ix. of solids - brookhaven national laboratory to thermal expansivity of solids values of thermal...
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A.
23 .
C.
D. E . F.
G .
H .
I .
J. K . L.
M.
N. 0.
P.
Q.
I X . THERMAL EXPANSIVITY OF SOLIDS CONTENTS
I n t r o d u c t i o n A l u n i num Be ry 11 i urn B e r y l l i u m C o p p e r Brass ( Y e l l o w ) C o n s t a n t a n C o p p e r Glass
1. C r o w n C - 1 2 . B o r o s i l i c a t e C r o w n BSC-1
4 . L i g h t B a r i u m C r o w n LBC-2 5 . D e n s e B a r i u m C r o w n DBC-1
11 11 DBC-3 6 . 7 . D e n s e F l i n t DF-2 8. E x t r a D e n s e F l i n t EDF-3 9 . B a r i u m F l i n t BF-1
11 3 . 'I BSC-2
1 0 . C r o w n F l i n t CF-1 11. E a s t m a n K o d a k KO. 11 1 2 . E a s t m a n K o d a k No. 3 2 1 3 . C a s t m a n R o d a k N o . 33 1 4 . E a s t m a n K o d a k N o . ,45 15. P y r e x 1 6 . S i l i c a 1 7 . Glass and C o p p e r >
I n c o n e l -
I n d i u m I n v a r I r o n L e ad
Mag n e s i urn Mo ne 1 N i c k e l N i o b i urn, N i o b i urn-T i t a n i urn
IX-INDEX-1
. - - _ _ . . _. -. , - .. . . . . . - . . .
R .
S. m I .
% P o
v. W.
X .
Y.
2 ,
P l a s t i c s
1. Xra ld i t e No.501 2 . F l u r o t h s n e 3 . L u c i t e 4 . Nylon 5 . P l e x i g l a s 6 . P o l y s t y r e n e 7. P o l y t h e n e 8 . T e f l o n 9 . Kel-F 10. Plastics and Cop?er
P l a t inum
Quartz
Silver
S o f t Solder
S t a i n l e s s S t e e l s
I. AIS1 304 2. " 310 3 , I' 3 1 6 4. I' 347 5. " 321
S t e e l SAE 1020, 9 xi S t e e l
T a n t a l u m
Tin (Whi t e )
. . . . - . - - _ .
AA. Zinc
IX-INDEX-%
INTRODUCTION TO THERMAL EXPANSIVITY O F SOLIDS
Values of t h e r m a l expansion are given i n t h e form of
(a ) t o t a l f r a c t i o n a l expansion, L293 - LT : and (b) by c o e f f i c i e n t 7
0 L 293
of expansion dL change per u n i t l e n g t h per K . For example L dT ’ t h e t o t a l f r a c t i o n a l expansion (o r c o n t r a c t i o n ) f o r copper f o r
a tempera ture change from 293.15OK (2OoC) t o 50°K is .00321
i n . / i n e , i . e . , a bar w i l l be .00321 inches s h o r t e r a t 50°K-.per
i n c h of l e n g t h than it w a s a t 293.15 OK. However, t h e co-
e f f i c i e n t of expansion f o r copper a t 50 0 K is .0000038 i n . / i n . - 0 K,
i . e . i t w i l l expand ( o r contract) .0000038 inches p e r inch per
0 0 K tempera ture change from 50 K.
Repr in ted from WADD TECH. REPORT 60-56
January 9, 1967
IX-A-1
. . . .. . . - _. .- . ....
THERMAL EXPANSION O F ALUMINUM
Source of Data: A l t m a n , Rubin and Johnston 1954,
O t h e r References: Ayres 1950, B i l l and Pullan 1955, Buffington and Latimer 1926, Ebe r t 1928, Gibbons 1958, Henning 1907, Hume-Rothery and Strawbridge 1947, Lindemann 1911, Nix and MacNair 1941.
Table of Se lec ted Values
Temp I K 0
0
10
20
30
40
50
60
70
80
90
100
L293 - LT L293
415
4 15
415
414
413
410
405
3 99
391
3 8 1
370
I t
I 1
t I
I t
I 1
I t
I t
I t
I t
I t
Taken from NBS 29
1 dL L d T
per K
-- 0
0
-.005 x 16' .02 '
.09
.22 It
.3a 11
.55 I'
.74 I t
.91 I'
1 . 0 7 'I
1 .22 I'
Temp. K 0
120
140
160
180
200
220
240
2 60
273
280
293 300
L293 - LT L293
343
312
277
240
201
160
118
75
45
30
0 -16
I t
I 1
II
I t
I1
I 1
I t
I t
I t
I 1
I t
__ . . . - 1 dL L dT
per K
-- 0
1 . 4 6
1.65
1 .79
1 .90
2 .oo 2.08
2.15
2 . 2 1
2.25
2 .27
2.30 2.32
I t
I 1
I t
I t
I 1
11
11
I t
I t
I 1
I 1
. . ... . - .
IX-B- 1
. - . . . . . - . .. . . -
THERMAL EXPANSION O F BERYLLIUM
Sources of Data: E r f l i n g 1939 Hidnert and Sweeney 1927
Other References:
Discussion:
H e a d and Lamer 1952
Aniso t ropic . The above v a l u e s w e r e cal- c u l a t e d from t h e r e l a t i o n , Mean Value = 113 ( I / )-t-2/3 ( A ) , where ( l i) and (I ) s i g n i f y t h e t h e same proper ty measured p a r a l l e l and per- pendicular , r e s p e c t i v e l y , t o t h e t r i g o n a l (Sb,Bi) or hexagonal (Be , Cd) axis .
Table of Se lec t ed Values
Temp. K 0
0
20
30
40
50
60
70
80
90
100
120
L - L 293 T
L293
131
131 'I
131 I'
131 I'
131 I'
131
130 'I
130 'I
129 I'
128 I'
124 "
L d3 per K
0.
o .OOL x1~-5 .003
,007 I'
.013 'I
.02 14
.04
.06
I1
I 1
.09 I1
.13 I 1
.22 II
Temp. K 0
140
160
180
200
220
240
2 60
273
2 80
293
300
Paken from NBS 29
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.
p e r OK
- -
.34
.47
.59
I 1
'I
. 7 1 I 1
. 82 I 1
.92 I 1
1. .01 11
1.06
L.08
. .12
L.14
I 1
I 1
11
It
..... -
135
I20
I05
90
75
60
45
30
15 0
-9
- .
_. __
THERMAL
EXPANSION .
Of BERYLLIUM
I
. . -.
, , .
. - ..
..
.
0
50 100
150 2 00
250 380
TEMPERATURE, *K
IX-c-2
.
.- -
.
. ..
..
__--
...
- .. ... ..-.
. .
.
.-
, .
-"- ....
&.
__ I. .
..
..
.
..
.
THERMAL EXPANSION OF BERYLLIUM COPPER
Sources o f D a t a : B e e n a k k e r and S w e n s o n 1955
O t h e r R e f e r e n c e s :
D i s c u s s i o n :
T e m p K 0
0
10
20
30
40
50
60
70
80
90
100 .
120
- T a k e n
L293 - LT L293
316
316 I'
316 It
316 'I
315 I'
313 I'
309
304 It
296
287
277 'I
255 I'
from NBS 29
2 B e , 0.3 Co, b a l . Cu (BERYLCO 25). O r i g i n a l l y ha l f -hard , t hen h e a t t r ea t ed for 2 h o u r s a t 200° C. d i f ference w a s found i n t h e t h e r m a l expans ions fo r t h e t w o s t a t e s of ha rdness .
