidnert and Sweeney 1927
Other References:
Discussion:
L - L
293 T
L293
131
131 'I
131 I'
131 I'
131 I'
131
130 'I
130 'I
129 I'
128 I'
124 "
Paken from NBS 29
L d3
per K
0.
Head and Lamer 1952
Anisotropic. The above values were calculated
from the relation, Mean Value = 113
(I/ )-t-2/3 (A ) , where ( li) and (I ) signify the
the same property measured parallel and perpendicular,
respectively, to the trigonal
(Sb,Bi) or hexagonal (Be, Cd) axis.
Table of Selected Values
Temp.
0
K
140
o .OOL x1~-5 160
.003
180
,007 I' 200
.013 'I 220
.02
14
240
.04
I1 2 60
.06
I1 273
.09
I1 2 80
.13
I1
293
.22 II 300
Ix-c-1
L - L
293 . T
L293
119 10'~
111
LOO
87.3
72.0 I'
54.6 I'
35.2
21.8 'I
14.3 I'
0.0 It
-7.9 .
--
1 dL
L dT.
per OK
.34
.47
.59
.71
.82
.92
1. .01
1.06
L.08
. .12
L.14
I1
'I
I1
I1
I1
11
I1
I1
11
It

-"- .... &. __ I. . . . . . . , . . - . . .
. .
... - .. ... ..-. .
__--
IX-c-2
0 50 100 150 2 00 250 380
TEMPERATURE, *K
..... -
-9
. - . ....
. .
0
Of BERYLLIUM I
.
. -. , , .
THERMAL EXPANSION .
15
- . _. __
.- - .
.
..
30
45
60
75
90
.
I05
I20
135

Temp
0
K
0
10
20
30
40
50
60
70
80
90
100 .
120
-
Taken
THERMAL EXPANSION OF BERYLLIUM COPPER
Sources of Data: Beenakker and Swenson 1955
Other References:
Discussion:
L293 - LT
L293
316
316 I'
316 It
316 'I
315 I'
313
309
I'
304
296
287
It
277 'I
255 I'
from NBS 29
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.
Table of Selected Values
--
1 dL
L dT
per OK
0.
-5
0.004 x 10
.009 I$
.05
I1
.14
I1
.27
I1
.43
I1
.65
I1
.84
I1
.96
I1
1.04
I1
1.16
It
IX-D-1
I
Temp.
0 L293 - LT
K
L293
140
160
180
200
220
240
2 60
273
280
293
300
231
206
179
151 I'
121 (I
90 I1
57 ID
35
23
0 l1
-13 I'
1
1 dL -7
L dT 1
ser OX
~~ ~~~~~
1.24 x
1.32 . 'I
1.38
11
1.45
11
1.52
11
1.60
11
1.67
11
1.72
11
1.74
11
1.79
11
1.81
11

In^
I
0
. .
e
-
0)
3
0
5
. _. .-
TEMPERATURE e OK
IX-D-2
.
.. . - ..

IX-D-3
w
I
I-
a
X
w
a
z
n.
I-

il
400
300 --
.
IX-D-4
/

Temp
0
K
0
10
20
30
40
50
60
70
80
90
.oo
.20
'aken
THERMAL EXPANSION OF BRASS (YELLOW)
Sources of Data: Altman, Rubin, and Johnston 1954
Other References: Beenakker and Swenson 1955
Fraser and Ebllis-Hallet 1955
Henning 1907
Keyston, MacPherson, and Guptill 1959
Discussion: 65 Cu, 35 Zn.
384
384
383 'I
382 I'
380 I'
375 I'
368 I'
360 I'
350 I'
339 I8
326 'I
299 'I
lrom NBS 29
Table of Selected Values
--
1 dL
L dT
per OK
0
0.001 xu-5
.OS II
.18 II
.37 II
.58
.76
.92
1.06
1.18
1.29
1.44
I1
II
I1
II
It
II
11
IX-E-1
Temp
0
K
14 0
160
180
200
220
240
2 60
273
280
2 93
300
L293 - LT
L293
269 x 10-5
237 It
204 'I
169 It
134 'I
98.4 'I
61.8 'I
37.3 'I
24.6 It
0.0 It
-13.3 I'
--
1 dL
L dT
per OK
1.54 10-5
1.63 . I'
1.69 I'
1.74 I'
1.78 'I
1.81 It
1.85 'I
1.87 I'
L.88 'I
1.90 'I
L.91
I

. . .
- -. .
._
.- ._ . . .
0 I
, ._ .
t
! /
- -______ 1'
IX-E-2
. - - . .. . . .. . .
I
. ._
! 0
-.

IX-E- 3

Temp.
0
K
THERMAL EXPANSION OF CONSTANT..
Sources of Data: Aoyama and Ito 1939
Krupkowski and deHzas 1928
Other References:
Discussion:
20
60
70
80
90
100
120
140
160
Faken
269
258 "
253 I'
247 'I
240
232
'I
214 I'
194 I'
172 "
rom NBS 29
Henning 1907
Krupkowski 1929
50 Cu, 50 Xi. The name Constantan is
applied to binary alloys in the range,
60 to 45 Cu, 40 to 55 Xi. The nost cmmon
composition is 55 Cu, 45 Xi, The above ex-
pansion data should represent all Constantans
within a few percent. Small expansiofi anomalies
of magnetic origin occur in this system. The -
ferromagnetic Curie points range from
0 OK for 40% Ni to roughly 150 0 K for
Table of Selected Values
--
1 dL
L dT
per OK
0.46
.56
.66 I'
.75 I'
.83
.96 'I
1.06
1.14 '@
Temp.
0
K
iao
200
220
240
2 60
273
280
293
300
IX-F-1
L293 - LT
L293
148 x
124 I'
98.1
71.8
45.0 'I
27.3 I'
17.8 'I
0,o I1
-9.6 *' -'
. .
-
1.21 x
1.26 It
1.30 I'
1.33
1.35
'I
1.36 'I
1.37
L.37
'I
b.38 - "
about
55% Ni .
!

