Cryogenics 41 (2001) 725–731
www.elsevier.com/locate/cryogenics
Description of removable sample mount apparatus for rapid
thermal conductivity measurements
A.L. Pope, B. Zawilski, T.M. Tritt
*
Clemson University, 118 Kinard Laboratory, Clemson, SC 29632-0978, USA
Accepted 31 August 2001
Abstract
Described in this paper is an apparatus in which bulk samples can easily be mounted on a removable puck for thermal conductivity measurements and then placed in the described measurement system. This rapid mounting and measurement system uses a
standard steady-state absolute thermal conductivity measurement but allows for rapid measurement and excellent thermal stability
coupled with the use of a closed cycle refrigerator. The distinction of this system is rapid mounting and measurement of thermal
conductivity over a broad temperature range without sacriﬁcing accuracy and precision in data acquisition. In addition, this system
allows for versatility in its use. The design of this apparatus, measurement speciﬁcations, and thermal conductivity data on several
standard materials measured in this system are presented. Ó 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Thermal conductivity; Closed cycle refrigerator; Rapid measurement
1. Introduction
The determination of the thermal conductance ðKÞ is
a solid-state measurement in which a temperature difference ðDT Þ across a sample is measured due to power
input ðPR ¼ I 2 RÞ into a resistive heater, essentially a
measure of the heat ﬂow through the sample. Thermal
conductivity ðkÞ is the same measurement with the dimensions of the sample taken into account and
k ¼ KL=A, where L is the length between thermocouples,
DT is the temperature diﬀerence measured, and A is the
cross-sectional area of the sample through which the
heat P ﬂows. In the thermal conductivity measurement
A
P ¼ kTOT
DT ;
L
where P is the power input into the sample, kTOT is the
total thermal conductivity.
Many methods exist for measuring thermal conductivity such as the 3x technique [1], thermal diﬀusivity,
and the steady-state (absolute or comparative) technique [2]. Each technique has its own advantages and
limitations. Our probe is designed to measure electrical
*
Corresponding author. Tel.: +1-864-656-5319; fax: +1-864-6560805.
E-mail address: [email protected] (T.M. Tritt).
conducting samples with approximate dimensions of
2 2 8 mm3 . It was determined that the absolute
steady-state technique would be most advantageous to
use for these samples. There are power loss terms ðPLOSS Þ
involved in the measurement of thermal conductivity
utilizing the steady-state technique that must be accounted for or minimized. Thus, one must determine the
true power through the sample ðP ¼ PIN PLOSS Þ that is
responsible for the temperature gradient.
2. Experimental considerations
Previously we developed a custom designed apparatus
for rapid thermopower and electrical resistivity measurements using dismountable integrated circuit chips
incorporated into a commercial cryocooler [3]. Utilization of the absolute steady-state technique (as used in
the dismountable puck system described here) requires
thorough understanding of the errors or losses involved
in this technique. A disadvantage to using an absolute
technique is the diﬃculty in determining exactly how
much heat is being lost; consequently, this loss must be
minimized or calculated to reduce this uncertainty. This
may be done through the use of small diameter wires
with low thermal conductance, high vacuum to reduce
convection and gas reduction loss and designs to reduce
0011-2275/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 1 1 - 2 2 7 5 ( 0 1 ) 0 0 1 4 0 - 0
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A.L. Pope et al. / Cryogenics 41 (2001) 725–731
radiation losses. For example, in order to minimize
conductive loss a diﬀerential thermocouple is utilized so
that there will only be two wires available as a heat leak
instead of four wires if standard thermocouples were
used. The absolute technique requires fewer thermocouples and provides a smaller quantity of places to
make poor thermal contacts than if a comparative
technique was used.
Radiative loss is also a major concern when using any
solid-state technique to measure thermal conductivity.
There are only a few design features that can be incorporated to overcome these losses and corrections to the
data are typically necessary. Matching of the temperature gradient on a radiation shield surrounding the
sample with the temperature gradient of the sample is
often used as a solution in larger samples. With smaller
samples, several mm in length, this correction shows
little reduction of radiative loss. Another method to
combat radiative loss with small samples is to incorporate a radiation shield that will reﬂect the heat back on
the sample. This is accomplished through the use of a
highly reﬂective surface on the inside of the radiation
shield. Also essential when making measurements is an
excellent vacuum which will minimize convection and
heat conduction in the system. Convection will lead to
heat transfer along the sample not associated with travel
through the sample. A sweep of power verses DT conducted at a stable temperature should be linear. If it is
not a straight line, there are losses due to convection
which need to be corrected for or minimized.
