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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
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URNr 4 32 03
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AUG 22 1967
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SROT
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HQ 13.09
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THERMAL CONDUCTIVITIES OF 90Sr HEAT SOURCE MATERIALS*:
.
:
E. E. Ketchen and R. E. McHenry
Isotopes Development Center.
Oak Ridge National Laboratory
Post Office Box *
Oak Ridge, Tennessee 37830
MASTER
ABSTRACT
thermal gradients in high power density isotopic
fuels limit the size of the sample which can be.
used; for instance, a temperature difference of
50°C exists across a slab of 0.134-in.-thick
one side of the slab.
The thermal conductivities of Sro, SraTi0s, and
SrTiO3 (of a composition which simulates these
compounds prepared from nuclear fission fuels
waste) are reported. The thermal conductivities
were measured using a comparator apparatus which
was altered to evaluate several factors necessary
to establish a procedure for the measurement of
the thermal conductivities of radioactive heat
source fuels. The errors in the reported values
are assessed and a procedure for high power den-
sity radioactive samples is described.
· The thermal conductivities reported in this paper
for Sro, SrIi0s, and SrTiOs were measured in a
thermal comparator apparatus** which was modified
to measure 1/2-in.-high by l-in.dia disc-shaped
samples without thermocouples. The data obtained
using several materials demonstrate that system-
atic error can be corrected by using empirical
calibration constants and that random error is
small. Additional modifications are required to
adapt the apparatus for the thermal conductivity
measurement of high power density radioisotopic
samples; the proposed procedure is discussed. .
INTRODUCTION
med
'
EXPERIMENTAL
.co... ons
The thermal conductivities of Sro, SraTi04, and
SrTiOs have been measured using a modified version
of a commercially available apparatus. The appara-
tus was modified in order to evaluate the effects
of several factors which are not subject to rig-
orous control in thermal conductivity measurements
of high power density radioactive materials.
Thermal conductivity data of radioactive Leat
• source materials are necessary for the calculation
of thermal gradients in heat sources. Although
the conductivities of radioactive materials which ..
. are suitable as beat sources were not measured in
this work and are not reported in the literature,
sufficient data and experience, have been accum-
lated to establish a proc:edure for such materials.
Apparatus and Materials
ambiente che non tanta boniter Thirththing and mother
o
Several Sosr isotopic power sources have been used
in a series of power generators (SNAP-7A, B, C,
D, and E) which were used in remote installa- . .
tions. (1) Second generation 9°Sr power generators
such as SNAP-23 will require an isotopic heat
source of 4 in. dia, which delivers 1200 watts of
thermal power. An accurate knowledge of the ther-
mal conductivity of these large sources will be
required..
A modified 3M TC-200 thermal conductivity appara-
.tus (2) was used to measure the thermal conduc.
itivity. A schematic diagram of the modified
apparatus is shown in Figure 1. The apparatus
is a thermal comparator in which a high flux (Q)
supplied by a heater (a) flows in sequence through
a specimen of known thermal conductivity (the
standard), a specimen of unknown thermal conduc-
tivity (the sample), and another standard to a
: beat sink (b). The first standard, the sample,
and the lower standard are referred to as Sa, Sa,
. and Sa, respectively. The assembly is referred
to as the thermal conductivity. stack. The tempera-
ture at which the thermal conductivity is measured
is controlled by a beater in the heat sink. The
heat (Q) flowing through the standards (Si and S3)
can be calculated from the equation:
:* :*
*
:
:*
*
:* :
:*
:*
:*
Q = KAAT
An
Conventional methods for the thermal conductivity
measurements of ceramic materials require large
well-instrumented samples. Unavailability of
. sufficient materials (e.g., 244cm) and the diffi-
culty of fabricating instrumented samples render
conventional methods infeasible. Also, large
where k = thermal conductivity of the standard,
*: 114
:-*:
+
+
+
ở:
,-4
1
*
-
*Research sponsored by the U. S. Atomic Energy Commission under contrect with the Union Carbide Corporation.
**3M Model TC-200 thermal conductivity apparatus.
"Superior numbers refer to similarly-numbered references at the end of this paper".
· DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED
..
.
...
.
.
.
3..
.
.
1.
..
.
..
A = cross sectional area of the standard,
Sample Preparation
AT = temperature drop in the standard over
A composition typical of material which results
a distance Ab.
from process waste of fission-product fuel was
chosen since the purpose of this work was to infer
The temperatures of the lower end of standard s, the thermal conductivity of 90Sr heat sources.
and the upper end of standard Sg are obtained by
The composition of the three compounds Sro, ..
extrapolating (using the equation) the tempera-
Sr T10.1, and SrTiOg are given in Table 1. Samples
tures measured at points 10 and ll to the ends of prepared with these compositions represent the
the standards Sg and Sr, respectively.