TEMPERATURE, O K
IX-F- 2

Source of Data:
Temp.
0
K
L293 - LT
L293
THERMAL EYSANSION OF COPPER
Rubin, T., Altman, H.W. and Johnston, H.L., J.Am.Chem.Soc. 76,
5289-93 (1954)
Other References:
Simmons,R.O. and Balluffi, R.W., Phys.Rev. 108, 278-80 (1957)
Beenakker, J.J.M. and Swenson, C.A., Rev.Sci.Instr. 26 1204 (1955)
Bijl,D. and Pullan H., Physica 21, 285 (1955)
Fraser, D,B. and Hollis-Hallet, A.C., Proc. 9th Intern. Congr.
Refrig. L, 1065 (1955)
Nix, F.C. and MacNair, D., Phys. Rev. 60, 597-605 (1931)
Aoyama, S. and Ito, T., Sci.Repts. Tohoku Univ. 27, 348-64 (1939)
Adenstedt, H., Ann. Physik 26, 69-96 (1936)
Simon, F. and Bergmann, R., 2. Physik Chem. €3, 255-80 (1930)
o
10
20
30
40
50
60
70
80
90
100
Mrupkowski, A. and DeHaas, W.J., Communs. Phys. Lab. Univ.
Leiden 194b (1928)
Keesom, W.H., Van Agt, F.P.G. and Jansen, A.T.J., Proc.
Acad .Sei. Amsterdam 29, 786-91 (1926)
Buffington, R.M. and Latimer, W.M., J.Am.Chem.Soc.
2305-19 (1926)
48
Sorelius, G. and Johansson, C.H., Ann. Physik 75, 23-36
Lindemann, C.L., Phys. 2. 12, 1197-99 (1911)
Henning, F., Ann. Physik (4) 22, 631-39 (1907)
Dorsey, H.G., Phys. Rev. 25, 88-102 (1907)
Keyston, MacPherson and Gupstill (1959)
Table of Selecteh Values
--
1 dL
L dz
per K
326 0
326 II
0.004 x
326 II .03
325 II
.10
324 II .23
321
It .38
316
I1 .55
3 10 II .70
302 II .84
293
II
.95
283
II 1.05
Taken from NBS 29
II
II
II
II
II
II
II
It
II
Temp.
0
K
120
140
160
180
200
220
240
260
273
280
293
300
IX-G-1
L293 - LT
1293
260
235 I'
208 'I
179 'I
149
118 I'
87
55
33
22 I'
0
-11
--
1 dL
L dg
per K
1.20
1.32 'I
1.41 'I
1.47 'I
1.52 I'
1.56 I'
1.59 'I
1.62 It
1.64 'I
1.65 I'
1.67 'I
1.68 'I
(1924)

1
0 50 10 0 I5 0 200 250 300
TEMPERATURE ,OK
1x4- 2

Sources of Data :
Other References:
Discussion:
Temp.
0
K
80
90
100
120
140
160
180
200
THERMAL EXPANSION OF CROWN C-1 GLASS
Mofby 1949.
Dorsey 1907.
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
134 x
130 "
126 I'
116 I'
105 It
95
82 I'
69 'I
Taken from NBS 29
-
IX-H-1.1
Temp.
0
K
220
240
2 60
273
280
293
300

THERMAL EXPANSION
TEMPERATURE OK
IX-H-1 e 2
-_ ..
..
..