No observable
Table of Selected V a l u e s
1 d L L d T
per OK
--
0.
0.004 x 10
.009 I$
.05
.14
.27
.43
.65
.84
.96
1.04
1.16
-5
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I t
I T e m p .
K 0 L293 - LT 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 L dT 1
1 1 dL
se r OX
-7
~~ ~~~~~
1.24 x 1.32 . 'I
1.38
1.45
1.52
1.60
1.67
1.72
1.74
1.79
1.81
11
11
11
11
11
11
11
11
11
. . _.
IX-D-1
. . . . . .. .- . . . - . . . . ...
THERMAL EXPANSION O F BRASS (YELLOW)
Sources of D a t a : Altman, Rubin, and Johnston 1954
O t h e r References: Beenakker and Swenson 1955 Fraser and E b l l i s - H a l l e t 1955 Henning 1907 Keyston, MacPherson, and G u p t i l l 1959
Discussion: 65 Cu, 35 Zn.
Temp K 0
0
10
20
30
40
50
60
70
80
90
.oo
.20
'aken
384
384
383 'I
382 I'
380 I'
375 I'
368 I'
360 I'
350 I'
339 I8
326 'I
299 'I
l r o m NBS 29
Table of Se lec t ed Values
1 dL L dT p e r OK
--
0
0.001 xu-5
.OS
.18
.37
.58
.76
.92
1.06
1.18
1.29
1.44
II
II
II
I 1
II
I1
II
I t
II
11
Temp K 0
14 0
160
180
200
220
240
2 60
273
280
2 93
300
L293 - LT
L293
269 x 10-5
237 I t
204 ' I
169 I t
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 I t
1.85 'I
1.87 I'
L.88 'I
1.90 'I
L.91
I
IX-E-1
- - -. .
... . . .
._
.- ._ . . .
t ! /
0 I
- -______ 1 '
! 0 I -.
IX-E-2
. ._ . - - . .. . .. .. . . , ._ .
THERMAL EXPANSION OF CONSTANT..
Sources of Data: Aoyama and Ito 1939 Krupkowski and deHzas 1928
O t h e r References:
Discuss ion:
Temp. K 0
20
60
70
80
90
100
120
140
160
Faken
269
258 "
253 I'
247 'I
240 'I
232
214 I'
194 I'
172 "
rom NBS 29
Henning 1907 Krupkowski 1929
50 Cu, 50 X i . The name Constantan i s app l i ed to b i n a r y alloys i n the range, 60 t o 45 Cu, 40 to 55 Xi. The n o s t cmmon composition i s 55 Cu, 45 X i , The above ex- pansion data should r e p r e s e n t all Constantans w i t h i n a few p e r c e n t . Small expansiofi anomalies of magnetic o r ig in occur i n this system. The - - ferromagnetic Curie poin ts range from 0 OK for 40% Ni to roughly 150 0 K for
Table of S e l e c t e d Values
1 dL L dT
p e r OK
- -
0.46
.56
.66 I'
.75 I'
.83
.96 'I
1.06
1.14 '@
Temp. K 0
i ao 200
220
240
2 60
273
280
293
300
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 'I
1.35
1.36 'I
1.37 ' I
L.37
b.38 - "
about 55% N i .
IX-F-1 !
THERMAL EYSANSION O F COPPER
L293 - LT Temp. K 0
L293
Source of D a t a :
R u b i n , T . , A l t m a n , H.W. and Johnston, H . L . , J . A m . C h e m . S o c . 76, 5289-93 (1954)
O t h e r R e f e r e n c e s : S i m m o n s , R . O . and B a l l u f f i , R.W., P h y s . R e v . 108, 278-80 (1957) B e e n a k k e r , J . J . M . and S w e n s o n , C .A . , R e v . S c i . I n s t r . 26 1204 (1955) B i j l , D . and P u l l a n H. , P h y s i c a 21, 285 (1955) Fraser, D , B . and H o l l i s - H a l l e t , A . C . , P r o c . 9 t h I n t e r n . Congr. R e f r i g . L, 1065 (1955) N i x , F . C . and M a c N a i r , D . , P h y s . R e v . 60, 597-605 (1931) A o y a m a , S. and Ito, T., S c i . R e p t s . T o h o k u U n i v . 27, 348-64 ( 1 9 3 9 ) A d e n s t e d t , H., Ann. Phys ik 26, 69-96 (1936) Simon, F . and B e r g m a n n , R., 2 . P h y s i k C h e m . €3, 255-80 (1930) Mrupkowski, A . and D e H a a s , W.J., C o m m u n s . P h y s . Lab . U n i v .
1 d L L dz
per K
- -
Leiden 194b (1928) K e e s o m , W . H . , V a n A g t , F . P . G . and Jansen, A.T.J., P r o c . A c a d .Sei. A m s t e r d a m 29, 786-91 (1926) B u f f i n g t o n , R.M. and L a t i m e r , W.M., J . A m . C h e m . S o c . 48
Sorel ius , G . and Johansson, C.H., Ann. P h y s i k 75, 23-36 Lindemann, C . L . , P h y s . 2. 12, 1197-99 (1911) H e n n i n g , F., Ann. P h y s i k (4) 22, 631-39 (1907) D o r s e y , H .G. , P h y s . R e v . 25, 88-102 (1907) K e y s t o n , MacPherson and G u p s t i l l (1959)
2305-19 (1926)
L293 - LT Temp. K 0
1293
(1924)
1 dL L dg
per K
--
Table of Selecteh V a l u e s
o 10 20 30 40
326 0 326 0.004 x 326 .03 325 .10 324 .23
I I
I I
I I
I I
I I
II
I I
5 0 60 70 80 90 100
321 316 3 10 302 293 283
I t
I 1
II
II
I I
I I
.38
.55
.70
.84
. 95 1.05
I I
I I
I I
II
I t
I I
120 140 160 180 200
220 240 260 273 280 293 300
260 235 I'
208 'I
179 'I
149
118 I'
87 55 33 22 I'
0 -11
1.20 1.32 'I
1.41 ' I
1.47 ' I
1.52 I'
1.56 I'
1.59 'I
1.62 I t
1.64 'I
1.65 I'
1.67 'I
1.68 'I
Taken f r o m NBS 2 9 IX-G-1
THERMAL EXPANSION OF CROWN C-1 GLASS
Sources of Data :
Other References:
Discussion:
Mofby 1949.
Dorsey 1907 .
Bausch and Lomb Co. d e s i g n a t i o n . Composition w a s n o t g iven .
Table of S e l e c t e d Values
Temp. K 0
80
90
100
120
140
160
180
200
-
134 x 130 "
126 I'
116 I'
105 I t
95
8 2 I'
69 'I
Temp. K 0
220
240
2 60
273
280
293
300
Taken from NBS 29
IX-H-1.1
THERMAL EXPANSION O F OPTICAL GLASS BSC-1
Sources of Data: Molby 1949.
O t h e r References: Dorsey 1907.
Discussion: Bausch and Lomb Co. designation. Composition w a s not given.
Table of Selected Values -
Temp. K 0
80
90
100
120
140
160
180
200
Taken
L2 93 - LT I L293 I
133
1 2 8 I'
124 I'
114 'I
104 'I
92 'I
80 I'
67 I'
~~~
from NBS 29
Cemp . K 0
2 20
240
2 60
273
280
293
300
L293 LT
L293
53 x 10
39
25 'I
15 I'
10
0
-5
- 6
IX-E-2.1
THERMAL EXPANSION OF OPTICAL GLASS BSC-2
Sources of Data: 0 Other References:
Discussion:
e
Temp. K 0
80
90
100
120
140
160
180
200
Molby 1949.