SºSr sample at the time of preparation (before
radiation damage and accumulated decay product,
The thermal. conductivity stack was surrounded by
zirconium, nccurs ).
a series of individually controlled guard heaters.
Bubble zirconia was used as an insulating media
The compounds were prepared/4) by adding the
between the guard heater wall and the thermal
desired amount oi Tioz in the form of a fine slurry
conductivity stack. The guard heater wail was
to the solution containing the strontium and pre-
held within £1°C with respect to the adjacent
cipitating the alkaline earths as carbonates. The
stack to ensure no appreciable heat loss or gain
alkaline-earth carbonate-Tioz mixture was calcined
from the thermal conductivity stack.
at 1200°C to decompose the carbonates to the
oxides and, at the same time, to react the result-
The Pyroceram 9606 standards were 1-3/4 in. long ing oxides with the Tioz to form the titanates.
and I in. in dia. Thermocouples ll and 13 in
standard S, and 8 and 10 in standard Ss were 1 in. Samples of strcntium fuel were prepared by hot
apart. Thermocouples 10 and 11 were located 1/8 pressing(5) at 1200°C (Sro at 1300°c) in a graphite
in. from the end surfaces of the standards. The
die at 4000 psi for 1 hr. Hot pressed. samples o
end surfaces of the standards and the sample were compounds which contained T102 were slightly sub-
polished flat and paralled. A l-mil platinum
· stoichiometric in oxygen (the oxygen deficiency
sheet was placed between the sample and the
was not, 0.006 moles of oxygen per mole of com-
standards to reduce the thermal resistance at the pound). The samples were oxidized to
interfaces. In all cases, the sample was ~1/2 in. stoichiometry by heating in air at 1200°C for 24
high and l in. in dia.
hr. Substoichiometric samples were black; stoi-
chiometric samples were white. The samples were
ground to size, and the top and bottom of the
Calibration of Apparatus
samples were ground flat and parallel before
polishing.
The apparatus as received from the manufacturer
was evaluated using the procedure recommended ir
The samples specimens were prepared without instru-
the manual(2) supplied with the apparatus. The
mentation (i.e., no thermocouples were inserted in
apparatus was tested with the standards and the
the sample specimen) in order to simulate the
sample of identical material whose thermal con-
radioactive samples as closely as possible. It
ductivities had been precisely measured. Tests
is infeasible to instrument radioactive samples.
were made using thermal conductivity stacks of
Pyroceram 9606 and Armco Iron. In both cases,
the samples were I in. In dia by 1 in. High with .XPERIMENTAL RESULTS
thermocouples installed as recoinmended by the
manufacturer. Thirteen measurements were made at
temperatures in the range of 65 to 900°C. The
Variance in Interface Conductivity
maximum deviation from the standard value was 5.
The average deviation for the 13 values was 2.3%. . Since samples without instrumentation were used
No tests were made using stanäards and samples
for this work and are planned for future work with
whose thermal conductivities differ a few percent, radioactive samples, the variation in the con-
since such standards were not available.
:ductivity of the interface between the sample and
standards and the resultant error was determined.
The apparatus was modified to measure n.-high : Data were taken in a series of ruris in which N
samples by increasing the length of the standards : and Q were measured across the interface between
to 1-3/4 in. (Figure 1). The samples were un-
two pieces of Pyroceram 9606. The temperatures
instrumented. Test runs were made using Pyroceram : were measured by two thermocouples placed 1/8 in.
9606 samples and Pyroceram 9606 standards whose
from the interfaces. The temperatures at the
thermal conductivity is standardized (3) and simi surfaces of the Pyroceram were obtained by extrapo-
lar to the thermal conductivities of the compounds lation using known values of thermal conductivity
to be measured. Empirical constants were obtained i and experimental values of Q and temperatures.
which were used to adjust the data taken using . The temperature drop acruss the interface was
material of similar but unknown thermal conduc-
normalized by dividing by Q. The average AT/Q is
tivity.
shown as a function of the interface temperature
LEGAL NOTICE
in Figure 2.
the commune sou6 and Armoreductivity contai. Tests
The ruport w prepared u w account of Government sponsored work. Neither the United
Status, for the Councineton, nor any person acting on behalf of the Commission:
d. Make my warranty or reprodonadon, sprchod or implied, with respect to the accu-
macy, completeness, or unafuldest of the taformation contained to this report, or that the use
of my tafor uation, apparatus, method, or procon declosed in this report may not Infringe
privately owned righte; or
B. ARUS any llabaute with roopact to the use of, or for damages romulting from the
an of any tatormation, appunto, method, or process dlaclound in this roport.