THERMAL EXPANSION OF OPTICAL GLASS BSC-1
Sources of Data: Molby 1949.
Other References: Dorsey 1907.
Discussion:
-
Temp.
0
K
80
90
100
120
140
160
180
200
Taken
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
L2 93 - LT I
L293 I
133
128 I'
124 I'
114 'I
104 'I
92 'I
80 I'
67 I'
~~~
from NBS 29
Cemp . 0
K
2 20
240
2 60
273
280
293
300
IX-E-2.1
L293 LT
L293
53 x 10
39
25 'I
15 I'
10
0
- 6
-5

TEMPERATURE, O K
IX-H-2 2

Sources of Data:
Other References:
Discussion:
THERMAL EXPANSION OF OPTICAL GLASS BSC-2
Temp.
0
K
80
90
100
120
140
160
180
200
Molby 1949.
Dorsey 1907.
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
L293 - LT
112
109
L293
105 'I
97 Ii
88 I'
77 'I
66 'I
57 It
Taken from NBS 29
TPP
K
IX-H-3.1
220
240
2 60
273
280
293
300
L293 - LT
45
33
L293
21 Ii
13 "

TEMPERATURE, OK
IX-H-3.2
4

THERMAL EXPANSION OF OPTICAL GLASS LBC-2
Sources of Data: Molby 1949.
Other References : Dorsey 1907.
Discussion:
Temp.
0
K
80
90
100
120
140
160
180
200
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
L
293 - 'T
L293
137
132 I'
128 It
117 'I
106
95
'I
a2 11
68 'I
raken from NBS 29
0
K
220
240
260
273
280
293
300
IX-H-4 1
'293 - =*
L293
54
40 'I
25 I'
15
10 I'
0
-5 "

Ix-H-4.2

Sources of Data:
THERMAL EXPANSION OF OPTICAL GLASS DBC-1
Molby 1949.
Other References : Dorsey 1907.
Discussion:
Temp
0
K
80
90
100
120
140
160
I
180
200
I
Taken from NBS 29
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
I
L293 -LT I
&I 110 x 10
107 'I
104 I'
95 I'
77 I1
67 "
56
I
IX-E9-5.1
240
260
273
28q
293
300

. .-
. .
TEMPERATURE, OK
IX-11-5.2

. . . . .
THERMAL EXPANSION OF OPTICAL GLASS DBC-3
Sources of Data: Molby 1949.
Other References: Dorsey 1907.
Discussion:
90
100
120
140
160
180
200
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
101 It
98 I'
90 I t
82 I'
73
63 I'
53
Taken from NBS 29
IX-H-6.1
220
240
2 60
273
280,
293
300
42
31 'I
20 It
12
8 'I
0 It
-4 1'

TEMPERATURE OK
IX-H-6.2

THEMU EXPANSION OF OPTICAL GLASS DF2
Sources of Data: Molby 1949.
Other References : Dorsey 1907.
Discussion:
Temp.
0
K
80
90
100
120
140
160
180
200
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
L2 93 - LT
L293
136 x
131 I'
126 I'
115 I'
104 'I
92 I'
79 I'
66 I'
Taken from NBS 29
IX-€1-7.1
Temp.
0
K
2 20
240
260
273
280
293
3 00
52
38 'I
24 'I
15 I'
9
0
I'
-5 '1

TEMPERATURE OK
IX-H-7.2

. I
THERMAL EXPANSION OF OPTICAL GLASS EDF-3
Sources of Data: Molby 1949
Other References: Dorsey 1907
Discussion:
80 1139 x
90
100
120
140
160
180
200
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
135
130
118
106
94
81
67
Taken from NBS 29
I1
I1
I1
I1
II
II
I1 L
Temp* 0
K
2 20
240
2 60
273
280
IX-H- 8.1
'293 - LT
'293
53
39
25
15
10
2 93 0
It
I1
II
I1
I1

'TX-H- 8.2
i

THERMAL EXPANSION OF QPTICAL GLASS BF-1
Sources of Data: Molby 1949.
Other References : Dorsey 1907.
Discussion:
Temp.
3
K
100
120
14 0
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
L293 - LT
133
122
L293
111 It
Taken from NBS 29
Temp.
0
K
240
2 60
273
280
293
300
IX-H-9.1
1 - L
293 T
1293
41
26 'I
16 I'
10 'I
0
-5 1'

IX-H-9.2

Sources of Data:
Other References :
Discussion:
TH3RMA.L EXPANSION OF OPTICAL GLASS CF-1
Temp.
0
?A
80
90
100
120
140
160
180
2 00
Molby 1949.
Dorsey 1907.
Bausch and Lomb Co. designation.
Composition was not given.
Table of Selected Values
5qXx L293
L2 93
L293 - LT
110 x lo-'
107 'I
104 "
95
87
77
67 I'
56 'I
Taken from NBS 29
240
2 60
273
280
IX-H-10.1
33
21 'I
13 'I
8 I'

li
I
t;:
cu
-1
I IO
IO0
75
50
25
0
-10
0 50 108 150 200 2 50 300
TEMPERATURE, OK
. .
IX-H-10.2
I
..
-. .
. _.

THERMAL EXPANSION OF OPTICAL GLASS NO.11
Sources of Data: Molby 1949
Other References : Dorsey 1907
Discussion:
remp.
0
K
80
90
100
120
140
160
180
200
Eastman Kodak Co. designation. .
Composition was not given.
Table of Selected Values
L293 -LT 1 'emp . 0
K
L293
LOO
220 42
97
11
240 31
94 It
2 60 20
88
I1
273 12
80
I1
280 8
72 It 2 93 0
63
It
300 -4
53 II
Taken from NBS 29
IX-H-11.1
L293 - LT
L293 -~
II
I1
I1
II
II
II

. - - -. . . . . -. .
0
. - - -10
..
0 ' 50 I00 150 200 250 300
'TEMPERATURE OK
IX-H-11.2

Sources of Data:
Other References:
Discussion:
THERMAL EXPANSION OF OPTICAL GLASS NO. 32
Temp.
0
K
80
90
100
120
140
160
180
200
Taken
_. _. , . , . . . - - - . .. . . . . . , - . . .
Molby 1949.
Dorsey 1907.
EasLvan Kodak Co. designation.
Composition was not given.
Table of Selected Values
99
96 I'
89 "
81 'I *
72 I'
63 'I
Temp
0
K
220
240
2 60
273
280
293
300
L293 - 'T
L2 93
42
31 I'
20 Ii
12 It
8
0
'I
-4 11
53 Ii
I
from NBS 29
IX-H-12.1 ,

IX-H-12.2

Sources of Data:
Other References:
Discussion:
- . . . - -. . . . . .
THERMAL EXPANSION OF OPTICAL GLASS N0.33
Temp.
0
K
80
90
100
120
140
160
180
200
Molby 1949.
Dorsey 1907
Eastman Kodak Co . . designation.
Composition was nct given.
Table of Selected Values
L293 I
92 10-5 1
L293 - LT 1
90
87
83 'I
74 I'
66 'I
58 I'
49
Taken from NBS 29
. . . . . . . . .
IX-H-13.1
Temp
0
K
220
240
2 60
273
280
293
300
L293 - LT
L293
. ..

1 IO
100
75
50
25
0
-18,
TEMPERATURE, O K
PX-H-13.2

Sources of Data:
Other References :
Discussion:
THERMAL EXPANSION OF OPTICAL GLASS N0.45
Temp,
0 K