Another issue that must be taken into consideration
when making thermal conductivity measurements is
thermal sinking of the sample. In order to make an accurate measurement, the sample must be in excellent
thermal contact with the cold ﬁnger and heater as well as
with the thermocouple. Kopp and Slack [4] present an
excellent discussion of thermal contacting problems with
thermocouples. Uncertainties in measurement of sample
dimension can also lead to a 5–10% uncertainty in the
thermal conductivity measurement since the thermal
conductivity depends on the cross-sectional area of the
sample and the length between the thermocouples. With
many systematic errors that must be considered, then a
5–10% uncertainty in the absolute magnitude of the
thermal conductivity is generally considered to constitute a relatively accurate measurement.
essential when designing this system was the ability to
thermally sink the samples to the cold ﬁnger. This was
achieved through the use of custom designed components at Clemson, coupled with the use of commercial
parts (speciﬁcally a removable puck and puck receptacle, provided by Quantum Design) and incorporating
these into a commercial cryocooler system. The commercial manufactured parts used here are also used in
the Quantum Design physical properties measurement
system (PPMS) to thermally sink experiments to the
cold ﬁnger of the PPMS. The sample puck is made of
oxygen-free high-conductivity copper that couples directly to the puck receptacle that houses the thermometer. The sample puck is keyed so that it may only be
inserted into the receptacle in the correct orientation [5].
Another concern alleviated though the use of commercial parts was the eﬀect of thermal cycling on the puck/
receptacle junction since this had been adequately tested
previously.
In order to facilitate rapid throughput of samples, the
puck was designed to accommodate two samples, using
an absolute steady-state technique. The two mounted
samples can be measured simultaneously. Samples are
mounted on the dismountable puck and tested for
readiness (good electrical contact) in a custom designed
test box before they are plugged into the closed cycle
refrigerator. A good ‘‘rule of thumb’’ is that excellent
electrical contact as well as mechanical stability is reﬂected into excellent thermal contact. Additionally, the
dismountable puck allows all sample mountings to be
performed under a microscope and ensures virtually no
‘‘down time’’ in the operation of the closed cycle refrigerator.
Components necessary to thermally couple the puck
receptacle to the cold ﬁnger were machined (see Fig. 1).
A brass piece is screwed into the cold ﬁnger of the closed
3. Description of removable puck system
With the desire to design for a system in which samples for thermal conductivity measurements could be
easily introduced into the cold cycle refrigerator, several
requirements were considered. The foremost concern
when designing this system was the reproducibility and
accuracy of the measurement. One requirement that was
Fig. 1. Pieces necessary for assembling the thermal conductivity receptacle for the dismountable puck. These pieces are assembled on the
cold ﬁnger of the closed cycle refrigerator.
A.L. Pope et al. / Cryogenics 41 (2001) 725–731
cycle refrigerator. This brass piece is essential to slow
down the cooling rate of the sample to prevent thermally
shocking the sample. It also provides better temperature
control for thermal cycling of the system and stabilizing
at a desired temperature. The brass piece acts as a
thermal decoupler, due to its low thermal conductivity
(k 100 W/m K at T 300 K) and provides thermal
inertia between the sample and the copper cold ﬁnger
(k 400 W/m K at T 300 K).
A small copper cup was designed and machined and is
screwed into the brass piece. There is a small hole in the
side of the copper cup through which the electrical lead
wires can be inserted into its interior. The lead wires are
thermally sunk to this Cu cup with thermally conductive
epoxy, called Stycastâ . The wires run from the puck
receptacle to the electrical outlet connectors in the
closed cycle refrigerator. This Cu cup is necessary to
electrically connect to the puck receptacle, which has its
electrical lead pins at the bottom of the receptacle. The
cup also acts as an isothermal environment for the wires
leading to the puck receptacle, minimizing any unwanted or extraneous thermal voltages.
