i ncRMOELECTRIC REFRIGERATION FOR

TEMPERATURES BELOW 100 K:

A STUDY OF TITANIUM SESQUIOXIDE

R. Radebaugh

D. Linenberger

E. Spellicy

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

May 1982

k QC

lUU

. U56

c2-1665

1982

NATIONAL BUREAtf OF STANDARDS

LIBRARY NBSIR 82-1665 H -3. ?

NASA CR-1 66343

THERMOELECTRIC REFRIGERATION FOR

TEMPERATURES BELOW 100 K:

A STUDY OF TITANIUM SESQUIOXIDE

R. Radebaugh

D. Linenberger

E. Spellicy

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

May 1982

Prepared for: National Aeronautics and Space Administration

Washington, DC 20546

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

1, Report No. NBSIR 82-1665 2. Government Accession No. NASA CR- 166343

3. Recipient's Catalog No.

4. Title and Subtitle Thermoelectric Refrigeration for Temperatures Below

100 K: A Study of Titanium Sesquioxide

5. Report Date May 1982

6. Performing Organization Code

7. Author(s) Ray Radebaugh, Del Linenberger, Elizabeth Spellicy8. Performing Organization Report No.

10. Work Unit No.

9. Performing Organization Name and Address National Bureau of Standards

325 Broadway

Boulder, CO 80303

11. Contract or Grant No. P.O. No. A-63249B fDDAl

13. Type of Report and Period Covered Contractor Report 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration

Washington, DC 20546

14. Sponsoring Agency Code

15. Supplementary Notes Technical Monitor: Peter Kittel, Mail Stop 244-7, NASA Ames Research Center,

Moffett Field, CA 94035 (415) 965-6525 or FTS 448-6525

16. AbstractPrevious measurements of the specific heat of V-doped Ti 203 at low

temperatures could be explained by a model which also suggested the material

would have a high thermoelectric figure-of-merit . This paper describes the

sample preparation, experimental apparatus, and the results of measurements

on the thermal conductivity, thermoelectric power, and electrical resistivity

of a single crystal T^Og - 4% V sample. The results are used to derive the

thermoelectric figure-of-merit between 5 and 300 K. The figure-of-merit is

much smaller than expected and of little practical value because of the very

high phonon thermal conductivity.

17. Key Words (Suggested by Author(s)

)

Cryogenics; figure-of-merit; refrigeration; resistivity; thermal conductivity; thermoelectric power; T^O^

vanadium

18. Distribution Statement

Unclassified - Unlimited

SUBJECT Category - 37

19. Security Classif. (of this report) Unclassified

20. Security Classif. (of this page) Unclassified

21. No. of Pages 13

22. Price*

‘For sale by the National Technical Information Service, Springfield, Virginia 22161
1

"

'

' :V

’

.
THERMOELECTRIC REFRIGERATION FOR TEMPERATURES BELOW 100 K: A STUDY OF TITANIUM SESQU IOX IDE

R. Radebaugh, D. Linenberger, and E. Spell icy

Thermophysical Properties Division

National Bureau of Standards

Boulder, Colorado

Previous measurements of the specific heat of V-doped Ti^Og at low temperatures could

be explained by a model which also suggested the material would have a high thermoelectric

f i gure-of-merit . This paper describes the sample preparation, experimental apparatus, and

the results of measurements on the thermal conductivity, thermoelectric power, and electrical resistivity of a single crystal T

i

2 03

- 4% V sample. The results are used to derive the

thermoelectric figure-of-merit between 5 and 300 K. The figure-of-merit is much smaller

than expected and of little practical value because of the very high phonon thermal conductivity.

Key words: cryogenics; figure-of-merit; refrigeration; resistivity; thermal conductivity;

thermoelectric power; T

i

2 O 3 ; vanadium.

1. INTRODUCTION

Thermoelectric refri geration of small devices has the advantage of extreme reliability which

cannot be matched by any other refri geration technique. Thermoelectric coolers have demonstrated a MTBF (mean time between failure) in excess of 300,000 hours which is equivalent to 35 years of continuous operation. For temperatures considerably below room temperature thermoelectric devices achieve a coefficient of performance (COP) of only 1-2% but this low efficiency is of little concern for cooling

of small devices where the total power input may be only 50 W. Presently the lowest temperature

achieved with a multiple stage thermoel ectric cooler is about 134 K [1,2]. Click and Marlow [3]

reached 145 K in a similar refri gerator . In each stage the maximum temperature drop is given by [4]

( T

h

- V/T

c

= 1/2 ZT

c’ W

where T^ is the hot temperature, Tc is the cold temperature, and Z is the thermoelectric figure-ofmerit. For a single material Z is given by

Z = a

2 /k P , (2)

where a is the thermoelectric power, or Seebeck coefficient, k is the thermal conductivity, and p is the electrical resistivity. In an actual refrigerator the figure of merit for a junction of material

1 and 2 is

1
Z

1 2 (al - cc (2a)2

) 2 /[(k

1 pI ) 1/2

+ (k 2

p

2

) 1/2

] 2

.