As rood in the whom, "pornon acttes on behalf of the Commissdoa" Includes my on-
auch employee or contractor of the Com. e or employme of much contractor preparou,
demostrates, or provides accen to, any trformation partant to his employmeat or contract
with the Couumiandon, or his employment with touch contractor.
........
***',:..
...;
.
...
.
Measurement of the Thermal Conductivity
Titanium Oxide. The thern conductivity of a
hot pressed specimen of 99.9% pure TiO2* (9
theoretical density was measured to evaluate the
operation of the modified apparatus. The thermal
conductivities obtained are show in curve i of
Figure 3; curve 2 gives the thermal conductivities
of 99.5% pure TiO2 of 98% theoretical density
recommended by the Bureau of Standards. (6) The
experimental values have been corrected using the
calibration constant obtained using Pyroceram
9606 standards and sample
as possible the exact setup for an experimental
run as for a calibration run, the errors resulting
from factors other than the variance in the inter-
face conductivity were held to a small fraction of
the error due to the interface. This conclusion
is supported by the excellent agreement of data
taken with a material using different values for
the calibration constants (Figure 4 and Tables 3
and 4). Also, the data obtained for TiO2 (Figure 3)
is in good agreement with published values.
· Interface Conductivity
Strontium. Oxide. The thermal conductivity of a .
hot pressed Sro pellet of 95.9% theoretical gen-
sity (4.44 g/cm3) was measured. The pellet was
handled in such a manner as to prevent CO2 and :
moisture of the air from reacting with Sro before
the measurement. Due to the reactivity of Sro in
air, it was not metallographically examined. The
thermal conductivity of the pellet is given in
Table 2; the thermal conductivity values (Figures
4 and 5) have been corrected to theoretical den-
sity using Loeb's equation.
***
The data for 30 values of AT are given in Figure 2.
A straight line was fitted to the data by using the
method of least mean squares. The estimated vari-
ance of the points in Figure 2 from the line is
0.832°C/watt. The estimated variance of the points
from the true line is 0.95°C/watt. Since there are
two interiaces in each determination, the total
estimated variance for the two interfaces by propa-
gation of errors is y2 x 0.95°C/watt or 1.3°C/watt.
A band which will include 95% of the points is
obtained 11 twice the total variance is added to
and subtracted from the mean; this band is 2.6°C
watt. Since the average AT/watt for the sample is
9°C the error due to the interface will be greater
than +29% for 5% of the thermal conductivity deter-
minations. Fifty percent of the thermal conduc-
tivity determinations will have interface conduc-
tivity errors of less than £10%.
Strontium Orthotitanate. The thermal conductivity
of Sr T10,** (density, 4.92 g/cms) is given in
Table 3 and Figures 4 and 5. A photomicrograph
of a typical sample is shown in Figure 6. The
.photomicrograph shows what appears to be shallow
holes or a clear phase. . Since the density is so
similar to the theoretical density, 799.5%, it
was assumed that the slightly darker areas are
optically clear phases in the gray matrix material.
Thermal Conductivity
Strontium Titanate. The thermal conductivity of
SrTiO3 (đensity, 5.11 g/cms) is given in Table 4
and Figures 4 and 5. A photomicrograph of the
theoretically dense pellet is shown in Figure 7.
The data for the thermal conductivity of Sro,
Sr Ii0s, and SrTiOs were correlated under the
assumption that the predominant mode of conduction
in the range investigated is by phonons, Under
this assumption, the thermal conductivity is pro-
.
DISCUSSION
perature. This function is linear and fits the
data well. The function was fitted by least mean
squares. The confidence limit (95%) 18 snown for
the curves in Figure 4. The functions for Sro,
SraTi04, and SrTiO3 were used to calculate the
curves for the range of experimeatal values and
for extrapolation outside that range. The thermal
conductivity versus temperature is shown in Figure
5. It is believed that the extrapolation is useful
for the range shown.
Calibration Constant
The calibration constants (defined as the ratio
of the measured value to the standard value of
the thermal conductivities obtained varied as
much as 15% at a given temperature (Figure 8).
However, the data obtained during a single cali-
bration run fitted a straight line with a maximum
deviation of <2%. Several sources of error which
could contribute to the variation in the calibra-
tion constant can be identified: (1) variation
in the thermal conductivity of the bubble zirconia,
(2) caanges in the composition of thermocouples
due to contamination, and (3) variance in the
interface conductivity. By reproducing as closely
.