Dorsey 1907.
Bausch and Lomb Co. des igna t ion . Composition w a s n o t g iven .
Table of Selected Values
L293 - LT
L293
112
109
105 'I
97 Ii
88 I'
77 'I
66 'I
57 I t
T P P K
220
240
2 60
273
280
293
300
L293 - LT
L293
45
3 3
2 1 Ii
13 "
Taken from NBS 29
IX-H-3.1
THERMAL EXPANSION O F OPTICAL GLASS LBC-2
Temp. K 0
Sources of Data: Molby 1949.
293 - 'T L
L293
O t h e r References : Dorsey 1907.
220
240
260
273
280
293
300
Discussion:
54
40 'I
25 I'
15
10 I'
0
-5 "
Bausch and Lomb Co. designat ion. Composition was not given.
Table of Selected Values
80
90
100
120
140
160
180
200
137
132 I'
128 It
117 'I
106 'I
95
a2 11
68 'I
raken from NBS 29
'293 - =* K 0
L293
IX-H-4 1
THERMAL EXPANSION OF OPTICAL GLASS DBC-1
0 Sources of Data: Molby 1949.
O t h e r References : Dorsey 1907.
Discussion:
Temp K 0
80
90
100
120
140
160
180 I 200 I Taken
Bausch and Lomb Co. designation. Composition was not given.
Table of Selected Values I L293 - L T I &I 110 x 10
I 107 'I
104 I'
95 I'
77 I1
67 "
56
from NBS 29
240
260
273
28q
293
300
0 IX-E9-5.1
- . - ... . ... . ._. , . . . 8 . 2 . _ . . ... - . .
e
220
240
2 60
273
280,
293
300
THERMAL EXPANSION O F OPTICAL GLASS DBC-3
Sources of Data: Molby 1949.
Other References: Dorsey 1907.
42
31 'I
20 I t
12
8 ' I
0 I t
-4 1'
Discussion:
90
100
120
140
160
180
200
Bausch and Lomb Co . d e s i g n a t i o n . Composition was n o t g iven .
Table of Se lec t ed Values
101 I t
98 I'
90 I t
82 I'
73
63 I'
53
Taken from NBS 29
IX-H-6.1
. . .. . .
T H E M U EXPANSION O F OPTICAL GLASS DF2
Sources of Data: Molby 1949.
Other References : Dorsey 1907.
Temp. K 0
80
90
100
120
140
160
180
200
Discussion:
L2 93 - LT L293
136 x
131 I'
126 I'
115 I'
104 'I
92 I'
79 I'
66 I '
Bausch and Lomb Co. designat ion. Composition was not given.
Table of Selected Values
Temp. K 0
2 20
240
260
273
280
293
3 00
52
38 'I
24 'I
1 5 I'
9 I'
0
-5 '1
Taken from NBS 29
IX-€1-7.1
. I
THERMAL EXPANSION O F OPTICAL GLASS EDF-3
Sources of D a t a : Molby 1949
O t h e r References: Dorsey 1907
Bausch and Lomb C o . des igna t ion .
Temp* K 0
2 20
240
2 60
273
280
2 93
Discussion:
'293 - LT
53
'293
39
25
15
10
0
I1
II
I 1
I1
I t
Composition was n o t given.
Table of Se lec ted Values
90
100
1 2 0
140
160
180
200
80 1139 x
135
130
118
106
94
81
67
I 1
I 1
I1
I1
I I
II
I 1 L Taken from NBS 29
IX-H- 8.1
THERMAL EXPANSION OF QPTICAL GLASS BF-1
Temp. K 0
Sources of Data: Molby 1949.
- L T 1
293
1293
O t h e r References : Dorsey 1907.
Temp. K 3
Discussion:
L293 - LT L293
0
240
2 60
273
280
293
300
Bausch and Lomb Co. d e s i g n a t i o n . Composition w a s n o t g iven .
Table of Selected Values
4 1
26 ' I
1 6 I'
10 'I
0
-5 1'
100
120
14 0
133
122
111 I t
Taken from NBS 29
IX-H-9.1
~~
TH3RMA.L EXPANSION O F OPTICAL GLASS CF-1
240
2 60
273
280
Sources of D a t a :
O t h e r References :
33
2 1 'I
13 'I
8 I'
Discussion:
Temp. ?A 0
8 0
90
100
1 2 0
140
160
180
2 00
Molby 1949.
Dorsey 1907.
B a u s c h and Lomb C o . designat ion. Composition w a s no t given.
Table of Selected Values
L293 - LT L2 93
110 x lo-' 107 'I
104 "
95
87
77
67 I'
5 6 'I
5 q X x L293
Taken from NBS 29
IX-H-10.1
li t;: I
cu -1
I IO
IO0
75
50
25
0
-10 0 50 108 150 200 2 50 300
TEMPERATURE, O K
. _. - - . .
IX-H-10.2
. .. I
. .
THERMAL EXPANSION OF OPTICAL GLASS NO.11
Sources of Data: Molby 1949
O t h e r References : Dorsey 1907
Discussion:
remp. K 0
80
90
100
120
140
160
180
200
E a s t m a n Kodak Co. designat ion. . Composition was no t given.
Table of Selected V a l u e s
L293 - L T 1
97
94 I t
88
80
72 I t
63
53
11
I 1
I 1
I t
II
L293
LOO
' e m p . K 0
220
240
2 60
273
280
2 93
300
Taken from NBS 29
IX-H-11.1
L293 - LT
L293 -~
42
31
20
12
II
I 1
I1
8 II
0 II
-4 II
THERMAL EXPANSION OF OPTICAL GLASS NO. 3 2
Sources of Data:
O t h e r References:
Discussion:
Molby 1949.
Dorsey 1907.
EasLvan Kodak Co. designation. Composition w a s not given.
Table of Selected Values
Temp. K 0
80
90
100
120
140
160
180
200
Taken
99
96 I'
89 "
81 'I *
72 I'
63 'I
53 Ii
I from NBS 29
Temp K 0
220
240
2 60
273
280
293
300
L293 - 'T
L2 93
42
31 I '
20 Ii
12 I t
8 ' I
0
-4 11
0 IX-H-12.1 ,
... - _ . _. , . , . . . . - - - . .. . . . . . , - . . .
THERMAL EXPANSION OF OPTICAL GLASS N0.33
Sources of Data:
Other References:
Discussion:
Temp. K 0
80
90
100
120
140
160
180
200
Molby 1949.
Dorsey 1907
Eastman Kodak Co . . designat ion. Composition w a s n c t given.
Table of Selected Values
L293 - LT 1 L293 I 92 10-5 1 90
87
83 'I
74 I'
66 'I
58 I'
49
Taken from NBS 29
. .. . . . . . . . - . . . - -. . . . . .
Temp K 0
220
240
2 60
273
280
293
300
L293 - LT
L293
IX-H-13.1
.. ..
THERMAL EXPANSION O F OPTICAL GLASS N0.45
Sources of Data:
O t h e r References :
Discussion:
Temp, 0 K
80
90
100
120
14 0
160
180
200
Molby 1949.
Dorsey 1907.
Eastman Kodak Co. designat ion. Composition was not given.