80
90
100
120
14 0
160
180
200
Molby 1949.
Dorsey 1907.
Eastman Kodak Co. designation.
Composition was not given.
Table of Selected Values
L2 93 - LT
L293
96 loo5
94 'I
91 II
a5 11
78
70 'I
62 "
52 I'
Taken from NBS 29
Temp
0 K
220
240
2 60
273
280
293
300
IX-H-14.1
L293 - LT
42
L2 93
31 "
20 II
12 I'
0
-4
8 I'

.. . .
TEMPERATURE, * K
IX-H-14 2
.-
. ..
.
c

THERMAL EXPANSION OF PYREX
Sources sf Data: Head and Laquer 1952
Other References: Buffington and Lather 1926
Tool and Saunders 1948
Winter-Klein 1950
Discussion:
T&"P '
K
0
20
40
60
80
100
120
140
160
Table of Selected Values
54.7 x lo-:
55.7
56.7
56.2 I'
53.7
50.2
46.2
'I
41.7 'I
37.2 'I
Taken from NBS 29
1 273
IX-H-15.1
L2 93 - LT
L2 93
32.2
27.2
21.7
15.7
10.2
6.2
4.2
0 .o
-2 -3
..

.
TEMPERATURE, OK
IX-H-15.2
-- -- - - ..
..
.. . . ._
I_

Sources of Data:
Discussion:
Other References:
THERMAL EXPANSION OF SILICA GLASS
TpP
K
-
0
20
40
.
60
80
100
120
14 0
160
-
I L293 - LT
I
Table of Selected
1
Values
L293
-8 x
'2 93
-6.60 'I
-4.90
-3.02
-1.41 'I
-0.12
t0'.87
Keesom and Doborzynski 1934
Scheel and Heuse 1914
The thermal expansion of silica glass
(fused silica, vitreous silica) quartz
glass), though small, is variable from
sample to sample. The above values are
thought to be fairly representative of
average behavior. The temperature of
0
minimum length can vary from 180 to 230 K.
Variations from the above values as large
as 2~10'~ below 180°K and 50% from 180 to
300°K are possible
Beattie et al. 1941 ..
Dorsey 1907.
Head and Laquer 1952, Henning 1907, Scheel
1907, Scott 1933, Sosman 1927, Souder and
' Hidnert 1926, Valentiner and Wallot 1915.
1.61 'I
2.08 li
Taken from NBS 29
~
Temp
0
K
180
200
220
240
2 60
273
280
293
300
IX-H-16.1
-
- LT
I L293
2.32 x 10-5
2.36 'I
2.18
1.81 "
1.26
0.81 I'
0.54 It
0 .o
-0.29 II

TEMPERATURE, OK
.. ..

IX-H-17

THERMAL EXPANSION OF INCONEL
Sources of Data: Altman, Rubin, and Johnston 1952
Other References: Lucks and Deem 1958
Discussion:
Temp.
0
K
0
10
20
30
40
50
60
70
80
90
100
120
229
229 'I
229 'I
229
228
227 I'
224 I'
221
217 I'
211
205 'I
191 (I
Taken from NBS 29
. -. . - . . . .
80 Ni,14 Cr, 6 Fe.
Table of Selected Values
0.
--
1 dL
L dT
per OK
0.003 XLO-~
803
II
.10 II
.19 II
.2a I1
3a
.40
.57
.65
.79
II
I1
II
II
I1
IX-1-1
Temp,
0
K
140
160
180
200
2 20
240
2 60
273
280
293
300
L293 - LT
L293
174
154 I'
134
112
89.1 I'
65.6 'I
41.4 'I
25.2 I'
16.6 I'
0.0 Io
-9.0
1 .91
'1
.oo
1.07 I'
1.12
--
1 dL
L a:
per K
1.16 I'
1.20 ,I1
1.23 I'
1.25 'I
1.26 I'
1.29 I'
1.30 It

I-
-J
1 %
;r
-.I%
PX-1-2

Source of Data:
Other References :
Discussion:
Temp
0
K
0
10
20
30
40
50
60
70
80
90
LOO
L
293- LT
706
706
701
691
67 6
658
638
617
5 95
572
54 9
7
L293
Taken from WADD 60-56
II
II
II
I1
II
II
It
I1
11
II
THERMAL EXPANSION OF INDIUM
Swenson 1955.
Hidnert and Blair 1943.
In the two investigations above, the experimental
methods and sample purities were
very similar. Yet the two points by Hidnert
and Blair, (L273 - L &/ L and (L -
L axe respectively 7% aZZ34% less2Z2an
273
Swenson's corresponding points. Swenson's
data have been adopted solely because they
include more points over .a wider temperature
range .
Table of Selected Values
-- 1 dL
L ds
per K
0.
0.2 x
0.7
1.3
1.7
1.91
2.04
2.15
2.24
2.32
2.39
It
I1
I1
It
II
I1
II
II
II
Temp.
0
K
120
140
160
180
200
220
240
2 60
273
280
293
300
IX- J- 1
L293 - LT
L293
500
448
3 94
339
282
2 24
165
104
63
42
0
-22
II
I1
II
II
II
11
II
It
11
II
--
1 dL
L dT
per OK
2.52 x 10
2.63
II
2.72
I1
2.79
II
2.86
II
2.93
II
3.01
It
3.08
II
3.13
II
3.15
II
3.20
11
3.22
II

. _.
. ._
. __ .
. .
85 0
8 00
700
600
12
n 500
208
-- ---- 100
0
-5 0
IX-J-2

. . ._ __ . . . _. -
THERMAL EXPANSION OF INVAR
Sources of Data: Beenakker and Swenson 1955
Other References : Chevenard 1914
Gregg 1954
Masumoto 1934
Molby 1912
Scheel 1921
Discussion:
Temp
0
K
0
10
20
30
40
50
60
70
80
90
100
120
The expansions of the Invar alloys are
sensitive to composition and heat treat-
ment. The above data are for an alloy
believed to be 42 Ni, 0.8 Mn, bal. Fe,
annealed (Lloyd B. Nesbitt, Private
Communication). Although Beenakker and
Swenson referred to this as "Invar", this
composition approximates 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.
Table of Selected Values
- L
L293 T
52
52
52
52
52
52
52
51
50
49
47
43
L293
Taken from NBS 29 IX-K-1
11
II
II
I1
11
II
II
II
II
II
II
Temp.
0
K
140
160
180
20 0
220
240
2 60
273
280
293
300
L - L
2 93 T
L293
II 34
I1 29
II 23
II 18
II 14
8.6 'I
5.2 I'
3.4 II
0
-1.8 'I

56
50
40
30
20
10
-2
0
TEMPERATURE, OK
IX-K- 2
..

Temp
0
K
THERMAL EXPANSION OF IRON
Sources of Data: Ebert 1928, Nix and MacNair
Other References: Adenstedt 1936, Dorsey 1907
Bergmann 1930
Owen and Williams 1954.
0
20
30
40
50
60
70
80
90
100
120
198
198 It
198 II
197 'I
196 It
195 I'
192 'I
189 It
185 It
181 'I
170 It
'Taken from NBS .29
Table of Selected Values
-- 1 dL
L dT
perOK.
0
0.01 x 104
' .03 'I
.07
.13 'I
..20
.28
.35 II
.42
.49 II
.63
IX-L-1
Temp
0
K
140
160
180
200
220
240
2 60
273
280
293
300
L293 - "T
L293
156
140
122
102
82
60
38
23
15
0
-8
11
I1
II
It
11
I1
I1
I1
II
II
I
1941