The largest values of Z 12 occur when and «2 are large and of opposite sign. Thus in practical

refrigerators the junctions are made with an n-type material (negative a) and a p-type material (positive a).

Figure 1 shows the highest reported values of Z as a function of temperature for several thermoelectric materials. Shown for comparison is a curve for ZT = 1. Temperature drops for each stage

according to eq (1) become quite small for ZT much less than 1. For refrigeration just below room temperature the Bi^Teg alloys are used in both the n and p legs of the couple. Values of Z for these

two Bi^Teg alloys are from the work of Yim et al . [5] and Yim and Rosi [6]. The n-type Bi2Te3 alloy

is ( Bi2Te3) 9o(Sb2Te3) 5(Sb2Se3) 5 doped with Sb 1 3 to give a carrier concentration of 3.6 x 10 -19 cm“^ at room temperature. The p-type material is (Sb2Te3)72(Bi2Te3)25(Sb2Se3)3 doped with excess Te to give a carrier concentration of 2.1 x 10 - 1 9 cm~3 at room temperature. The Z value for these B^Tej alloys is reasonably high at room temperature but it falls off rapidly at low temperatures, especially that of

the p-type material. By changing the doping levels Click and Marlow [3] were able to increase the Z value of the p-type B^Teg alloy at low temperatures as shown in figure 1. This is the highest

reported Z value for a p-type material below 220 K. For n-type materials figure 1 shows that the low

temperature Z values are much higher. The data for undoped B

i 3

5 Sb ^ 5 and B^Sbpj are from the work of

Yim and Anith [7] and is the highest reported Z value for any material. Wolfe and Smith [8] first

showed that the application of a transverse magnetic field can enhance Z significantly in Bi-Sb

alloys. Yim and Amith [7] applied a transverse field of IT to their B

i 3

5 Sb ^ 5 sample and obtained the

results shown in figure 1. Higher fields will not increase the peak value but they can increase the

higher temperature Z values. Figure 1 shows that at intermediate temperatures the Bi 92 Sb 3 alloy doped

with 1 x 1018 cn -3 0 f sn gives the best Z values [3]. Low-temperature thermoelectric refrigeration is severely hampered by the lack of a good p-type material below 200 K. The purpose of this program was to investigate the thermoel ectric fi gure-of-merit for a p-type material which showed potential for a

2. NEW MATERIALS

The electronic part of the Seebeck coefficient is simply proportional to the electron molar

entropy S and is given by

where R is the gas constant. For ideal electrons S/R = 2.9 at the Fermi temperature Tp and it is linear in T somewhat below Tp. The entropy can be determined from specific heat measurements

through the relation

high Z.

a = (8.6 x 10" 5 V/K) S/R, (3)

(4)

0

where C is the specific heat and T‘ is the temperature. Thus, a material with a high electron or hole

entropy would be a good candidate material if the carrier concentration is relatively high to give a 2
12

10

8

co

i O 6

N

IT Magnetic Field

n-type material

p-type material

^* 85^15

^* 92^8

— Sn-doped Bi QO Sb

Low

Temperature Bi Te

3 Alloy

-type Bi 2Te3 Alloy

jp-type Bi 3Te2 Alloy

0 100 200 300

T, K

Figure 1. Thermoel ectric figure-of-merit , Z, as a function of temperature for

several high Z materials. Exact compositions are discussed in the text.

low resistivity. Pure metals have such high Tp (%6 x 10^ K) that the electron entropy is very small

below room temperature. Pure bismuth has a Tp of about 5 K [4], but the carrier concentration is only

3 x 1017 cm

-3

#

Sjostrand and Keesom [9] measured the low temperature specific heat of vanadium doped titanium

sesquioxide, Ti^Og, and found an anomalously large specific heat and entropy. They could explain

their data by using an electron gas model with a Fermi temperature of about 5 K for the sample with 4%

V doping. The carrier concentration is about 10^0 cm~3, which is much higher than that of bismuth.