Table of Selected Values
L2 93 - LT
L293
96 loo5
94 'I
91 II
a5 11
7 8
70 'I
62 "
52 I'
Temp 0 K
220
240
2 60
273
280
293
300
L293 - LT
L2 93
42
31 "
20 II
12 I'
8 I'
0 -4
Taken from NBS 29
IX-H-14.1
0 THERMAL EXPANSION O F PYREX
Sources s f Data: Head and Laquer 1952
O t h e r References: Buffington and L a t h e r 1926 Tool and Saunders 1948 Winter-Klein 1950
Discussion:
Table of Selected Values
T&"P ' K
0
20
40
60
80
100
120
140
160
54.7 x lo-: 55.7
56.7
56.2 I'
53.7
50.2 'I
46.2
41.7 'I
37.2 'I
Taken from NBS 29
1 273
L2 93 - LT
L2 93
32.2
27.2
21.7
15.7
10.2
6.2
4.2
0 .o - 2 -3
0
,
IX-H-15.1
. .
THERMAL EXPANSION OF S I L I C A GLASS
I L293 - LT
Sources of D a t a :
Discussion:
'2 93 I
Other References:
~
-8 x
-6.60 'I
-4.90
-3.02
-1.41 'I
-0.12
t0'.87
1.61 'I
2.08 li
T p P K
- 0
20
40
60
80
100
120
14 0
160
.
-
1 L293 - LT
I L293
Keesom and Doborzynski 1934 Scheel and Heuse 1914
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
The thermal expansion of s i l i ca g l a s s ( fused s i l i c a , v i t r e o u s s i l i c a ) quartz glass) , though s m a l l , i s v a r i a b l e from sample t o sample. The above va lues a re thought t o be f a i r l y r ep resen ta t ive of average behavior . The temperature of minimum length can vary from 180 t o 230 K . Var ia t ions from t h e above va lues as l a rge a s 2 ~ 1 0 ' ~ below 180°K and 50% from 180 t o 300°K are poss ib le
Beat t ie e t a l . 1941 . . Dorsey 1907. Head and Laquer 1952, Henning 1907, S c h e e l 1907, Sco t t 1933, Sosman 1927, Souder and
' Hidnert 1926, Valent iner and Wallot 1915.
0
Table of Selected Values
Temp K 0
180
200
220
240
2 60
273
280
293
300
- Taken from NBS 29
IX-H-16.1
0
1 .91
'1 .oo 1.07 I'
1.12
1.16 I'
1.20 , I 1
1.23 I'
1.25 'I
1.26 I'
1.29 I'
1.30 It
THERMAL EXPANSION OF INCONEL
Sources of Data: A l t m a n , Rubin, and Johns ton 1952
Other References: Lucks and D e e m 1958
Discussion:
Temp. K 0
0
10
20
30
40
50
60
70
80
90
100
120
229
229 'I
229 'I
229
228
227 I'
224 I'
2 2 1
217 I'
2 1 1
205 'I
1 9 1 (I
Taken from NBS 29
80 Ni,14 C r , 6 Fe.
Table of S e l e c t e d Values
1 dL L dT
per OK
--
0.
0.003 X L O - ~
803
.10
.19
II
II
II
.2a I 1
3a II
.40
.57
.65
.79
I 1
II
II
I 1
Temp, K 0
140
160
180
200
2 20
240
2 60
273
280
293
300
L293 - LT
174
L293
154 I'
134
1 1 2
89.1 I'
65.6 'I
41.4 'I
25.2 I'
16.6 I'
0.0 Io
-9.0
1 dL
p e r K
-- L a:
a IX-1-1
. -. . - . . . ..
THERMAL EXPANSION OF INDIUM
Source of Data:
O t h e r References :
Discussion:
Temp
K 0
0
10
20
30
40
50
60
70
80
90
LOO
293- LT L
7
L293
706
706
701
691
67 6
658
638
617
5 95
572
54 9
I I
I I
I I
I 1
I I
I I
I t
I 1
11
I I
Swenson 1955.
Hidnert and B l a i r 1943.
I n t h e two i n v e s t i g a t i o n s above, t h e ex- perimental methods and sample p u r i t i e s w e r e very similar. Yet t h e two p o i n t s by Hidnert and B l a i r , (L273 - L &/ L and (L - L axe r e s p e c t i v e l y 7% aZZ34% less2Z2an Swenson's corresponding p o i n t s . Swenson's d a t a have been adopted s o l e l y because they inc lude more p o i n t s over .a w i d e r temperature range .
273
Table of Selected Values
1 dL -- L d s
p e r K
0.
0.2 x
0.7
1.3
1.7
1.91
2.04
2.15
2.24
2.32
2.39
I t
I 1
I 1
I t
II
I 1
I I
I I
I I
Temp.
K 0
120
140
160
180
200
220
240
2 60
273
280
293
300
Taken from WADD 60-56
IX- J- 1
L293 - LT L293
500
448
3 94
339
282
2 24
165
104
63
42
0
-22
I I
I 1
II
I I
I I
11
I I
I t
11
I I
1 d L L dT
p e r OK
- -
2.52 x 10
2.63
2.72
2.79
2.86
2.93
3.01
3.08
3.13
3.15
3.20
3.22
I I
I 1
I I
I I
I I
I t
I I
I I
I I
11
I I
THERMAL EXPANSION O F INVAR
Sources of Data: Beenakker and Swenson 1955
O t h e r References : Chevenard 1914 Gregg 1954 Masumoto 1934 Molby 1912 Scheel 1921
Discussion:
. . . ._ _ _ . . . _. -
Temp K 0
0
10
20
30
40
50
60
70
80
90
100
120
The expansions of the Invar a l l o y s are s e n s i t i v e t o composition and heat t r e a t - ment. The above data a re for an a l loy believed t o be 42 Ni, 0.8 Mn, b a l . Fe, annealed (Lloyd B. Nesbitt , Pr iva te Communication). Although Beenakker and Swenson r e fe r r ed t o t h i s as "Invar" , t h i s composition approximates t h e a l loy , D u m e t , used f o r s ea l ing t o g l a s s . I n t h e iron- n i cke l a l l o y system, t h e minimum value of room temperature expansion c o e f f i c i e n t occurs a t about 36% N i .
Table of Selected Values
- L L293 T
L293
52
52
52
52
52
52
52
51
50
49
47
43
11
II
II
I1
11
II
II
II
II
II
II
Temp. K 0
140
160
180
20 0
220
240
2 60
273
280
293
300
Taken from NBS 29 IX-K-1
L - L 2 93 T
L293
34
29
23
18
14
II
I 1
II
II
II
8.6 'I
5.2 I'
3.4 II
0
-1.8 'I
THERMAL EXPANSION OF IRON
L293 - "T
L293
156
140
122
102
82
60
38
23
15
0
-8
11
I 1
II
I t
11
I 1
I 1
I 1
II
II
Sources of D a t a : Ebert 1928, N i x and M a c N a i r
1 d L L d T
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'
--
O t h e r R e f e r e n c e s : Adenstedt 1936, D o r s e y 1907 B e r g m a n n 1930 O w e n and W i l l i a m s 1954.
Table of Selected V a l u e s
T e m p K 0
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
1 d L -- L dT
p e r O K .
0
0.01 x 104
' .03 'I
.07
.13 'I
..20
.28
.35 II
.42
.49 II
.63
'Taken from NBS .29
T e m p K 0
140
160
180
200
220
240
2 60
273
280
293
300
1941
Simon and
I
IX-L-1
THERMAL EXPANSION OF LEAD
Sources of Data:
O t h e r References
Discussion:
Temp. K 0
0
5
10
20
30
40
50
60
70
80
90
100
Taken
293 - LT L
L293
708
708
707
700
68 6
667
64 6
624
60 1
5 77
552
5 28
I 1
I 1
I 1
11
I 1
I I
I 1
I 1
II
I1
I 1
Dheer and Surange 1958, Ebert 1928, Nix MacNair 1942, Olsen and R o h r e r 1957.
