SDN013.02 – Coefficient of Thermal Expansion
Revision C
1.
Introduction
For
the design of GNIRS, certain information on thermal expansion of materials is
required, and this is what is tabulated below. Specifically, we need
information on
contraction
from ambient (conventionally 293K) to the operating temperature of 60K, and to
80K, which is the temperature at which most mechanism testing will be done.
Also, values of the CTE at 60K are given for analysis of differential
temperature effects.
More
complete information on the CTE is given in section 3. Revision status is given
in section 4.
2.
CTE Tabulation
|
Material
|
|
Contraction, 293-80K (%)
|
Ave. CTE,
293-80K (ppm/K)
|
Contraction, 293-60K (%)
|
Ave. CTE
293-60K (ppm/K)
|
CTE at 60K (ppm/K)
|
|
6061 T651 Al
|
0.393
|
18.45
|
0.408
|
17.51
|
5.58
|
|
|
A356 Al
|
0.366
|
17.18
|
0.378
|
16.22
|
5.2
|
|
|
OFHC Cu
|
0.301
|
14.13
|
0.315
|
13.52
|
5.05
|
|
|
Naval Brass (46400)
|
0.382
|
17.92
|
0.402
|
17.25
|
5.0
|
|
|
G-10CR (glass fiber/epoxy), parallel to fibers
|
0.211
|
9.91
|
0.223
|
9.57
|
5.2
|
|
|
G-10CR (glass fiber/epoxy),
perp. to fibers
|
0.638
|
29.95
|
0.667
|
28.63
|
12.4
|
|
|
Vespel SP3
|
0.725
|
34.0
|
0.761:
|
32.7:
|
15::
|
|
|
302 stainless steel
|
0.287
|
13.47
|
0.297
|
12.75
|
3.8:
|
|
|
303 stainless steel
|
0.282
|
13.24
|
0.293
|
12.58
|
3.8:
|
|
|
440C stainless steel
|
0.177
|
8.31
|
0.182
|
7.81
|
1.8:
|
|
|
1075 carbon steel
|
0.187
|
8.78
|
0.192
|
8.24
|
2.2:
|
|
|
BaF2
|
|
0.313
|
14.69
|
0.325
|
13.95
|
4.8
|
|
CaF2
|
|
0.296
|
13.90
|
0.304
|
13.05
|
3.1
|
|
MgF2 (par. c-axis)
|
0.189
|
8.87
|
0.192:
|
8.2:
|
1.0:
|
|
|
MgF2 (perp c-axis)
|
0.103
|
4.84
|
0.104:
|
4.5:
|
0.5:
|
|
|
Schott SF6 glass
|
0.1482
|
6.96
|
0.1583
|
6.79
|
4.86
|
|
|
Schott SF57 glass
|
0.152:
|
7.1:
|
0.162:
|
6.95:
|
5.0:
|
|
|
Schott BK7 glass
|
0.1203
|
5.65
|
.1272
|
5.46
|
3.2
|
|
3.
Sources and Discussion
3.1
Aluminum
3.1.1
6061 T651
The
data used for the table are taken from the IR/EO Handbook, 3, 358
(1993). These values are ultimately derived from a single measurement by Arp et
al, Cryogenics, 2, 230 (1962). Data in other handbooks appear to
trace back to this same reference. The only other measurement that I could find
is in the Cryogenics Materials Data Handbook (1970), which shows
an average CTE about 4% less than the above values. The Arp et al sample is a
rod, whereas the second sample is a plate measured longitudinally. The values
given in MIL-HDBK-5G are a little more than 1% lower (average of 17.28
ppm/K to 60K); the sources of the data are not given.
Comparison
with measured values for other alloys suggests that a somewhat smaller value
may be more representative, but in the absence of more conclusive data I have
chosen to follow general practice. It is likely that the observed variation is
due in large part to real variations between samples and not just to
measurement errors. For this reason, the GNIRS design should avoid
situations in which knowledge of the CTE to better than about 2% is critical.