These results then prompted the proposal which led to this work. Dumas et al . [10], however, have

suggested that the high specific heat is mainly due to a spin glass behavior of a magnetic moment on the vanadium impurity. If that explanation is correct the figure-of-merit would not be high unless

the carriers can interact with the spins in such a way to sample their entropy.

Previous measurements on the thermoel ectric power of V-doped T

i

2 0 3 by Shim et al . [11] only

extend down to about 55 K. For 4% V their results show a nearly constant value of about +50 yV/K; for

a 2% V sample they find +100 yV/K. The positive value indicates the material is p-type. Resistivity

measurements [12] on a different sample of T

i

2O 3 + 4% V 2 O 3 give a value of about 5 x 10"^ n cm below

100 K. No measurements of thermal conductivity have been made to date. Using the Wi edemann-Franz law

for the thermal conductivity would give a figure-of-merit

3
( 5 )

where the Lorenz ratio L 0

= 2.44 x 10

" 8

V

2

/

K

2

. For a = 1 00 yV/K, ZT = 0.40. Lower V concentrations

increases a significantly but the phonon contribution to the thermal conductivity could dominate at low V concentrations and prevent any increase in Z.

A single crystal of T

i

2 O 3

- 4% V 2 O 3 was received from Prof. Keeson of Purdue University. This

sample was not the sane as the one on which they measured the specific heat. X-ray pictures were taken here to orient the sample since there could be some orientational dependence in the figure-ofmerit. A diamond saw was used to cut the sample to be measured. The sample size was about 1.5 mm x 2.0 mm x 10 mm with the long dimension along the a axis of the crystal . The crystal type for T

i

2 0 3

is rhombehedral [13] with a = 5.433 A and f = 56°34'.

3. EXPERIMENTAL APPARATUS

The figure-of-merit is determined from measurements of a, k, and p in eq (2). Figure 2 shows a schematic of the apparatus built to measure these three quantities simultaneously. Not shown in this

figure are the current and voltage leads to the sample. The voltage leads are placed at the same points along the sample as are the sample thermometers , except they are on the adjacent face. The

carbon thermometers are 220 ,Q, 1/8 U resistors which have been ground flat on one side. These resistors are then varnished to a small copper clamp with cigarette paper providing electrical insulation

between resistor and clamp. These clamps also have the junctions of a differential thermocouple

mounted on them with varnish. The clamp closest to the reservoir also has another thermocouple junction to measure the temperature difference between that junction and one in the liquid cryogen bath

outside the vacuum can. The thermocouples used are Au-0.07at% Fe versus KP [14]. The carbon thermometers are used for temperatures from 4 K up to about 50 K and the thermocouples are used from 50 K up to 300 K. The carbon thermometers were calibrated against a germanium thermometer that was mounted on the bottom of the reservoir. The R vs. T characteri Stic of the carbon thermometers were then fit to a power series of the form

The best fit was obtained when the curve was divided into two parts: one part below 20 K and the

other part above 20 K. Usually four terms were sufficient for a good fit.

He used silver paint to attach the voltage and current leads to the sample. The very small size

of the sample made it difficult to work with and the accuracy of the thermometer and voltage tap spacing was probably no better than ± 10%.

The procedure for making the measurements was to first fill the reservoir with liquid helium from

the outside bath. With no heat applied to the sample heater, the resistances of the carbon and ger- manium thermometers were measured using a commercial AC potentiometer. Next a small AC current was passed through the sample and the voltage drop between the potential leads was determined with a lockin amplifier. The lock-in amplifier was also used to measure the voltage drop across a 0.1 standard

4

N log T = X a. (log R)

i =0

( 6 )
To Pump

or Vent

Figure 2. Schematic diagram of the apparatus used for simultaneous measurements

of thermal conductivity, thermoelectric power, and electrical resistivity. Liquid heliun or liquid nitrogen surrounds the vacuum can.

The temperature of the reservoir volume is regulated by the needle

valve and a commercial temperature controller supplying current to the

reservoir heater.

resistor in series with the sample to give the current passed through the sample. These readings then

gave the resistivity of the sample. The next step was to apply a known current to the sample heater

and record the thermometer readings to derive the temperature gradient in the sample. The thermal

conductivity is then obtained from

k = QL/A-aT, ( 7 )

where Q is the heat flow through the sample, L is the length between the two thermometers , and A is the cross-sectional area of the sample. Usually the aT was about 5-10% of the absolute temperature.