Dorsey 1908, Gruneisen 1910, Head and L
and
que r 1952, Lindemann 1911, McLennan, Allen and W i l h e l m 1931.
Superconducting lead has a s l i g h t l y g r e a t e r volume and a s l i g h t l y smaller expansion coe f f i - c i e n t than normal l ead according t o da t a by Olsen and Rohrer covering t h e region from lo t o t h e t r a n s i t i t o n temperature, 7.2OK. For example, t h e d i f fe rence i n expansion coe f f i - c i e n t s a t 5OK is about 10%.
Table of Selected Values
1 dL L dT
per OK
- -
0
0.03
0.32 I'
1.1 I I
1.7
2 .o
I 1
I 1
2.2 I 1
2.3
2.4
I I
I 1
2.4 I 1
2.5
2.5
II
I 1
Temp. K 0
120
140
160
180
200
220
240
2 60
273
280
2 93
300
L293 - LT L293
477
425
372 I 1
318
2 63
208
15 2 I I
I 1
I 1
I 1
I 1
96
58
11
I 1
38
0
-20
I 1
1 dL L dT
per OK
--
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
I 1
I I
I 1
I I
I 1
11
I 1
I I
I 1
I 1
I 1
from NBS 29
IX-M- 1.
THERMAL EXPANSION OF MAGNESIUM
Sources of Data:
O t h e r References:
Discussion:
remp . K 0
0
10
20
30
40
50
60
70
80
90
100
120
L293 - LT L2 93
490
490
490
489
48 6
482
475
466
454
441
427
3 93
I 1
I 1
I 1
I 1
I 1
I 1
I 1
II
I 1
I 1
I 1
Taken from NBS 29
Ebert 1928 Goens and Schrnid 1936 Head and Laquer 1952
Gruneisen 1910 Hidnert and Sweeney 1928
Anisotropic. The above values w e r e ca l cu la t ed from t h e r e l a t i o n , Mean Value = 1/3 ( 1 1 1 + 2/3 (L), w h e r e ( 1 1 1 and (1) s i g n i f y t h e same property measured p a r a l l e l and perpendicular, respec t ive ly , t o t h e hexagonal a x i s .
Table of Se lec ted Values
1' dL L dT --
per OK
0.
0.005
.04
.14
.33
.57
.81
1.03
1 . 2 2
1.39
1.54
1 .76
I 1
I I
II
I I
I1
I 1
I 1
I 1
II
I1
Temp. K 0
14 0
160
180
200
220
240
2 60
273
280
293
300
L293 - LT L293
356
316 11
273 8 1
227 8 1
180 'I
132 I'
82.9
50.4 32.9 I I
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
I I
11
I I
I I
11
11
11
I I '
IX-N-1
THERMAL EXPANSION O F MONEL
Sources of D a t a : A l t m a n , R u b i n , and Johnston 1952
206 I'
O t h e r R e f e r e n c e s : A c k e r m a n 1936 Aoyama and I t o 1939 Fraser and H o l l i s - H a l l e t 1955 K r u p k o w s k i and de H a a s 1928
.a9 II
D i s c u s s i o n : 67 N i , 30 Cu, 1.5 Fey "cold-rolled" .
Temp a
K 0
0
1 0
20
30
40
50
60
70
80
90
100
120
Table of S'
251
251 It
251 'I
251 I t
250 'I
248 I'
245 I'
244 I'
236 I'
230 I'
223 I'
0 ,
0.003 x lo-'
.02
106
I t
t I
.14
.23
.34
.46
.57
.67
.75
I t
I t
I 1
I I
I t
I I
II
. e c t e d
Temp. K 0
140
160
180
200
2 20
240
2 60
273
280
293
300
Values
L293 - LT
1 8 7
L293
167 'I
144 It
1 2 1
96.4
70.9 'I
44.7 II
2 7 . 1 "
15 .1 I t
0.0
- 9.7 'I
1 dL L dT
per K
-- 0
T a k e n f r o m NBS 29
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
8
0
T H E W EXPANSION O F NICKEL
Sources of D a t a : K r u p k o w s k i and D e H a a s 1928, N i x and M a c N a i r 1941.
O t h e r R e f e r e n c e s : A d e n s t e d t 1936, A l t m a n , R u b i n and Johnston 1954, Aoyama and Ito 1939, D i s c h 1921, H e n n i n g 1907, S i m o n and B e r g m a n n 1930.
Temp. K 0
0
20
30
40
50
60
70
80
90
100
120
224
2 24
224
223
221
219
216
211
206
201
187
I1
I I
I 1
I 1
I I
I 1
I1
I 1
I t
I I
Taken f r o m NBS 29
Table of Selected V a l u e s
1 d L L dg
per K
- -
0.
0.02
,05
,10
.19
.28 I'
.38 I'
.47
.55 It
.6l
.75
Temp. K 0
140
160
180
200
220
240
2 60
273
280
2 93
300
L293 - LT
L293
171
15 2
13 2
111
88
65
41
25
16
0
I 1
I1
I1
I1
I I
I 1
11
I I
I I
-9 I I
1 dL -- L dg
per K
0.88 x
0.98 I'
1.05 I'
1.10 . I 1
1.15 ' I
1.19
1.22 I1
1.23 "
1.24 I '
1.26 ' I
1.26 I'
IX-P-1
8 THERMAL EXPANSION OF NIOBIUM
Sources of D a t a : E r f l i n g 1942.
O t h e r R e f e r e n c e s : H i d n e r t and K r i d e r 1933.
D i s c u s s i o n : Also termed columbium.
Table of Selected V a l u e s
Temp. K 0
0
10
20
30
40
50
60
70
80
90
100
120
L293 - LT
'293
14 3
14 3
143
14 1
13 9
13 7
13 3
129
125
121
111
I 1
11
I 1
I t
I1
I 1
11
I I
I 1
I 1
- 1 % L d T
p e r O K
0.
.03
.09
.17
.24 I'
.31
.36
.40
- 4 4
.47
.52
Temp. K , 0
14 0
160
180
200
220
240
2 60
273
280
293
300
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
I 1
I1 .
I 1
I 1
I1
I t
I 1
Taken from NBS 29
IX-Q-1 ,
I
THERMAL EXPANSION O F ARALDITE N0.501
Sources of D a t a : Laquer and H e a d 1952.
O t h e r R e f e r e n c e s :
D i s c u s s i o n :
Temp. K 0
0
20
40
60
80
100
120
140
160
180
Caken
E p o x y cast ing r e s i n made by C i b a C o . 40 g of t h e mater ia l w a s catalyzed w i t h 2 m l t r ie thanolamine. C u r e d 8 h r . a t 120° C and t h e n 24 h r . a t 180° C.
T a b l e of Selected V a l u e s
L293 - LT
L293 ~
LO61 x 10-5
LO51 I1
LO22
983 I'
935 'I
880 I'
819 I'
751 I'
676
594 II
Temp K 0
200
220
240
2 60
273
2 80
2 93
300
L293 - LT
L293
505 x 10-5
410 I'
308 'I
199 II
1 2 2
81 'I
0
-46 I'
i r o m NBS 29
IX-R-1.1
I150
I100
IO00
900
h
ro ' 800 0 n
=J 700
ZI
W
0 > -
- Q .-
4- - 600 i
v
500 Yr) 0 ru -I 400
300
200 THERMAL EXPANSION
of AWALDITE NO, 501 100
0 50 100 150 200 2 TEMPERATURE, O K
3 300
IX-R-1.2
THERMAL EXPANSION OF FLUOROTHENE o r KEL-F
Sources o f D a t a : Laquer and Head 1952.