Some
relevant data are plotted below. (The curve from the Cryogenics Materials
Data Handbook is not plotted because it is not available in tabular
form.)
3.1.2
A356
Data
for A356, which is an alloy commonly used for casting, are also shown. This was
because we considered the consequences of casting the GNIRS cryogenic structure
out of this material. A356 has a silicon content of 7%, and has a CTE which is
lower than that of 6061 by roughly the same amount.
The
cryogenic data on A356 are less extensive. The data plotted and tabulated are
from Arp et al; the MIL-HDBK-5G curve is almost 2% lower for the
contraction to 60K.
3.2 Copper and Brass
3.2.1
OFHC Cu
The
CTE for OFHC copper is known fairly accurately, certainly to better than 1%.
This is probably because it is a nearly pure material. A curve is plotted
below. The OFHC data used are taken, again, from the IR/EO Handbook, 3,
359. The pure copper curve is from Materials at Low Temperature, ed. R.
P. Reed & A. F. Clark (1983), but is not significantly different from the
pure copper curve in the IR/EO Handbook.
3.2.2 Naval Brass
This
is also known as 46400. This is used in GNIRS mainly for gears. It has a
composition that is roughly 60% Cu, 40% Zn and 0.7% Sn. There were no data for
material of this exact composition down to 60K. Down to 77K there care CTE data
for simlar materials, and these were averaged and interpolated to get the 80K
value. Data from Arp et al for 70:30 brass were used to extrapolate to 60K. The
CTE ratio of 60:40 to 70:30 brass was taken as 1.13 for this purpose. The
overall uncertainty in the CTE values (judging from the scatter in the data at
77K) is about 4%. The higher CTE of brass appears to be due to the Zn, which
has a much higher CTE than that of Cu.
3.3
G-10CR
G-10
is a composite material of glass fibers in a polyester resin. This means, first
of all, that it is not isotropic, but in addition one would not expect its
properties to be particularly uniform. G10-CR is a cryogenic grade of G-10,
which is somewhat more tightly specified (see Kasen et al., Adv Cryo Eng, 26,
235 [1980])
The
data in the table are taken from Materials at Low Temperature, ed. R. P.
Reed & A. F. Clark (1983). These data are also presented by Kasen et al. R.
B. Scott (Cryogenic Engineering, 1959) gives values for “molded
ployester rod reinforced with glass fiber” that is about 20% larger than the
CTE parallel to fibers quoted above. Additional curves can be found in the Cryogenic
Materials Data Handbook and elsewhere, including manufacturer’s literature
for room temperature.
The
data are plotted below.
3.4
Vespel
The contraction to 80K is based on a measurement by Steve Rath of
contraction between room temperature and liquid nitrogen. The measurement is
dominated, undoubtedly, by systematic errors.
The
extrapolation to 60K is based on noting that plastics in the literature
typically contract additionally, in going to 60K, by about 5% of the
contraction down to 80K.
The
CTE at 60K is a very rough estimate, and is simply a rough average of
composite/plastics with similar overall contraction. It is probably good to 5
ppm/K.
3.5
Steel
It
is important to note that the CTE values of steels vary significantly from one
alloy to another – more than for aluminum – so it is important to check which
alloy is being used. Values are tabulated for 302 and 303 stainless, which are
very similar, and for 44C stainless and for 1075 carbon steel.
3.5.1
302 Stainless
The
data given in previous versions of the SDN were taken from the IR/EO
Handbook. However, although this refers back to the Touloukian et al.
volumes, the handbook tabulation does not seem to correspond to any of the
values given there. The values now listed are taken from Arp et al, and are
corroborated by data from the Cryogenic Materials Handbook. The CTE
values are now about 7% larger.
3.5.2
303 Stainless
The
CTE values for this alloy are similar to those for 302 stainless. Note that
other 300-series alloys have similar CTE values, although the values may differ
from one another by several percent. Data are taken from Arp et al., and
corroborated by the Cryogenic Materials Handbook.
3.5.3
440C Stainless
This
is used in most of the GNIRS bearings. The CTE of this (and other 400 series
alloys) is lower than that of the 300 series alloys.