5
At the sane tine that the thernoneters were being read, the voltage between the potential taps was neasured with a sensitive digital voltneter to give the thernoelectric power of the sanple according

to the equation

a = aV/aT. (8)

The sanple heater was then turned off and power applied to the reservoir heater to bring it up to the next higher tenperature. For tenperatures above 4 K, there was no liquid He in the reservoir. A temperature controller was used to maintain a constant reservoir tenperature while measurements were

being made. For best temperature control, it was found necessary to open the needle valve slightly to provide some cooling power for the reservoir. The use of a needle valve is much more economical with

liquid He than is a cryostat which has a semi -weak thermal link between the reservoir and the sur- rounding liquid helium bath. At higher temperatures (-v-50 K) the sensitivity of the thermocouples

became high enough to use them as the thermometers instead of the carbon resistors. For temperatures

above 77 K, the liquid He in the outside bath was replaced with liquid Ng.

4. RESULTS AND DISCUSSION

Figure 3 shows the resistivity of the T

i

2

O 3

- 4% V sample as a function of temperature. The curve is about 30% lower than that published by Van Zandt and Eklund [12], also for a T

i

2 O 3 sample

doped with 4% V. The shape of the two curves are very much the same. The difference between their

curve and ours is most likely due to small differences in V doping. The uncertainty of our curve is about ± 10%.

Figure 4 shows the thermoel ectric power of the sample as a function of temperature. For temperatures above about 100 K, a is independent of temperature and equal to about 60 pV/K. This value is

consistent with the measurements of Shin et al . [11] who measured a above 54 K for T

i

2 0 3 doped with

various amounts of V. Below about 50 K we find that a drops off nearly linearly with temperature.

The uncertainty in a is about ±10% except in the region between about 15 and 40 K where difficulty in measuring a small temperature gradient gave rise to considerable scatter in the data as seen in figure

4. The thermal conductivity was very high in this region, which made it difficult to maintain a rea- sonable temperature gradient.

The thermal conductivity of the sample is shown in figure 5. The peak observed around 25 K was quite surprising, since we thought that with 4% V doping phonon scattering would be sufficiently high to eliminate a high peak. Previous measurements on T i 0^ (rutile) [15] showed that its peak in thermal

conductivity was essentially eliminated just with a hydrogen reduction, as shown by the dashed curve

in figure 5. Even the oxidized samples of Ti

O

2 showed a lower intrinsic thermal conductivity than our sample of T

i

2 O 3

- 4% V for temperatures above about 50 K. Also shown in figure 5 is the thermal

conductivity of p-type B^Teg [5]. Uncertainty of the thermal conductivity is about ±10%, except near the peak wh ere the imprecision is about ± 20% because of the difficulty in maintaining a sufficiently

large aT with adequate temperature control.

The thermoel ectric fi gure-of-merit for the T

i

2 O 3

- 4% V sample was calculated from the p, k, and

a curves by using eq (2). This fi gure-of-merit is shown as a function of temperature in figure 6 .

6
TEMPERATURE, K

Figure 3. The electrical resistivity of T i 2^3 ~ 4% V as a function of

temperature for current along the a axis of the crystal

.

Shown for comparison are experimental curves for a p-type BigTeg alloy [5] and for the Kondo systems

[16] CePdg and Celng. We had expected that Z of the TigOg with V doping would be higher than that of

BigTeg below about 100 K. Unfortunately the very high phonon thermal conductivity greatly reduces the

f igure-of-merit for T i 2^3 - If we were to neglect the phonon contribution to the thermal conductivity,

we would then expect the IJiedemann-Franz law to be a good approximation and the figure-of-merit to be given by eq (5). The dashed curve in figure 6 for TigOg - 4% V then gives the value expected for Z from the IJiedemann-Franz law, which represent approximately the maximum we could expect from the material .

I

7
Figure 4. The thermoel ectri c power, or Seebeck coefficient, as a function of

temperature for a T i 2^3 " 4% V sample. The dashed line shows a curve proportional to temperature.

From the work of Shin et al . [11], we know that lower V doping gives a higher a. For V concen- trations in the range of about 1-5%, it appears that a is inversely proportional to the V concentration. Thus, according to eq (5) we would expect the fi gure-of-merit to increase inversely with the

square of the V concentration. Figure 6 shows the expected Z for a sample with 2% V doping and with

the phonon contribution to the thermal conductivity neglected. The behavior of this curve below 50 K is somewhat uncertain since we do not know the concentration dependence of a below 50 K. We did not measure a below 50 K for a 2% V sample since we did not expect that the actual Z would change much.

For lower V concentrations, p would increase rapidly, but because the thermal conductivity is dominated by phonon conductivity, it would also increase somewhat instead of decrease.