Simon and
--
1 dL
L dT
per OK
0.76 x
0.86 I'
0.94 It
1.00 It
1.05 I'
1.09 It
1.13 I'
1.14 'I
1.15 'I
1.16 I'
1.17 I'

225
200
I75
I50
I25
100
75
50
25
0
- I5
0 50 IO0 150 200 250 300
TEMPERATURE, "K
IX-L- 2

Sources of Data:
Other References
Discussion:
Temp.
0
K
0
5
10
20
30
40
50
60
70
80
90
100
Taken
L
293 - LT
708
708
707
700
68 6
667
64 6
624
60 1
5 77
552
5 28
L293
I1
I1
I1
11
I1
II
I1
I1
II
I1
I1
from NBS 29
THERMAL EXPANSION OF LEAD
Dheer and Surange 1958, Ebert 1928, Nix and
MacNair 1942, Olsen and Rohrer 1957.
Dorsey 1908, Gruneisen 1910, Head and L que r
1952, Lindemann 1911, McLennan, Allen and
Wilhelm 1931.
Superconducting lead has a slightly greater
volume and a slightly smaller expansion coefficient
than normal lead according to data by
Olsen and Rohrer covering the region from lo
to the transititon temperature, 7.2OK. For
example, the difference in expansion coefficients
at 5OK is about 10%.
Table of Selected Values
-- 1 dL Temp.
0 L293 - LT -- 1 dL
L dT
K
L dT
per OK
L293 per OK
0
0.03
0.32 I'
1.1 II
1.7
I1
2 .o
I1
2.2
I1
2.3
II
2.4
I1
2.4
I1
2.5 II
2.5
I1
120
140
160
180
200
220
240
2 60
273
280
2 93
300
IX-M- 1.
477
425
I1
372 I1
318
I1
2 63
I1
208
I1
15 2 II
96
11
58
I1
38
0
-20
I1
2.56 x
2.63
2.68
2.72
2.75
2.78
2.82
2.85
2.88
2.89
2.9
2.9
I1
II
I1
II
I1
11
I1
II
I1
I1
I1

IX-M- 2

emp . 0
K
Sources of Data:
Other References:
Discussion:
0
10
20
30
40
50
60
70
80
90
100
120
L293 - LT
490
490
490
489
48 6
482
475
466
454
441
427
3 93
L2 93
Taken from NBS 29
I1
I1
I1
I1
I1
I1
I1
II
I1
I1
I1
THERMAL EXPANSION OF MAGNESIUM
--
Ebert 1928
Goens and Schrnid 1936
Head and Laquer 1952
Gruneisen 1910
Hidnert and Sweeney 1928
Anisotropic. The above values were
calculated from the relation, Mean Value =
1/3 (11 1 + 2/3 (L), where (11 1 and (1)
signify the same property measured parallel
and perpendicular, respectively, to the
hexagonal axis.
Table of Selected Values
1' dL
L dT
per OK
0.
0.005
.04
.14
.33
.57
.81
1.03
1.22
1.39
1.54
1.76
I1
II
II
II
I1
I1
I1
I1
II
I1
Temp.
0
K
IX-N-1
14 0
160
180
200
220
240
2 60
273
280
293
300
L293 - LT
356
L293
316 11
273 81
227 81
180 'I
132 I'
82.9
50.4
32.9 II
0.0 11
-17 -8 It
--
1 dL
L dT
per .OK
1.94
2.10
2.22
2.32
2.39
2.44
2.48
2.51
2.52
2.54
2.55
11
11
II
11
II
II
11
11
11
II '

TEMPERATURE, 'K
IX-N-2
250 300

THERMAL EXPANSION OF MONEL
Sources of Data: Altman, Rubin, and Johnston 1952
Other References: Ackerman 1936
Aoyama and Ito 1939
Fraser and Hollis-Hallet 1955
Krupkowski and de Haas 1928
Discussion: 67 Ni, 30 Cu, 1.5 Fey "cold-rolled" .
Temp a
0
K
0
10
20
30
40
50
60
70
80
90
100
251
251 It
251 'I
251 It
250 'I
248 I'
245 I'
244 I'
236 I'
230 I'
223 I'
120 206 I'
Taken from NBS 29
0,
Table of S'
0.003 x lo-'
.02
106
.14
.23
.34
.46
.57
.67
.75
.a9
It
tI
It
It
I1
II
It
II
II
II
.ected
Temp.
0
K
140
160
180
200
2 20
240
2 60
273
280
293
300
Values
L293 - LT
187
L293
167 'I
144 It
121
96.4
70.9 'I
44.7 II
27.1 "
15.1 It
0.0
- 9.7 'I
--
1 dL
L dT
0
per K
0.99 x lo-!
1.08 'I
1.15 'I
1.20 . I g
1.25 'I
1.29 It
1.33 I'
1.35 'I
1.36 'I
1.38 'I
1.39 I'
IX-0-1 1

TE.MPERATURE, OK
I
IX-0-2
8
0

T H E W EXPANSION OF NICKEL
Sources of Data: Krupkowski and DeHaas 1928, Nix and
MacNair 1941.
Other References: Adenstedt 1936, Altman, Rubin and Johnston
1954, Aoyama and Ito 1939, Disch 1921, Henning
1907, Simon and Bergmann 1930.
Temp.
0
K
0
20
30
40
50
60
70
80
90
100
120
224
2 24
224
223
221
219
216
211
206
201
187
Taken from NBS 29
I1
II
I1
I1
II
I1
I1
I1
It
II
--
1 dL
L dg
per K
0.
0.02
,05
,10
.19
.28 I'
.38 I'
.47
.55 It
.6l
.75
Table of Selected Values
Temp.
0
K
140
160
180
200
220
240
2 60
273
280
2 93
300
IX-P-1
L293 - LT
L293
171
15 2
13 2
111
88
65
41
25
16
0
-9
I1
I1
I1
I1
II
I1
11
II
II
II
-- 1 dL
L dg
per K
0.88 x
0.98 I'
1.05 I'
1.10 .I1
1.15 'I
1.19
1.22 I1
1.23 "
1.24 I'
1.26 'I
1.26 I'

225
200
175
I50
125
100
75
50
25
0
0 50 100 I50 200 250 300
TEMPERATURE, "M
IX-P-2

THERMAL EXPANSION OF NIOBIUM
Sources of Data: Erfling 1942.
Other References : Hidnert and Krider 1933.
Discussion:
Temp.
0
K
0
10
20
30
40
50
60
70
80
90
100
L293 - LT
14 3
14 3
143
14 1
13 9
13 7
13 3
129
125
121
'293
120 111
I1
Taken from NBS 29
I1
11
I1
It
I1
I1
11
II
I1
Also termed columbium.
Table of Selected Values
- 1 %
L dT
perOK
0.
.03
.09
.17
.24 I'
.31
.36
.40
-44
.47
.52
Temp.
0
K ,
14 0
160
180
200
220
240
2 60
273
280
293
300
IX-Q-1 ,
99.4
87.7
75.5
63 .O
50 .O
36.7
23.1
14.1
9.2
0 .o
-5.0 , '
--
1 dL
L dT
per OK
.56 x
.59
.62
.64
.66
.67
.68
.69
.69
.70
.70
c
I1
I1 .
I1
I1
I1
It
I1

TEMPERATURE, OK
IX-Q-2

IX-Q-3
W O N *
9 9
8 0 0
!.I I I I I I I I 1 I I I
0
0
N
0
m

I
THERMAL EXPANSION OF ARALDITE N0.501
Sources of Data: Laquer and Head 1952.
Other References:
Discussion:
Temp.
0
K
0
20
40
60
80
100
120
140
160
180
Caken
Epoxy casting resin made by Ciba Co.
40 g of the material was catalyzed with
2 ml triethanolamine. Cured 8 hr. at
120° C and then 24 hr. at 180° C.
Table of Selected Values
L293 - LT
L293
~
LO61 x 10-5
LO51 I1
LO22
983 I'
935 'I
880 I'
819 I'
751 I'
676
594 II
irom NBS 29
IX-R-1.1
Temp
0
K
200
220
240
2 60
273
2 80
2 93
300
L293 - LT
L293