3.5.4
1075 Carbon Steel
These
are data from Arp et al. Carbon content is ~0.8%. Carbon steel (as opposed to
alloy steel, which contains substantial amounts of other elements) has a CTE
that it close to that of pure Fe; the CTE of the latter is about 4% higher than
the values tabulated for 1075 steel, and this suggests that the CTE for a
lower-carbon steel will be slightly higher than the values in the table.
3.5
Optical Materials
Data
are given for those IR optical materials used in GNIRS. These comprise several
fluoride materials and some Schott glasses.
3.6.1
Barium Fluoride
The
primary source used for these values was NBS Technical Note 993 (Feldman
et al, 1978), supplemented by data quoted in Touloukian et al Thermophysical
Properties of Materials. Note that Touloukian et al give a “recommended”
curve which was not used, although it is plotted below; this is
different from the tabulated data that were used.
Note
that these values differ slightly from those used in the initial optical
analysis. The average CTE is about 0.65 ppm/K larger than the value previously
used, which affects radii and thickness at a level of 0.015%. I am note sure
what the difference is due to, probably a combination of the additional data
and the extrapolation to 60K.
The
average CTE values are probably good to about 1%, but the value at 60K is
probably not much better than 1 ppm/K.
3.6.2 Calcium Fluoride
There
are more data available for calcium fluoride. These include the source cited
for BaF2 plus Browder and Ballard (Applied Optics, 8, 793
[1969]). The latter source gives measurements for IRTRAN materials, which are
not single-crystal materials, and may thus have slightly different properties.
The data are nonetheless fairly similar.
The
values given above are, again, somewhat higher than those used in the initial
optical analysis, this time by about 1.15 ppm, which will affect dimensions at
the 0.03% level.
Again,
the uncertainties are about 1% in the average CTE values and perhaps 0.5 ppm/K
in the CTE at 60K.
3.6.3
Magnesium Fluoride
MgF2
is an anisotropic material, with a CTE that depends on directions. Both values
are given and plotted below; they come from Feldman et al (1978) only since the
equivalent IRTRAN material measured by Browder and Ballard is a mixture of
material at all orientations. The Ballard and Browder data are used to help
extrapolate to 60K, since the CTE there is quite uncertain (see curves below).
This
material is used only for the GNIRS Wollaston prism, so precise knowledge of
the CTE is less critical. However, it should be noted that the difference in
the contraction along the 2 axes is almost 0.1% to 60K, which corresponds to
several thousandths over the width of the prism elements.
3.6.4 Schott SF6 Glass
These
data were measured for NOAO and CFHT by Schott (Germany) between –180 and 100C.
3.6.5
Schott SF57 Glass
No
cryogenic data were available for this glass. The CTE near room temperature is
roughly 2.5% greater than for SF6, so values were adopted that were 2.5%
greater overall. This assumption is adequate given that the SF57 glass is used
only for cross-dispersion prisms. A 10% uncertainty in the CTE, which is
plausible, has only minimal effects on the overall design.
3.6.6
Schott BK7 Glass
Again,
no cryogenic data were available for this glass (somewhat surprisingly).
However, Molby (JOSA 39, 600 [1949]) measured several glasses to ~77K,
including two with similar properties (index, dispersion) whose room
temperature CTE values bracket those of BK7. An average of the two glasses
(BSC-1 & BSC-2) was used that was weighted to have the same room
temperature CTE as BK7. Some other curves were plotted in order to see whether
a match to SF57 (see above) could be obtained, but none of the glasses measured
by Molby were as close as SF6.
4.
Revisions
Revision
A, 10/07/99 – Added to discussion of G-10. Correction to discussion of change
from previous values of CaF2. No changes to tabulated CTE values.
Revision
B, 10/29/99 – Added A356 data. Added discussion of MIL-HDBK-5G data.
Corrected some typographical errors. No changes to tabulated CTE values.
Revision
C, 12/27/99 – Added brass and steel data. 302 stainless data have changed;
see discussion.
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