Other References:
Discussion:
Temp. K . 0
0
20
40
60
80
100
120
14 0
160
Polychlorotrifluoroethylene. The samples w e r e , r e spec t ive ly , froma 5 i n . diameter rod of Fluorothene made by Union Carbon and Carbide and from a 1/16 i n . t h i c k s h e e t of Kel-F made by M.W. Kellog and Co.
Table of Se lec ted Va lues
'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 . K 0
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
Sources of D a t a :
O t h e r References:
Discussion:
THERMAL EXPANSION O F LUCITE
Laquer and Head 1952.
Po Pyme t hy lme t hacry la te . DuPont Luc i t e ' ' . from rod s tock .
" Probably Average of t w o samples
T a b l e of Se lec ted Values
Temp. K 0
0
20
40
60
03
too -20
-40
.60
1134
1123
1092
1048
995
93 6
869
796
717
x lo-! I 1
I 1
I 1
I 1
I 1
I 1
II
I 1
Temp K 0
180
200
220
240,
2 60
273
280
293
300
I - LT 293 L
L293
63 2
540
441
335
220
13 6
91
0
-53
x lo-!
II
Taken from NBS 29
IX-R- 3.1
Sources of Data:
O t h e r References:
Discussion:
Temp. K 0
0
20
40
6 0
80
100
120
140
160
raken
- Laquer and Head 1952.
From 3/4 inch diameter rod. "Probably E.I. DuPont de Nemours and Co.
Table of Selected Values
L293 - LT
L293
1389 x lov5
L379 I(
1352
1308 "
L247 I'
1172 'I
L O 8 8 I'
996 I'
896 'I
Temp K 0
180
200
220
240
260
273
280
300
L293 - LT L293
irom NBS 29
8
789 x 10''
673 I'
548 I'
412 'I
2'65 'I
161 @I
107 I'
0
- 6 1 I 1
IX-R-4 1
grade FM-1".
THERMAL EXPANSION OF PLEXIGLAS
Sources o f D a t a : D a t a from Laquer and Head 1952. ( I n a d d i t i o n t o t h e substances l i s t e d i n t h e t ab le , d a t a have been given f o r 16 s p e c i a l l y compounded rubbers by Dunsmoor e t a l . 1958 and Trepus e t a l . 1959. These d a t a c o n s i s t mainly of va lues o f (L -L ) 293 78 L293
O t h e r References: Wood, Bekkedahl and Peters 1939,
Discussion: Polymethylmethacrylate made by Rohm and H a a s Co . D a t a from Giauque, Geballe, Lyon and F r i t z 1952.
Table of Se lec ted Values I
Temp. K 0
- 0
20
40
60
80
100
120
140
160
180
L293 - LT
L293
1210 I'
1160 ' I
1110 I'
LO50 'I
Taken from NBS 29
Temp. K 0
200
220
240
2 60
273
28 0
293
298
300
L293 - LT
L293
590
490 I'
-55 I'
IX-K-5.1
THERMAL EXPANSION O F POLYSTYRENE
Sources of Data:
O t h e r References :
Discussion:
Laquer and Head 1952. ( In addi t ion t o t h e substances l i s t e d i n t h e t a b l e , da t a have been given for 16 s p e c i a l l y compounded rubbers by Dunsmoor e t a l . 1958 and Trepus e t a l . 1959. These d a t a c o n s i s t 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
Tgmp . K
u 20
40
60'
80
l o o 120
140
160
180
1550 x
1552 I'
1466 'I
1394 'I
1308 " "
1 2 1 1 It
1105 It
992 I'
874 I'
752 'I
Taken from NBS 29
Temp K 0
2.0 0
220
240
260
273
280
293
298
300
293 - LT L
L293
626 x 10-5
499 'I
368 I '
232 I'
141 I'
93 I'
0 "
-51 II
IX-R-6.1
THERMAL EXPANSION OF POLYTHENE
Sources of Data: Laquer and Head 1952. ( In add i t ion t o t h e substances l i s t e d i n t h e table, d a t a have been given for 16 s p e c i a l l y compounded rubbers by Bunsmoor e t a l . 1958 and Trepus e t a l . 1959. These d a t a cons i s t .ma in ly of values o f (L -L
8 293 78
Other R e ference s : W O Q ~ , Bekkedahl and Peters 1939.
Discussion: Polyethylene made by E.I. Du Pont de Nemours and Co.. Molded under 2000 p s i p ressure a t l5OoC f o r 1 0 min. w e r e n e g l i g i b l e . See a l s o Hunter and Oakes 1945. Five f i l l e d polythenes w e r e measured
Di rec t iona l v a r i a t i o n s
remp . K 0
0
20
40
60
80
too L20
L40
160
-80
by Head and Laqyer 1952.
Table of Se lec ted Values
L293 - LT
L293 2449 x 10-5
2439 I 1
2404 I1
2349 I 1
2279 I 1
2194 11
2089 I 1
1964 I 1
1814 I 1
1639 I 1
Temp. IC 0
200
220
240
2 60
293
2%0
293
298
300
- L L293 T
1439 10-5 L293
1199
919 'I
594
359 'I
239
0
-131
Taken from NBS 29
IX-R- 7.1
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
3L
@
aJ
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 8 Sources of Data: Laquer and Head 1952
O t h e r References: Dunsmoor e t a l . 1958 Trepus e t a l . 1959 Wood, Bekkedahl and Pe te r s 1939.
Discussion: Polytetraf luoroethylene . Extruded and annealed sample measured by Kirby 1956. He found t h a t s t r a i n e d samples could have expansions larger o r smaller than those of annealed Teflon, t h e d i f f e rences being as l a rge a s 20%. Laquer and Head (1952) measured two samples of DuPont Teflon rod taken normal and p a r a l l e l t o t h e ex t rus ion d i r e c t i c n . The expansions p a r a l l e l w e r e roughly 15% larger than those normal, and t h e average i s 10 t o 15% larger than t h e t h e above da ta by Kirby. The da t a o f Laquer and Head w e r e used only t o guide t h e ex t r apo la t ion of Kirbyts va lues below 80°K. Teflon has a f i r s t order t r a n s i t i o n a t 2OoC. Therefore we use 25O C as a reference temperature and t a b u l a t e lo5 (L298-LT) L298 above.
Table of Selected Values
Temp
K 0
0
20
40
60
80
LOO
120
140
L293 - LT
L293
2140 x 2110
2060 I'
2000 I1
1930 I'
1850 I'
1760 'I
1660 It
Temp, OK
160
180
200
2 20
240
2 60
273
298
L2 93 - LT
L293
1540 x lom5 1400
1240
1050
855
645
500
0
11
I 1
I 1
I1
I 1
I 1
11
Taken from NBS 29
IX-R-8.1
2200
2000
1750
I500
h
m - b >r 1250 n Q) 3 0 1
-
750 I- -1
I ' c ) 4? 2-1 A
500
250
0
-200
THERMAL EXPANSION
50 100 150 200 2 50 300 0
TEMPERATURE, O K
IX-R-8.2
THERMAL EXPANSION OF PLATINUM
Sources of D a t a : Nix and M a c N a i r 1942.
O t h e r R e f e r e n c e s : D o r s e y 1907. H e n n i n g 1907. Onnes and C l a y 1096. S c h e e l 1907. Schee l and H e u s e 1907. V a l e n t i n e r and Wallot 1915.