505 x 10-5
410 I'
308 'I
199 II
122
81 'I
0
-46 I'

I150
I100
IO00
900
h
ro
' 800
0
ZI
n
-
W
=J 700 0
>
-
Q
.-
4- - 600
i
v
500
Yr)
0
ru
-I
400
300
200
100
THERMAL EXPANSION
of AWALDITE NO, 501
0 50 100 150 200 2
TEMPERATURE, O K
IX-R-1.2
3 300

Sources of Data:
Other References:
Discussion:
THERMAL EXPANSION OF FLUOROTHENE or KEL-F
Temp.
0
K.
0
20
40
60
80
100
120
14 0
160
Laquer and Head 1952.
Polychlorotrifluoroethylene. The
samples were, respectively, froma
5 in. diameter rod of Fluorothene made
by Union Carbon and Carbide and from a
1/16 in. thick sheet of Kel-F made by
M.W. Kellog and Co.
Table of Selected Values
'293 - LT
L293
L/35 x lo-s
L1L4 I'
LO70 'I
LO19 I'
962 'I
900 'I
834 'I
763 I'
686 I'
Taken from NBS 29
Pemp . 0
K
180
2 00
220
240
260
273
280
293
300
604
517 'I
424 'I
324 'I
214 I'
134 'I
90 Io
0 , 'I
-52 II

I
IX-R-2.2
8

Sources of Data:
Other References:
Discussion:
Temp.
0
K
0
20
40
60
03
too
-20
-40
.60
THERMAL EXPANSION OF LUCITE
Laquer and Head 1952.
Po Pyme t hy lme t hacry late .
DuPont Lucite''.
from rod stock.
Table of Selected Values
1134
1123
1092
1048
995
93 6
869
796
717
x lo-!
Taken from NBS 29
I1
I1
I1
I1
I1
I1
II
I1
IX-R- 3.1
Temp
0
K
180
200
220
240,
2 60
273
280
293
300
" Probably
Average of two samples
L
293
L293
63 2
540
441
335
220
13 6
91
0
-53
- LT
x lo-!
II
I

IX-R- 3.2

Sources of Data:
Other References:
Discussion:
Temp.
0
K
0
20
40
60
80
100
120
140
160
raken
Laquer and Head 1952.
From 3/4 inch diameter rod. "Probably
E.I. DuPont de Nemours and Co. grade FM-1".
Table of Selected Values
L293 - LT
L293
1389 x lov5
L379 I(
1352
1308 "
L247 I'
1172 'I
LO88 I'
996 I'
896 'I
irom NBS 29
Temp
0
K
180
200
220
240
260
273
280
300
IX-R-4 1
-
L293 - LT
L293
789 x 10'
673 I'
548 I'
412 'I
2'65 'I
161 @I
107 I'
0
- 61
I1

IX-R-4.2

THERMAL EXPANSION OF PLEXIGLAS
Sources of Data: Data from Laquer and Head 1952. (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 (L -L )
293 78
L293
Other References: Wood, Bekkedahl and Peters 1939,
Discussion:
Polymethylmethacrylate made by Rohm and
Haas Co. Data from Giauque, Geballe,
Lyon and Fritz 1952.
Table of Selected Values
I
Temp.
0
K
-
0
20
40
60
80
100
120
140
160
L293 - LT
L293
1210 I'
1160 'I
1110 I'
LO50 'I
180
Taken from NBS 29
IX-K-5.1
Temp.
0
K
200
220
240
2 60
273
28 0
293
298
300
L293 - LT
590
L293
490 I'
-55 I'

IX-R-5.2

Sources of Data:
Other References :
Discussion:
THERMAL EXPANSION OF POLYSTYRENE
Tgmp .
K
u
20
40
60'
80
loo
120
140
160
Laquer and Head 1952. (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 (L -L )/L293.
293 78
Wood, Bekkedahl and Peters 1939.
Average of two samples from rod stock,
both "probably American Phenolic Corp.
grade 912A.
Table of Selected Values
1550 x
1552 I'
1466 'I
1394 'I
1308 " "
1211 It
1105 It
992 I'
874 I'
180 752 'I
Taken from NBS 29
Temp
0
K
2.0 0
220
240
260
273
280
293
298
300
IX-R-6.1
L
293 - LT
L293
626 x 10-5
499 'I
368 I'
232 I'
141 I'
93 I'
0 "
-51 II

I-
-%
* a
%J
200
0
- 100
IX-R-6.2
a

THERMAL EXPANSION OF POLYTHENE
Sources of Data: Laquer and Head 1952. (In addition to
the substances listed in the table, data
have been given for 16 specially compounded
rubbers by Bunsmoor et al. 1958 and Trepus
et al. 1959. These data consist.mainly of
values of (L -L
293 78
Other Re ference s : WOQ~, Bekkedahl and Peters 1939.
Discussion: Polyethylene made by E.I. Du Pont de Nemours
and Co.. Molded under 2000 psi pressure at
l5OoC for 10 min. Directional variations
were negligible. See also Hunter and Oakes
1945. Five filled polythenes were measured
by Head and Laqyer 1952.
remp .
0
K
0
20
40
60
80
too
L20
L40
160
-80
Table of Selected Values
L293 - LT
L293
2449 x 10-5
2439 I1
2404 I1
2349 I1
2279 I1
2194 11
2089 I1
1964 I1
1814 I1
1639 I1
Taken from NBS 29
Temp.
0
IC
200
220
240
2 60
293
2%0
293
298
300
IX-R- 7.1
- L
L293 T
L293
1439 10-5
1199
919 'I
594
359 'I
239
0
-131

I-
? %
m N
m-l
N
-I
-200 0
TEMPERATURE, OK
IX-R- 7.2

LL
a
3
0
aJ
a
.
L
4-
L
E
?
0 0
I
0
tu
M
0
a3
(u
0
d-
(u
0
0
N
Y
a
3
0
c
L
c
3 L
@ a J
E
e
-
3
5
3
D
>
t
>
w
2
w
J
>.
I
I-
w
).
J
0
a
a2
0
U
w
z)
a
l-
a
U
w
a
2
w
I-
C/)
' 3
C/)
U
w
>
z
0
C/)
2
X
w
-I
-
a
a
a
z
E
w
I
I-
IX-R-7.3

THERMAL EXPANSION OF TEFLON
Sources of Data: Laquer and Head 1952
Other References: Dunsmoor et al. 1958
Trepus et al. 1959
Wood, Bekkedahl and Peters 1939.
Discussion: Polytetrafluoroethylene . Extruded and
annealed sample measured by Kirby 1956.
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 DuPont Teflon rod taken normal
and parallel to the extrusion directicn.
The expansions parallel were roughly 15%
larger than those normal, and the average
is 10 to 15% larger than the the above data
by Kirby. The data of Laquer and Head were
used only to guide the extrapolation of Kirbyts
values below 80°K. Teflon has a first order
transition at 2OoC. Therefore we use 25O C
as a reference temperature and tabulate lo5
(L298-LT) L298 above.
Temp
0
K
0
20
40
60
80
LOO
120
140
Table of Selected Values
L293 - LT
L293
2140 x
2110
2060 I'
2000 I1
1930 I'
1850 I'
1760 'I
1660 It
Taken from NBS 29
Temp,
OK
160
180
200
2 20
240
2 60