.
.
Systematic Error
The thermal conductivity of TiO2 was determined in
order to evaluate the systematic error. Since the
TiO2 data agreed well with the weighted average of
36 sets of data analyzed by the National Bureau of
Standards, it is believed that the systematic error
*The Tioz used to obtain the data was slightly substoichiometric in oxygen (see Experimental section
this report).
**These data were taken using a fully oxidized sample. Other data given in Table 4 show that within the
limits of error for this apparatus, no difference was observed between stoichiometric and substoichio-
metric samples. .
does not greatly exceed the icrecision. Systematic
error can result when the thermal conductivity of .
the standard differs significantly from the sample.
For this reason, the systematic error should be
less for SraTi04 then for Sro or SrTiO3.
REFERENCES
(1) Corliss, W. R. and Harvey, D. G., Radivo
isotope Power Generation, Prentice-Hall, Inc.,
Englewood, N. J., 1964, p. 167.
FUTURE WORK
(2) Operating Instructions on the 3M Model TC-200
Thermal Conductivity Apparatus, Minnesota
Mining and Manufacturing Co., St. Paul,
Minnesota.
The work described in this report was undertaken
for two purposes: (1) to obtain the thermal con-
ductivity of strontium fuels under the condition
of no radiation damage or accumulated decay product
within the strontium fuel and (2) to develop a pro-
cedure for the determination of the thermal conduc-
tivity of radioactive fuels. In particular, it
was desired to determine the error resulting from
thermal conductivity measurements made on small
uninstrumented samples. The data described in
this report show that the thermal conductivity
using 1/2-in.-high by l-in.-dia uninstrumented
discs can be determined with acceptable errors.
Flynn, D. R., Thermal Conductivity of Semi-
conductive Solids, Method for Steady-state
Measurements on Small Desk Reference Samples,
NBS Rpt. 7740, U. S. Dept. of Commerce,
National Bureau of Standards (Oct. 29, 1962).
(4)
Baker, P. S., Rupp, A. F., and associates,
Isotope Production and Development, Isotop.
Radiat. Technol. 1(1): 37-9 (Fall 1963).
(5)
Quinby, T. C., Pierce, E. E., and McHenry,
R. E., Hot Presses for Glove Box and Manipu-
lator Cell Use, USAEC Rpt. ORHL-IM-1900,
Oak Ridge National Laboratory (to be
published).
Powell, R. W., Ho, C. Y., and Liley, P. E.,
Thermal. Conductivity of Selected Materials,
NSRDS-NES8, U. S. Dept. of Commerce, National
Bureau of Standards (Nov. 25, 1966).
The thermal conductivity of radioactive fuel wili
be measured using essentially the same apparatus
with the same type of sample. However, with radio-
active samples the method will be absolute rather
than comparative. The beat flux, Q, will be sup-
plied by the sample; Q can be accurately determined
by calorimetric methods. 1 The top beater, which
is not required, will serve
standard S, (see Figure 1) will be replaced by a
temperature monitor or low thermal conductivity.
The top guard will be adjusted to give zero AT
(and zero heat flow for the two thermocouples in
the temperature monitor. The temperature of the
monitor will be the same as the temperature at the
top of the sample. The temperature at the bottom
of the sample will be determined using the bottom
monitor (which will replace the bottom standard).'
The bottom monitor will also measure the heat flow
from the sample and indicate the correctness of the
adjustment of the guard beaters. The sample heiglat
Por severai radioactive fuels for a AT of 50°C is
given in Table 5.
Posey, J. C., Calorimetry for Measuring
Radioactivity, Isotop. Radiat. Technol. 1(1):
92-6 (Fall 1963).
+
-
-
-
ILLUSTRATIONS
Figure 1. Cross Section of Thermal Conductivity
Apparatus.
Figure 2. Error Due to Variable Interface
Conductivity.
Figure 3. Thermal conductivity of T102.
Figure 4. Correlation of Thermal Conductivity
Data for Sro, SraT104, and SrTiO3.
Figure 5. Thermal conductivity of Sro, SrTi04,
and SrTiO3.
Figure 6. SraTi04.
Figure 7. SrTiO3.
Figure 8. Calibration Constant Using Pyroceram
9606.
.
The major source of error in the thermal conduc-
tivity measurements is expected to result from the
variation of the conductivity of the bottom inter-
face. The error for the interface conductivity of
a nonradioactive sample has been discussed pre-
viously in the report. The error resulting from
the variation of a single interface is expected to
be greater for radioactive samples due to the dif-
ficulty of preparing smooth parallel surfaces.