I
Discussion:
IX-s-1
8 THERMAL EXPANSION OF QUARTZ (CRYSTALLINE 1 1 )
Sources of D a t a : Buffington and L a t i m e r 1926
O t h e r References : Dorsey 1908 Lindemann 1912 N i x and M a c N a i r 1941 Scheel 1907 Sosman 1927
Discussion: Measured p a r a l l e l t o t h e o p t i c ax is . N i x and MacNair measured expansions perpendi- c u l a r t o t h e o p t i c a x i s bu t presented only a coarse graph of t h e resukts , from w h i c h t h e following va lues of 10 (dL/LdT) w e r e taken: 7 a t 100°K, 10 a t 150°, 1 2 a t 200°, 1 3 a t 250°, 14 a t 300°K.
Table of Se lec ted Values
Temp. K 0
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
Temp. K 0
1 dL L dT
per OX
--
0.27
, 3 1 It
.37 I1
.42 II
.47 I)
.51 It 300
.55 I1
.59 II
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
. 7 1 II
.72 'I
.75 I'
.76 I'
IX-T-1
THERMAL EXPANSION OF SILVER
Sources of D a t a : E b e r t 1928, N i x and M a c N a i r 1942.
Other References: Ayres 1905, Buff ington and Latimer 1926, Dorsey 1907, Henning 1907, K e e s o m and Jansen 1927, Lindemann 1911. K e e s o m and Kohler 1933. Owen and W i l l i a m s 1954. Shea re r 1950.
Table o f S e l e c t e d Values
8
Taken from NBS 29
IX-u-1
THETFAL EXPANSION O F SOFT SOLDER
Sources of D a t a : D o r s e y 1907
O t h e r R e f e r e n c e s :
D i s c u s s i o n :
Temp. K 0
90
100
1 2 0
1 4 0
160
183
200
467
447 "
407 'I
365 I'
3 2 1 'I
276 I'
229 I'
Taken f r o m NBS 29
50 Pb, 5 0 Sn.
Table of Selected Values
1 dL L d T
per OK
--
1.96
2.00 It
2.07 'I
2.14 I'
2.22 'I
2.29 'I
2.35 I'
Temp. K 0
220
240
2 60
273
280
293
300
182 x
133 I'
83 It
5 1 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 "
IX-v-1
THERMAL EXPANSION O F STEEL A I S 1 304
Sources of Data: Altman, Rubin, and Johnston 1954
O t h e r References : Fontana 1948 Beenakker and Swenson 1955
Discussion:
Temp. K 0
0
10
20
30
40
50
60
70
80
90
100
120
Faken
Fontana, Bishop, and Spretnak 1953 Furman 1950 Composition l i m i t s f o r t h i s a l l o y are: 0.08 max. C, 2 max. Mn, 1 max. S i , 18-20 C r , 8 - 11 N i . Altman e t a l . , found small i r r e v e r s i b l e e f f e c t s and, below 35OK, small negative values of expansion c o e f f i c i e n t . W h i l e we have given t h e i r r e s u l t s i n f e r i o r weight i n t h i s region, t h e e f f e c t s w e r e undoubtedly r e a l and a t t r i b u t - able t o m a r t e n s i t i c t ransformation on cooling (Reed and Mikesel1,1958). I n t h i s a l l oy t h e ex ten t of t ransformation t h a t i s produced by cool ing is s e n s i t i v e t o composition and has been found t o vary from zero t o about 50%. ( R .P .Reed, p r i v a t e communication) . Complete t ransformation would be accompanied by a mean increase i n l i n e a r dimension of roughly 1% (Ward, Jepson, and Rait , 1952; and Fiedler , Averbach, and Cohen, 1955.)
Table of Selected Values
L293 - LT L2 93
296 x 10-5
296 I'
296 I'
296 'I
296 I'
294 I'
291
285 'I
279 I'
2 7 1 I'
261 'I
241 I'
from NBS 29
1 dL
per K
-- ilT
0,
0.001 x lo'? ,002 'I
. ,062 'I
* 11 11
.23
* 43
61
75
II
I 1
II
I I
.87
.96
II
I1
1.09 I 1
Temp. K 0
- 14 0
160
180
200
220
240
2 60
273
28 0
293
300
218
193
167 I 1
139
111
I 1
II
II
81.7 I '
51.4 'I
31.4 'I
20.5 I'
0.0
-11.1
1 dL L dT
per OK
- -
1 . 2 0
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'
IX-w-1.1
320
300
250
200 h
In I 0
n
2 P
h
- 150
ZI Q - .- .I- - E' v
IO0
50
0
1.92
iao
1.50
50 100 150 200 250 300
TEMPERATURE, O K
Y 0
5 Q
160 - urn "1' -1-J
1.30
3
IX-w-1.2
C I c 0 0
M
I
'0
C
) v I
" -
i.
- 0 I
\ i I-
- "J 0
I
0
pa
3J
ad
U
O!S
UD
d%
3 IDlLl.I.7111
n 0 I
Y L
1' I P:'
Q
IX-W-1.3 .I
THERMAL EXPANSION O F STEEL AIS1 310
Sources of Data: Furman 1950
0 t h e r Re fer e nce s :
Discussion:
Temp K 0
90
100
120
140
160
180
200
L293 - LT
L293
246
237 'I
2 1 8 I'
198 I'
176 I'
152 'I
1 2 7 I'
0.11 C, 1 . 5 1 Mn, 0.42 S i , 0 .01 S, 0.02 P, 27.2 C r , 21.6 Ni, ba l . Fe. Annealed 30 min. a t 1950° F and w a t e r quenched.
T a b l e of S e l e c t e d Values
- 1 % L gT
per K
0.89
.91 I 1
.98
1.07
1.14
1 . 2 1 (I
1.27
II
I 1
II
I t
Temp K 0
220
240
2 60
273
280
2 93
300
L293 - LT
L293
74.5
46.9 I'
28.6 "
18.7 I'
0.0
-10.2
- 1dJ L dT
p e r K 0
1.32
1 .36 I '
1.40 'I
1.42 I'
1.43 I'
1.45 'I
1.46 'I
Taken from NBS 29
IX-w-2.1
0
I_
_- \ \ . -
........
.. -. ......
....
-- ..
..
........
\ ... \
..
.
.......
..
.
..
.
._
..
.......
__ -
.....
\ \ ..
__ . .-
._ -
-. .
- 0 I
N
I d
..
. --..
...
.. ._ I
.
..
\ \ .....
...
IX-w-2.3
...
... .
.....
___ -.
.. -
-.
.- ._ ,-
\' I' 1
. ._ .......
-. .
....
__ ..
x UI
8 THERMAL EXPANSION OF STEEL AIS1 316
Sources of D a t a : Beenakker and Swenson 1955.
Other References Furman 1950 Lucks and D e e m 1958
Discussion:
- remp . K 0
- 0
10
20
30
40
50
60
70
80
90
too 120
L293 - LT '293
Composition and h e a t t r ea tmen t of sample n o t s t a t e d . Composition l i m i t s fo r t h i s a l l o y are: 0.10 ( m a x . ) C, 2 (max.) M n , 1 ( m a x . ) S i , 16-18 C r , 10-14 N i , 2-3 M o , b a l . Fe.
Table of Se lec t ed Values
- 1 & L d T
p e r K 0
0,
0 .004 lom5 .009
.05
.14
.27
.43
.65
.82
.94
1.02
1.13
II
I 1
II
I 1
II
II
II
I 1
II
Temp. K 0
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
1 dL L dT
per K
-- 0
1 . 2 1
1 . 2 7
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
Taken from NBS 29
IX-W-3.1
h
I--- \ ..