In order to attain excellent thermal sinking, a copper
ring was machined to ﬁt snugly around the puck receptacle and securely in the copper cup. The copper ring
is screwed to the puck receptacle. Twisted pair wires are
thermally sunk with grease to the side of the copper cup
and then attached to the leads on the puck receptacle. A
Si diode is imbedded into the puck receptacle, providing
excellent thermal coupling as well as placement close to
the sample. The ring/receptacle assembly is placed in the
copper cup using thermal grease to enhance thermal
contacting. The copper cup and copper ring/receptacle
are fastened together with countersunk screws securing
the puck receptacle in place. This system provides a
hardwired mount to plug the puck into without sacriﬁcing the excellent thermal contact required for reliable
thermal conductivity measurements. In addition, a Cu
radiation shield (can) which has been polished on the
inside and sputtered with high reﬂectivity Au is placed
around the samples and thermally sunk to the base. See
Fig. 2 for an assembly drawing.
4. Mounting conﬁguration
The Quantum Design puck is then modiﬁed to accommodate samples for the thermal conductivity measurement. A small copper plate with four screw holes is
attached with Stycastâ to the thin copper ﬁlm on the
removable puck. Small copper blocks with screw holes
to fasten to the copper block on the removable puck are
machined with a hole in the center. This hole acts as a
solder pot with which to thermally contact the sample to
the cold ﬁnger. Stycastâ may also be used to thermally
adhere the sample to the base. Samples are thermally
727
Fig. 2. Assembly drawing of removable thermal conductivity mounting system.
sunk into the copper solder pots and subsequently attached to the modiﬁed removable puck from Quantum
Design. Consequently, the sample is in excellent thermal
contact with the puck, which in turn is thermally adjoined to the entire system.
The next challenge in showing the viability of this
dismountable mounting system is in attaining accurate
and reproducible data by setting up an absolute thermal
conductivity measurement on the removable puck
(Fig. 3). The measurements were performed on a set of
available standards. The sample mounting technique is
taken from Uher [8]. In order to measure thermal conductivity using the absolute technique a strain gauge is
employed as a resistive heater (120 X resistor). The
strain gauges are used as heaters due to the fact that
their small size allows for better thermal contact with the
sample as well as less surface area for radiative loss. The
strain gauges are attached to the sample with a very thin
layer of 5 min epoxy providing very good thermal contact even though the thermal conductivity of the epoxy
is low. The existing leads of the strain gauge (Cu,
k 400 W/m K at 300 K) are removed and replaced
with phosphor-bronze (k 20 W/m K at 300 K) wires
due to their low thermal conductivity and consequently
minimized heat loss. A two-wire resistance measurement
is made from the sample to the puck and a four-wire
measurement is made from the puck to the measurement
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A.L. Pope et al. / Cryogenics 41 (2001) 725–731
Ω
establishing a vacuum of 106 Torr in order to minimize
convective losses. The sample chamber is then evacuated
with a roughing pump and then a turbo pump (typical
vacuum 106 torr).
5. Data acquisition
Fig. 3. Two samples are mounted on a removable puck. Each sample
is mounted as pictured above.
equipment. This two-wire measurement introduces a
small error (<1%) in the power input and thus the
thermal conductivity, which must be and is corrected for
in the calculation. Two #38 AWG (0.004 in.) insulated
copper wire ﬂags are placed parallel to one another and
perpendicular to the length of the sample. Once the
Stycastâ is dry, the coating on the tops of the copper
wires are scraped to provide a surface on which the
(0.001 in.)Cn–chromel junction of the diﬀerential thermocouple is soldered. This Cu–thermocouple junction
provides excellent thermal contact. The copper ﬂags
help not only with thermal contact, but also ensure that
the diﬀerential thermocouple is not shorted to the
sample resulting in erroneous voltage measurements.
This speciﬁc type of thermocouple was chosen due to its
low thermal conductance, which will assist in reducing
error due to conductive loss. A single diﬀerential thermocouple is used in this system instead of two thermocouples in an eﬀort to further minimize conductive
losses through the wires (2 wires lead away from the
sample instead of 4).
Once the sample has been examined to ensure all the
wires are installed properly and none of the wires are
electrically shorted, the puck is placed in the puck receptacle on the cold ﬁnger of the closed cycle refrigerator and three shields are placed over the sample. The
inner shield matches the temperature gradient around
the samples in an eﬀort to minimize the radiative loss.