However, since only one interface is involved, the
errors are expected to be approximately the same
as reported for nonradioactive samples. The over-
all error should be less since an absclute method
will be used.
Table 4.
Thermal Conductivity of SrTi
Table 1. Composition of Sro, SrzTi04, and SrTiO3
Composition,
Compound
wt%
Sro
SraTi04
SrTiO3
Sro
. 91.69 65.56 51.03
Cao
3.10
2.42
Bao
3.46
2.47
1.92
MgO
0.51
0.37
0.28
Tila
-
28.50
44.35
4.34
421
497
Thermal conductivity, wa
Temp.,
First run
Second runa
394
0.0415
408
0.0409
0.0410
489
0.0388
0.0392
515
0.0383
.650
0.0361
696
0.0335
0.0347
0.0341
816
0.0313
0.0317
861
0.0313
Cusing slightly substoichiometric sample.
736
Temp.
813
'
'
• 411
Table 2. Thermal Conductivity of Sro
Thermal conductivity, watts/cm°c
Experimental
Corrected
405
0.02298
0.0240
0.02257
0.0235
592
0.02155
0.0225
682
0.02036
0.0212
747
0.01956
0.0204
491
249
Theoretical density.
Table 5. Sample Height for at of 50°C
Radioactive fuel
Sample height, in. .
-
90sro
0.40
90sr2[104
90SrIi03
1709m 03
0.55
0.68.
0.20
0.14
244c1203
1
.
A
Table 3. Thermal Conductivity of Srzli04
Thermal conductivity, watts/cm°c
Temp.,
First run
Second run
359
0.03400
0.03195
465
0.03267
495
0.03063
0.03293
0.03001
652
0.03219
0.02937
728
0.03199
749
0.02982
577
592
692
.......... -----------------
--
---.
..em comme
ORNL-DWG 67-6388
PRESSURE

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Fig. I Cross Section of Thermal Conductivity Apparatus.

ORNL-DWG 67-6694
AVERAGE A/watt FOR SAMPLE=9° C
:.5% OF K DETERMINATION HAVE ERRORS
OF GREATER THAN † 29%
50% OF K DETERMINATION HAVE ERRORS
OF LESS THAN † 10%
800
400
500
. 700
INTERFACE TEMPERATURE (°C)
Fig. 2 Error Due to Variable interface Conductivity.
ORNL-DWG 67-6389
-
-
-
--
-
"
-
THERMAL CONDUCTIVITY (watt /cm °C).
• CURVE NO. 2 RECOMMENDED VALUE NBS
• CURVE NO. 1 THIS RESEARCH +
.
.
300
oo
800
.

400 500 600 700
TEMPERATURE (°C)
Fig. 3 Thermal Conductivity of TiO2.
ORNL-DWG 67-6672
SrTiOz k=0.0185 + 15,592
SrTi04 k=0.0261 +
Sro k= 0.0135 + 7:4:15
K, THERMAL CONDUCTIVITY (watt/cm °C)
CONFIDENCE LIMIT
ON CURVE (P=0.95)
0.01
0.80 0.90 1.00 1.10 1.20 1.30 1.40 9.50 1.60
1C0O / T (OK)
Fig. 4 Correlation of Thermal Conductivity Data for Sro, Sration,
and SrTiO3.

ORNL-DWG 67-6674
SrTiO3
K, THERMAL CONDUCTIVITY (watts/cm°C)
Sr.
SrTiO4 -
Sre--t-
400
800
1200
1600
TEMPERATURE (°C)
Fig. 5 Thermal Conductivity of Sro, Sration and SrTiO,

.
.
1
.
.
...
.....
.
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...
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..,'
;
::.:.:..:.o
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THE 16T5 TO 250x Ty Tin
TTT
Fig. 6.
Sr2T104
. .
.
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.
.
8
250xom
NT-
Fig. 7. SrTi03
.......
... .....
ORNL-DWG 67-6390R
·
110
KTHIS WORK
ACCEPTED
100* KACCEPTED
O NO. 1 CURVE RAN ON NOV 7, 1966
A NO. 2 CURVE RAN ON JAN 26, 1967
A NO. 3 CURVE RAN ON MARCH 17, 1967
80
350
850

450
550
650
750
TEMPERATURE (°C)
Fig. 8 Calibration Constant Using Pyroceram 9606.
END
.
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.
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L'i
-
DATE FILMED
10 / 4 /67








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