We see from the curves of figure 6 that a T i 2^3 " 2% V sample could have a much larger figure-ofmerit than p-type Bi^Teg below 200 K if some means of greatly decreasing the phonon conductivity could

be found that does not affect the carrier conductivity. We had hoped that even 2% V would have been

sufficient to greatly reduce the phonon contribution, but for some reason V is not a very effective

phonon scatterer in Ti^Og.

8
Figure 5. The thermal conductivity of T i 2^3 " 4% V as a function of temperature

Shown for comparison are curves for oxidized and hydrogen reduced TiOp

(rutile), as well as p-type BipTeg.

It is of some interest to compare a with that expected from eq (3). The specific heat measurements of Sjostrand and Keesom [9] give S/R ^0.27 T for the carriers in a 3.9% V sample of T

i

2 0 3 at temperatures below about 2 K. Substituting this value into eq (3) gives an expected thermoelectri

c

power of a = 23 T pV/K. Experi mental 1 y we find that a «1.3 T pV/K. Thus, according to this comparison, it would seem that the high specific heat of the V-doped T

i

2 0 3 is not due to free carriers as had

been originally proposed [9]. The spin glass behavior suggested by Dumas et al . [10] would be consistent with the observed behavior of a below 50 K.

Since it is known that transverse magnetic fields can enhance the figure-of-merit in some material s [7], measurements of p, a, and k were made at 77 K in a transverse field of 1.2 T. There was no detectable change in any of these quantities with the field applied.

9
Figure 6 . The therrnoel ectri c fi gure-of -merit for T

i

2 0 3

" 4% V as a function of

temperature. The dashed curves give the fi gure-of-rnerit if the phonon

conductivity were neglected. The p-type B^Teg has the highest known

fi gure-of-rnerit for any p-type material. The other curves are disdiscussed in the text.

5. CONCLUSIONS

We conclude that contrary to initial expectations, based on the high specific heat, the thermoelectric fi gure-of-merit of V doped T

i

2 0 3 is not sufficiently high to be of any practical value. Even for the optimum V concentration we do not expect the figure-of-meri t to be as high as p-type BigTeg.

The fi gure-of-merit for V doped TigOg could be greatly enhanced, and even exceed that of p-type

B

i

2 T

e

3 , if some means could be found to greatly reduce the high phonon thermal conductivity without

decreasing the carrier conductivity.

10
6 . REFERENCES

[ 1 ]

[ 2 ]

[3]

[4]

[5]

[ 6 ]

[7]

18 ]

[9]

[ 10 ]

[ 11 ]

[ 12 ]

[13]

[14]

[15]

[16]

R. J. Bui st, J. W. Fenton, and D. Tuomi , "Low Temperature Cooler for 145 K Operation," U.S. Army

Night Vision Laboratories , Fort Belvoir, V A, Technical Report AD888757L (1971) (Borg-Warner Thermoel ectrics)

.

R. J. Buist, J. Fenton, G. Lichniak, and P. Norton, "Low Temperature Thermoel ectric Cooler for

145 K Detector Array Package," U.S. Army Night Vision Laboratories , Fort Belvoir, V A, Technical

Report ADB008934 (1976) (Borg-Warner Thermoel ectrics )

.

P. B. Click, Jr., and R. Marlow, "Low Temperature Thermoelectric Cooler for Operation at 145 K,"

U.S. Army Night Vision Laboratories , Fort Belvoir, V A, Technical Report AD875928 (1970) (Nuclear

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R. Wolfe and G. E. Smith, Appl . Phys. Lett. 5 (1962).

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J. Dumas, C. Schlenker, J. L. Tholence, and R. Tournier, Solid State Commun. J_7, 121 5 (1975).

S. H. Shin, G. V. Chandrashekhar , R. E. Loehman, and J. M. Honig, Phys. Rev. B 8., 1364 (1973).

L. L. Van Zandt and P. C. Eklund, Phys. Rev. B 7, 1454 (1973).

W. B. Pearson, Handbook of Lattice Spacings and Structures of Metals , Vol . 2, Pergamon Press,

Oxford (1967).

L. L.

W. R.

R. J.

Sparks and R.

Thurber and A.

Gambino, W. D.

L. Powel 1 , J

.

J. H. Mante,

Grobman, and

Res. Nat. Bur. Stand., 76A, 263 (1972).

Phys. Rev. A 139, 1655 ( 1965).

A. M. Joxen , Appl. Phys. Lett. 22 , 506 (1973).

1 1

GPO 836-069