The middle shield helps minimized radiation loss from
the cold ﬁnger. The outermost shield is a vacuum shield,
Thermal conductivity measurements are made using
state-of-the-art electronics (measurement equipment
described below) and data acquisition software. Using
LabViewâ , a visual programming language, a custom
designed data acquisition program is developed that
automates the data acquisition process. The cross-sectional area of the samples, which have been measured
using an optical microscope or a set of calipers, is entered into this program. The length between the thermocouples is measured from the inside edge of the two
copper ﬂags and entered into the program. Measurement from inside the wires is necessary because the
copper wires are of much higher thermal conductivity
than the samples that are being measured, generally two
orders of magnitude. The copper wire essentially provides a thermal short across its small diameter.
The LabViewâ program controls a Lakeshoreâ 340
temperature controller which allows stabilization of
temperature to 50 mK. In fact, the program requires
that the base temperature remain within 50 mK before
data is acquired. Once the temperature is stable, a small
power or current (depending on the temperature) is independently input into each strain gauge, 120 X resistors, by two Kepcoâ power supplies. The heat is input
into the sample until the heat ﬂow is uniform and stable,
typically 2–3 min. The power and DT are recorded. The
current through the heater is slightly increased, the
temperature diﬀerence allowed to equilibrate, and then
the power and DT are recorded using a Keithley 2001
multimeter. This sequence is repeated several times, resulting in a power verses DT sweep at a given temperature. This power sweep is then ﬁt to a straight line, the
slope being proportional to the thermal conductivity.
This measurement is repeated at desired increments of
temperature from 10 to 300 K. Both samples have independent power supplies attached to their respective
heaters. A typical measurement sequence for the entire
temperature range will take 24–48 h to run two samples
on this apparatus.
6. Reproducibility and accuracy of data
Data is taken in the thermal conductivity system while
the apparatus is warming from 10 to 300 K. It is much
easier to thermally stabilize the experiment in the
warming mode than the cooling mode of the closed cycle
refrigerator. Representative data can be seen in Fig. 4.
A.L. Pope et al. / Cryogenics 41 (2001) 725–731
(a)
729
determined, being the diﬀerence between kT and
kE ðkL ¼ kT kE ). The lattice contribution is usually
observed to have a very characteristic shape, in this case
the curve goes as 1=T from 80 to 150 K. Above 150 K,
the curve deviates from this ﬁt. When performing thermal conductivity measurements the sample temperature
is given by ðT þ DT Þ and upon doing a Taylor expansion
4
4
of ½ðTSAM Þ ðTSURR Þ the radiation loss to ﬁrst order is
found to be proportional to T 3 DT . Consequently, the
radiation loss is proportional to T 3 as a function of
overall temperature. If a curve of the measured lattice
thermal conductivity kL is plotted in conjunction with
the extrapolated lattice ðkLC ¼ Að1=T Þ, where A ¼ constant) and the diﬀerence between the two is called D
(where D ¼ kL kLC ), it is observed that near room
temperature the diﬀerence in the calculated and assumed
lattice thermal conductivity is on the order of 1 W/m K
(Fig. 4(b)). The diﬀerence, D, is assumed to be due to
radiation loss proportional to T 3 . If D is plotted verses
T 3 , since there is a temperature dependence of the
thermal conductivity, it is seen (see inset in Fig. 4(b))
that the relationship is linear, indicating that the diﬀerence is indeed due to radiative losses. The total thermal
conductivity corrected for radiative losses can be determined by adding the calculated electronic thermal
conductivity and the corrected lattice thermal conductivity together. Using this iterative process, corrections
for radiative losses can be achieved.
The true test of any measurement technique’s viability
comes through the accuracy and reproducibility of the
measured data. In Fig. 5, thermal conductivity from
NIST 1461 standard stainless steel is shown with the
corresponding data taken in the system described above.
(b)
Fig. 4. (a) Total measured thermal conductivity with electronic and
lattice contributions shown. The electronic thermal conductivity ðkE )
can be extracted using the Wiedemann–Franz Law. (b) Lattice thermal
conductivity ðkL ) is extracted and subtracted from the total thermal
conductivity ðkTOT Þ. A radiation term ðDÞ can then be determined as
described in the text.
One of the drawbacks to using a standard steady-state
method is that above 150 K radiation loss can become
a serious problem. For larger samples (1–2 sq in.), the
radiation eﬀects are typically negligible below 150 K.