.- .....
...
-- -. -
-_ .. I .._
I
0
_- \ \ ..
I__. __
- - ._
I
........
......
.
..........
......... -- -
.. ....- .
....
(u
0
1- . -- . .I-- ....
\I - ........ ..............
I \I
.I_._
-_ I - -__ _. F
......
._ i I ............ .. 1
.... .- I ......
....... 1. I .... - .
.........
W a
IX-W-3.3
THERMAL EXPANSION OF STEEL A I S 1 347
Sources of D a t a : Furman 1950.
O t h e r R e f e r e n c e s : Lucks and D e e m 1958.
D i s c u s s i o n : 0.07 C, 1.74 Mn, 0.56 S i , 0.006 5, 0.019 P, 18.65 C r , 11.3 Ni, 0.77 Nb, bal. Fe. Annealed 30 m i n . a t 1950° F
L293 -, 'T
L293
T e m p . K 0
1 dL L dT
per OK
-7
90
100
120
140
160
180
200
109
T a k e n
1.40
L293 - LT
80.2 "
50.6 I'
30.9 I'
20.2 I'
0.0
-11.0
L293
1.46 I'
1.50 'I
1.53 I'
1.54 I'
1.56 'I
1.57 'I
262
253 'I
233 I'
211
187 'I
163 I'
136 I'
f r o m VBS 29
and w a t e r quenched.
Table of Selected Values
1 dL L dT
per OK
--
0.94 x l om5 .98 'I
1.05 I'
1.13 I'
1.21
1.28
1.34 'I
Tgmp . K
220
240
2 60
273
280
293
300
IX-W-4.1
I-
-J
of STEEL A.I.S.I. 347
T ' g 82
0 50 100 I00 200
TEMPERATURE, O K
250 300
1.62
1.50
1020
0.30
0
IX-W-4.2
I I
C C ~ I
C
C I
0 0
pr, I 0
0
d-
I - 0 F
... . __
__. ...
0
”. 0
0
(\J
I +
ua3J a d
m
0
a3 cu
0
Tt N
Y
a, .. L
h
E
I- a,
O
N - 0
OD
3
d-
a
CT: UI
THERMAL EXPANSION OF STEEL, S .A.E. 1020
Sources o f Data: Altman, Rubin and Johnston 1952
O t h e r References: Beenakker and Swenson 1955 Dorsey 1910 Gregg 1954
Discussion:
Temp.
K 0
0
10
20
30
40
50
60
70
80
90
100 1.20 Taken
L293 - LT
293 L
202
202
201
201
200
198 I'
195 'I
192 I'
187
1 8 2 I'
170 'I
from NBS 29
0.18 Cy 0.33 Mn, 0 .01 Si , b a l . Fe. According t o Beenakker and Swenson, c a s t i ron had the same t h e r m a l expansion a s 1020 steel within t h e i r experimental uncer ta in ty of + 3 ~ 1 0 ' ~ i n AL/L.
Table of Se lec ted Values
0.
-5 0.001 x 10
.03
.08
I 1
II
.14
.23
.31
.40
II
II
II
II
.48 II
.55
.68
II
$1
Temp. K 0
140
160 180
200
2 20
240
2 60
273
28 0
293
300
155
138 'I
120
1 0 1 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 I'
1.11
1.14 I'
1.15 'I
1 . 1 7 I'
1.19
LX-x-1
LL L
z 3 0
ai
e
L
- n r.5 I-
0
(u
m
0
00 cu
0
d
(u
.
0
0
(u
Y
aJ ” L
02
- Y? 0
) 9.
0)
E
I-
D
N
- 3
r)
3
$
3
‘IX-X- 3
THERMAL EXPANSION OF TANTALUM
Sources af Data: N i x and M a c N a i r 1942
O t h e r R e f e r e n c e s : Disch 1921 H i d n e r t 1929
Table of Selected V a l u e s
I'emp . K 0
0
10
20
30
40
50
60
70
80
90
LOO
120
L293 - LT
293 L
14 3
143
143
142
1 4 1
13 8
135
1 3 1
1 2 7
1 2 2
117
106
10'~ I I
I I
I I
I I
11
I I
I1
I I
I I
I 1
0.
0.005 x I 1 .04
.11
.20
.2%
.35
.41
.45
.49
.52
.55
I1
I I
I 1
11
I 1
I 1
I 1
I 1
I1
1
L293 - LT
'293
95.1 x lo-! 83.5
71.5
59.3
47 .O
34.4
21.6
1 3 . 1
8.5
0 .o -4.6
1 dL
per K
- - L a;
0.58 x 10 - .59 It
.60 "
.61 I '
.62 'I
.63
.65 I'
.65 'I ,
.66 'I
.66 I'
.66 'I
T a k e n from NBS 29
IX-Y-I.
3
-I
0.68
0.60
0.50 - lo
I 0
n
-
0) 3 -
0.40 5 - a .- c - i 5 v
L 0.30
0) a L
Ai- WI-0
-1-1
0.20
0.10
0
1 %
2-J r n N
IX-Y - 2
THERMAL EXPANSION O F T I N (WHITE)
Sources o f Data: E r f l i n g 1939
O t h e r References: Cohen and O l i e 1910 Dorsey 1907 Gruneisen 1910
Discussion:
Temp K 0
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
I1
I I
I 1
I1
I 1
I 1
II
I t
I I
I I
11
Anisotropic . The above va lues w e r e c a l c u l a t e d from t h e r e l a t i o n , Mean Value = 1/3 ( 1 1 ) + 2/3 (J.), w h e r e ( 11 ) and (I.) s i g n i f y t h e same property measured p a r a l l e l and perpendicular , r e spec t ive ly , t o t h e t e t r a g o n a l a x i s .
T h e w l i s and Davey (1954) measured t h e l a t t i c e parameter of grey t i n , a b r i t t l e form w i t h diamond-type l a t t i c e t h a t is s t a b l e below 18OC. T h e i r d a t a cover t h e range, -130 t o +20°C, and are, represented by a cons tan t expansion co- e f f i c i e n t , dL/LdT = 4.7 x 10-6deg'1C. See a l s o Cohen and O l i e (1910) . The ord inary d u c t i l e v a r i e t y ( w h i t e t i n ) i f pure may t ransform t o grey t i n a t low ambient temperatures . but i s s t a b i l i z e d by impur i t i e s .
Table of
- 1 3 L dT
per O K
0. -5
.07 x 10
.3
.6
.9
1.1
1.2
1.3
1.42
1.50
1.56
1.64
I 1
11
II
I 1
I1
I t
I 1
II
I 1
I1
Selec ted Values
Temp. K 0
140
160
180
200
220
240
2 60
273
280
293
300
293 - LT L
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
pe r 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
I 1
I 1
I I
I I
II
I 1
I 1
I 1
Taken from NBS 29 IX-2-1
'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
I I
11
I 1
II
I1
I t
II
11
I1
II
1 d L L dT ---, pi"" 9
--
0
.03 10-5
* 3
.R
1 . 3 1 *7
2.1
2.2
2.3
2.36
2.42
II
I 1
11
I f
II
II
I 1
II
I 1
II
II
I'
I1
II
Il
II
11
II
II
1 dI, - -., p r 9 L dT . ___ . .. 2.53 10-5
2.63- , 1'
2.73
2.81
2.87 I t
2.51
2.911..
2.56..
f l
' II
2.97 ' It
2-.35
2.93 ' . I t
3.m , . .
- . __ - .. .
. .
I
IX-AA-1
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