273
298
IX-R-8.1
L2 93 - LT
L293
1540 x lom5
1400
11
1240
I1
1050
I1
855
I1
645
I1
500
I1
0
11

h
m
-
b
2200
2000
1750
I500
>r 1250
n
Q)
- 3
0
1
I-
-1
I ' c )
4?
2-1
A
750
500
250
-200
0
0
THERMAL EXPANSION
50 100 150 200 2 50 300
TEMPERATURE, O K
IX-R-8.2

THERMAL EXPANSION OF PLATINUM
Sources of Data: Nix and MacNair 1942.
Other References: Dorsey 1907.
Henning 1907.
Onnes and Clay 1096.
Scheel 1907.
Scheel and Heuse 1907.
Valentiner and Wallot 1915.
Discussion:
I
IX-s-1

3
1 %
;3
-I
IX-s-2

Temp.
0
K
THERMAL EXPANSION OF QUARTZ (CRYSTALLINE 11 )
Sources of Data: Buffington and Latimer 1926
Other References : Dorsey 1908
Lindemann 1912
Nix and MacNair 1941
Scheel 1907
Sosman 1927
Discussion: Measured parallel to the optic axis. Nix
and MacNair measured expansions perpendi-
cular to the optic axis but presented only
a coarse graph of the resukts, from which
the following values of 10 (dL/LdT) were
taken: 7 at 100°K, 10 at 150°, 12 at 200°,
13 at 250°, 14 at 300°K.
90
10 0
120
14 0
160
180
200
220
Taken
107 lod5
104 I'
97.7 'I
89.8 'I
80.9 I'
71.2 I'
60.5 I'
49.1 I'
irom NBS 29
--
1 dL
L dT
per OX
0.27
Table of Selected Values
,31 It
.37 I1
.42 II
Temp.
0
K
.47 I)
.51 It 300
.55 I1
.59 II
IX-T-1
36.7 x lo-!
23.6 I'
14.6 I'
9.6 I'
0.0 II
- 5.3 II
--
1 dL.
L dT
per OK
0.64
.68 'I
.71 II
.72 'I
.75 I'
.76 I'

110
TEMPERATURE, OK
IX-T- 2
0
0.88
0.80
-0.08
1
8

THERMAL EXPANSION OF SILVER
Sources of Data: Ebert 1928, Nix and MacNair 1942.
Other References: Ayres 1905, Buffington and Latimer 1926,
Dorsey 1907, Henning 1907, Keesom and
Jansen 1927, Lindemann 1911.
Keesom and Kohler 1933.
Owen and Williams 1954.
Shearer 1950.
Taken from NBS 29
Table of Selected Values
IX-u-1

I-
-1m
l a
(u
-f
KY
-20
TEMPERATURE, OK
IX-u-2

THETFAL EXPANSION OF SOFT SOLDER
Sources of Data: Dorsey 1907
Other References:
Discussion:
Temp.
0
K
90
100
120
140
160
183
200
467
447 "
407 'I
365 I'
321 'I
276 I'
229 I'
Taken from NBS 29
50 Pb, 50 Sn.
Table of Selected Values
--
1 dL
L dT
per OK
1.96
2.00 It
2.07 'I
2.14 I'
2.22 'I
2.29 'I
2.35 I'
IX-v-1
Temp.
0
K
220
240
2 60
273
280
293
300
182 x
133 I'
83 It
51 I'
33 II
0 It
-18 'I
--
1 dL
L dT
per OK
2.41
2.46 'I
2.50 'I
2.52 I'
2.53 'I
2.54 'I
2.55 "

TEMPERATURE, OK
IX-v-2

THERMAL EXPANSION OF STEEL AIS1 304
Sources of Data: Altman, Rubin, and Johnston 1954
Beenakker and Swenson 1955
Other References : Fontana 1948
Fontana, Bishop, and Spretnak 1953
Furman 1950
Discussion:
Composition limits for this alloy are:
0.08 max. C, 2 max. Mn, 1 max. Si, 18-20 Cr,8-
11 Ni. Altman et al., found small irreversible
effects and, below 35OK, small negative values
of expansion coefficient. While we have given
their results inferior weight in this region,
the effects were undoubtedly real and attributable
to martensitic transformation on cooling
(Reed and Mikesel1,1958). In this alloy the
extent of transformation that is produced by
cooling is sensitive to composition and has
been found to vary from zero to about 50%.
(R .P .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,
Averbach, and Cohen, 1955.)
Temp.
0
K
0
10
20
30
40
50
60
70
80
90
100
120
Faken
L293 - LT
L2 93
296 x 10-5
296 I'
296 I'
296 'I
296 I'
294 I'
291
285 'I
279 I'
271 I'
261 'I
241 I'
from NBS 29
Table of Selected Values
--
1 dL
ilT
per K
0,
0.001 x lo'?
,002 'I
. ,062 'I
* 11 11
.23 II
* 43
61
75
.87
.96
I1
II
II
II
I1
1.09 I1
Temp.
0
K
-
14 0
160
180
200
220
240
2 60
273
28 0
293
300
IX-w-1.1
218
193
I1
167 I1
139 II
111 II
81.7 I'
51.4 'I
31.4 'I
20.5 I'
0.0
-11.1
--
1 dL
L dT
per OK
1.20
1.28 I'
1.34 I'
1.40 'I
1.45 'I
1.49 II
1.53 It
1.55
1.56 'I
1.59
1.60 I'

h
In
I
0
h
320
300
250
200
n
- 2 150
P
- ZI
.- Q
.I- -
E'
v
IO0
50
0
50 100 150 200 250 300
TEMPERATURE, OK
IX-w-1.2
1.92
iao
1.50
Y
0
5
Q
160 -
1.30
3
"1'
-1-J
urn

. I
IX-W-1.3
pa3Jad UO!SUDd%3 IDlLl.I.7111
0
" - i. -
0
I
"J
0
I
n
0
I
' 0
C)
v
I
0
M
I
Q
I- -
\ i
L
Y
1' I
P:'
c I
C

Temp
0
K
90
100
120
140
160
180
200
THERMAL EXPANSION OF STEEL AIS1 310
Sources of Data: Furman 1950
0 the r Re fer e nce s :
Discussion:
L293 - LT
246
L293
237 'I
218 I'
198 I'
176 I'
152 'I
127 I'
Taken from NBS 29
0.11 C, 1.51 Mn, 0.42 Si, 0.01 S, 0.02 P,
27.2 Cr, 21.6 Ni, bal. Fe. Annealed 30
min. at 1950° F and water quenched.
Table of Selected Values
- 1 %
L gT
per K
0.89
.91
.98
1.07
I1
1.14 II
1.21 (I
1.27
II
I1
It
Temp
0
K
220
240
2 60
273
280
2 93
300
IX-w-2.1
L293 - LT
L293
74.5
46.9 I'
28.6 "
18.7 I'
0.0
-10.2
- 1dJ
L dT
0
per K
1.32
1.36 I'
1.40 'I
1.42 I'
1.43 I'
1.45 'I
1.46 'I

IX-w-2.2
136
I1.50
1.20
X60
1.30
Y
L
a,
a
8

IX-w-2.3
0
-
0
I
d
I
N
. _
-. .
...
.....
\'
I '
1
x
UI
__ ..
._ -
\ \
._ ,-
....
. . .
..
....
. . .
__ . .-
.
.-
-. .
.......
..
.. ._ I
-.
. ._
.......
. -. ......
...
.....
\ \
...
.. -
. --..
___ -.
........
........
\
... \
__ -
..
.....
\ \
. -
.......
.
. . . .
...
--
.
_-
I_
.

THERMAL EXPANSION OF STEEL AIS1 316
Sources of Data: Beenakker and Swenson 1955.
Other References Furman 1950
Lucks and Deem 1958
Discussion:
-
remp . 0
K
-
0
10
20
30
40
50
60
70
80
90
too
120
L293 - LT
'293
Taken from NBS 29
Composition and heat treatment of sample