These large samples are usually very diﬃcult to obtain in
research grade samples. Thus, in order to correct for
radiation eﬀects in our smaller samples the following
procedure is employed. Once the thermal conductivity
(kT ) is measured, the Wiedemann–Franz law
ðkE ¼ L0 rT ; where L0 is the Lorentz number, r is the
electrical conductivity and T is the temperature) is used
to extract the electronic contribution (kE ) to the thermal
conductivity. From this the lattice contribution (kL ) is
Fig. 5. Thermal conductivity of stainless steel as measured in the
closed cycle refrigerator with no corrections compared to NIST 1461
Stainless Steel standard data for stainless steel.
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A.L. Pope et al. / Cryogenics 41 (2001) 725–731
With corrections made for radiative loss and conduction
along the wires we conclude that our data is accurate to
within 6% of the NIST data. However, the temperature
dependence is identical. Much of the diﬀerence in magnitude is due to uncertainty in the measurement of the
sample dimensions as well as conductive and convective
losses, which may be estimated and corrected for. Low
thermal conductivity samples will give oﬀ a smaller
signal, so care must be taken to get a very low noise level
from the thermocouples.
The thermal conductivity measurement is found to be
very accurate, with essentially the same temperature
dependence and magnitude of the stainless steel standard. However, precision and reproducibility of the
measurement are also very important. In order to check
these issues, four AlCuFe quasicrystalline samples were
cut from the same boule. These samples were all
mounted for thermal conductivity measurements, dimensions were ascertained, and thermal conductivity
recorded. In Fig. 6(a), thermal conductivity of the four
samples is shown. The data are all within 10% of one
another. This variability is probably due to dimensional
uncertainties as well as possible slight variation in
sample composition between the samples measured. If
the data are normalized (Fig. 6(b)), it is seen that the
curves lie on top of one another. The slight deviation at
higher temperatures is most likely due to diﬀerences in
sample size leading to diﬀerent amounts of radiation
contributions. This data shows that our system has very
good precision and reproducibility. In addition, our
quasicrystalline data show an excellent agreement with
the values in the literature [6].
7. Conclusions
(a)
(b)
In conclusion, a custom designed measurement system in which thermal conductivity can be measured
accurately and precisely using a dismountable mounting
system has been developed. This system utilizes an absolute thermal conductivity technique, but has the advantage that two samples are mounted on a puck that is
easily introduced into a closed cycle refrigerator. This
system oﬀers enhanced throughput of samples and ease
of mounting. One added advantage to this system is its
versatility in the type of measurement to be executed on
the dismountable puck. For example, a system has also
been developed to measure thermal conductivity of very
thin ﬁbers (A 0:0001 to 0:01 mm2 ) using a modiﬁcation of this design and incorporating with an extensive
data acquisition program [7]. This parallel thermal
conductivity (PTC) technique measures a background
thermal conductance of the wire heaters and platform
and then the sample is placed in parallel with the
background and measured again. By subtracting the
background the thermal conductance of the sample may
be determined.
Acknowledgements
Fig. 6. Thermal conductivity of four AlCuFe samples cut from the
same boule and measured in the dismountable puck system. (a) As
measured data and are the same to within 10% or roughly the error in
measuring the dimensions of the sample. (b) Normalized data are
shown to behave the same with a slight variation at higher temperature
due to radiation from the sample.
We acknowledge Matt Marone for his work on the
ﬁrst generation of this thermal conductivity system.
Michael Kaeser measured thermal conductivity data for
Fig. 4 in this paper. Thanks are due to Roy Littleton IV
for his help in modifying the experimental setup for
better temperature control. We would like to thank Ian
Fisher, Paul Canﬁeld, and Cynthia Jenks at Ames National Lab for providing us with the AlCuFe samples
presented in this paper. A special thanks to Ctirad Uher
for useful ideas and discussion on mounting samples for
thermal conductivity measurements. We would also like
A.L. Pope et al. / Cryogenics 41 (2001) 725–731
to thank Quantum Design for providing the parts and
support necessary to design this system. We acknowledge
support from ONR, ARO, DARPA (ONR No. N0001498-0271, ONR/DARPA No. N00014-98-0444, and
ARO/DARPA No. DAAG55-97-0-0267) and from research funds provided (TMT) from Clemson University.
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