not stated. Composition limits for this
alloy are: 0.10 (max.) C, 2 (max.) Mn, 1
(max.) Si, 16-18 Cr, 10-14 Ni, 2-3 Mo,
bal. Fe.
Table of Selected Values
- 1 &
L dT
0
per K
0,
0 .004 lom5
.009
.05
.14
.27
.43
.65
.82
.94
1.02
1.13
II
I1
II
I1
II
II
II
I1
II
IX-W-3.1
Temp.
0
K
14 0
160
180
200
220
240
2 60
273
280
293
300
214
189 'I
163
136 "
109
80.1 I'
50.6 I'
30.9 'I
20.2 'I
0.0
-11.0 'I
-- 0
1 dL
L dT
per K
1.21
1.27
1.32 I'
1.36 I'
1.41
1.45 I'
1.50 I'
1.53 'I
1.54 I'
1.57 'I
1.58 'I

IX-w-3.2
8
e

IX-W-3.3
0
.._I
0
(u
I
. ....- .
-_
.
1 ............ ..
.........
-
-- -
._ i
-.
......
I
I
.... - .
.
--
.
\I .I_._
I
F
-_
1 .
. .- I ......
.......
...
.
1- . --
\ I
. .I-- ....
I
- ........ ..............
- -__ _.
.- .....
......
W
a
........
I
..
- - ._
....
I__. __
..
_- \
\
I---
\
h

THERMAL EXPANSION OF STEEL AIS1 347
Sources of Data: Furman 1950.
Other References: Lucks and Deem 1958.
Discussion: 0.07 C, 1.74 Mn, 0.56 Si, 0.006 5,
0.019 P, 18.65 Cr, 11.3 Ni, 0.77 Nb,
bal. Fe. Annealed 30 min. at 1950° F
and water quenched.
Temp.
0
K
90
100
120
140
160
180
200
Taken
L293 - LT
L293
262
253 'I
233
211
I'
187 'I
163 I'
136 I'
from VBS 29
Table of Selected Values
--
1 dL
L dT
per OK
0.94 x lom5
.98 'I
1.05 I'
1.13 I'
1.21
1.28
1.34 'I
IX-W-4.1
Tgmp .
K
220
240
2 60
273
280
293
300
L293 -,
109
L293
'T
80.2 "
50.6 I'
30.9 I'
20.2 I'
0.0
-11.0
1 dL -7
L dT
per OK
1.40
1.46 I'
1.50 'I
1.53 I'
1.54 I'
1.56 'I
1.57 'I

I-
T'g
-J
82
of STEEL A.I.S.I. 347
0 50 100 I00 200
TEMPERATURE, OK
IX-W-4.2
250 300
1.62
1.50
1020
0.30
0

+ua3J a d
-
0
...
0 (\J ”.
0 0
I
0
0
d-
I
3
d-
__.
0
pr,
I
. . __
0
OD
O
N -
I
C
C
h
E
I- a,
a
CT:
UI
Y
a, .
L
C
C
~
I
0
Tt
N
I
I
F
0
a3
cu
m

THERMAL EXPANSION OF STEEL, S .A.E. 1020
Sources of Data: Altman, Rubin and Johnston 1952
Other References: Beenakker and Swenson 1955
Dorsey 1910
Gregg 1954
Discussion:
Temp.
0
K
0
10
20
30
40
50
60
70
80
90
100
1.20
Taken
L293 - LT
L
293
202
202
201
201
200
198 I'
195 'I
192 I'
187
182 I'
170 'I
from NBS 29
0.
0.18 Cy 0.33 Mn, 0.01 Si, bal. Fe.
According to Beenakker and Swenson, cast
iron had the same thermal expansion as 1020
steel within their experimental uncertainty
of +3~10'~ in AL/L.
Table of Selected Values
-5
0.001 x 10
.03
.08
.14
.23
.31
.40
.48
.55
.68
I1
II
II
II
II
II
II
II
$1
Temp.
0
K
140
160
180
200
2 20
240
2 60
273
28 0
293
300
LX-x-1
155
138 'I
120
101 II
80.7 It
59.6 'I
37.7 It
22.9
15.1 'I
0.0
-8.3 It
--
1 dL
L dT
per OK
-5
0.78 x 10
.87 I'
.94
.99 I'
1.04 I'
1.08
1.11
I'
1.14 I'
1.15 'I
1.17 I'
1.19

TEMPERATURE, OK
IX-x- 2

‘IX-X- 3
3
3
$
3
r)
D
N -
3
e
0
.5
L
ai -
n
I-
L
z
LL
Y
aJ ”
L
0 2
- Y?
0)
9.
E
0)
I-
0
(u
0
d
(u.
0
00
cu
0
(u
m

I'emp . 0
K
0
10
20
30
40
50
60
70
80
90
LOO
120
THERMAL EXPANSION OF TANTALUM
Sources af Data: Nix and MacNair 1942
Other References : Disch 1921
Hidnert 1929
L293 - LT
L
293
14 3
143
143
142
141
13 8
135
13 1
127
122
117
106
10'~
Taken from NBS 29
II
II
II
II
11
II
I1
II
II
I1
Table of Selected Values
0.
0.005 x
.04
.11
.20
.2%
.35
.41
.45
.49
.52
.55
I1
I1
II
I1
11
I1
I1
I1
I1
I1
1
IX-Y-I.
L293 - LT
'293
95.1 x lo-!
83.5
71.5
59.3
47 .O
34.4
21.6
13.1
8.5
0 .o
-4.6
--
1 dL
L a;
per K
0.58 x 10 -
.59 It
.60 "
.61 I'
.62 'I
.63
.65 I'
.65 'I ,
.66 'I
.66 I'
.66 'I

3
1 %
rnN
2-J
-I
IX-Y - 2
0.68
0.60
0.50 - lo
I
0
-
n
0)
- 3
0.40 5
0.30
0.20
0.10
0
-
.- a
- c
i
v
5
L
0)
a
L
Ai-
WI-0
-1-1

Sources of Data: Erfling 1939
THERMAL EXPANSION OF TIN (WHITE)
Other References: Cohen and Olie 1910
Dorsey 1907
Gruneisen 1910
Discussion:
Temp
0
K
0
10
20
30
40
50
60
70
80
90
00
20
447
447
445
441
433
423
412
399
385
371
356
3 24
Taken from NBS 29
I1
II
I1
I1
I1
I1
II
It
II
II
11
Anisotropic. The above values were calculated
from the relation, Mean Value = 1/3 (11 ) +
2/3 (J.), where ( 11 ) and (I.) signify the same
property measured parallel and perpendicular,
respectively, to the tetragonal axis.
Thewlis and Davey (1954) measured the lattice
parameter of grey tin, a brittle form with
diamond-type lattice that is stable below 18OC.
Their data cover the range, -130 to +20°C, and
are, represented by a constant expansion coefficient,
dL/LdT = 4.7 x 10-6deg'1C. 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.
Table of
- 1 3
L dT
per OK
0.
-5
.07 x 10
I1 .3
.6
.9
1.1
1.2
1.3
1.42
1.50
1.56
1.64
11
II
I1
I1
It
I1
II
I1
I1
Selected Values
Temp.
0
K
140
160
180
200
220
240
2 60
273
280
293
300
IX-2-1
L
293 - LT
L293
290
255 I'
219 It
183 I'
145 I'
106 I'
66.7 I'
40.7 'I
26.5 'I
0.0
-14.4 'I
--
1 dL
L dT
per OK
1.71 x
1.77
1.82
1.87
1.91
1.95
1.99
2.01
2.03
2.05
2.06
II
11
I1
I1
II
II
II
I1
I1
I1

TEMPERATURE, O K
IX-2-2

'emp .
'K
--
0
10
20
30
40
50
60
70
80
90
30
653 10-5
a 3
682
677
667
652
633
611
588
565
541
II
11
I1
II
I1
It
II
11
I1
II
I
---, pi"" 9
1 dL
L dT
--
0
.03 10-5
*3
.R
1.3
1 *7
2.1
2.2
2.3
2.36
2.42
II
I1
11
If
II
II
I1
II
I1
IX-AA-1
II
II
I'
I1
II
Il
II
11
II
II
1 dI,
- -., pr 9
L dT
. ___ . .
2.53 10-5
2.63- , 1'
2.73
2.81
2.87 It
2.51
2.911..
2.56..
2.97 '
2-.35
fl
' II
It
2.93 '.It
, ..
3.m
- . __ - . .
..

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