APPLIED PHYSICS LETTERS
VOLUME 77, NUMBER 15
9 OCTOBER 2000
Investigation of the thermal conductivity of the mixed pentatellurides Hf1À x Zrx Te5 B. M. Zawilski, R. T. Littleton IV, and Terry M. Tritta) Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634
共Received 3 July 2000; accepted for publication 10 August 2000兲 Transition-metal pentatellurides (HfTe5 and ZrTe5 ) exhibit a promising power factor 共electronic properties兲 for possible use as a thermoelectric material. For complete characterization of these crystals, thermal conductivity measurements are necessary. In this letter, we report measurements of the thermal conductivity for this group of materials using the parallel thermal conductance technique which is well adapted for needle-like samples. Thermal conductivity is presented as a function of temperature and composition of the pentatelluride solid solution Hfx Zr1⫺x Te5 with 0⭐x⭐1 in which the magnitude of the room temperature thermal conductivity varies from 5 to 8 W/共m K兲. Dependence on the cross-sectional area and possible size effects 共or sample quality兲 is also presented and discussed. These results also indicate the importance of sample quality on the low-temperature thermal conductance maximum max . © 2000 American Institute of Physics. 关S0003-6951共00兲00941-4兴
which the temperature difference, ⌬T is determined. These standard steady state techniques are regularly used for many materials but are not compatible with samples of these dimensions. For this reason we have developed a different technique12 called parallel thermal conductance 共PTC兲, which is well suited for the measurement of the thermal conductance of ribbon-like samples such as pentatellurides, carbon fibers, or other needle-like low-dimensional materials. As with any method, accurate determinations of the sample dimensions are required in order to accurately determine the thermal conductivity. In order to enhance or optimize the figure of merit, one must either maximize the power factor or minimize the thermal conductivity. Because of the difference in the specific masses between Hf 共91 amu兲 and Zr 共178 amu兲, doped crystals of the pentatellurides, Hfx Zr1⫺x Te5 , may exhibit lower thermal conductivity due to enhanced phonon scattering 共alloy or mass fluctuation scattering兲. In this letter we present thermal conductivity measurements of pentatellurides, both the parent compounds (HfTe5 and ZrTe5 ) and the intermediate materials, Hfx Zr1⫺x Te5 . A brief description of the PTC technique will also be presented. Possible influences of either the composition, sample quality or sample size will be discussed. Pentatelluride samples were prepared via an iodine transport method similar to previously reported techniques.13 The composition of the samples were checked by electron probe microanalysis 共EPM兲, that confirmed relatively good agreement with the nominal composition, which is determined by mixture proportions used in the growth process. We performed EPM measurements on a whole series of samples and found that typically the measured concentration was somewhat less than expected nominal composition.14 After cleavage, typical sample sizes are approximately 0.1 ⫻0.05⫻3.0 mm3. The dimensions of the sample were determined either using an optical stereo zoom microscope 共up to 70⫻ magnification兲 or in a metallurgical microscope 共up to 500⫻ magnification兲. The samples have somewhat irregular
Transition-metal pentatellurides of the orthorhombic1 polytype2 structure ZrTe5 and HfTe5 exhibit large resistivity anomalies at T⬇150 K3 and T⬇80 K,4 respectively. Associated anomalies in these materials are observed in other properties such as the Seebeck coefficient5 and the Hall coefficient.6 By analogy with similar resistive behavior in NbSe3 , a phase transition was suggested7 as an onset of a charge density wave transition.3,8 However, properties such as heat capacity were not observed to be singular9 which excludes a classical phase transition. Subsequently, a charge density wave or spin density wave transition was finally rejected leaving the origin of the resistive anomaly undetermined. Other attempts were made in order to explain the origin of the anomalies in the resistivity and thermopower in these pentatellurides,10 however, to date no conclusive theory exists. The potential of a thermoelectric material is evaluated by the dimensionless thermoelectric figure of merit: ␣ 2 T/ T , where ␣ is the Seebeck coefficient, T is the absolute temperature, is the resistivity, and T is the total thermal conductivity. Primarily due to a high power factor, given by ␣ 2 T/ , the pentatellurides have been suggested for potential thermoelectric applications.11 The power factor of the doped pentatellurides is larger than that of the current state-of-theart material, alloys of Bi2Te3 , over a broad range of temperature, but especially in the range, 150–250 K. However, to evaluate the potential of these materials for thermoelectric applications, thermal conductivity () measurements are necessary. These materials grow as single crystals with typical dimensions of 0.1⫻0.05⫻3.0 mm3, which does not allow for the possibility of using the more typical thermal conductivity measurement methods where Power 共P兲 vs ⌬T sweeps are performed at fixed base temperatures. The thermal conductivity is determined via the relationship P⫽(A/L)⌬T, where L is the length between thermocouple leads between a兲
Author to whom correspondence should be addressed; electronic mail:
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© 2000 American Institute of Physics
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Appl. Phys. Lett., Vol. 77, No. 15, 9 October 2000
FIG. 1. Thermal conductivity of Hfx Zr1⫺x Te5 for several values of the concentration, x, as a function of temperature. The following designation is used: 䊊 (x⫽0), 䉲 (x⫽0.05), 䊐 (x⫽0.25), 〫 (x⫽0.75), and 䉱 (x ⫽1). The inset shows the high temperature exponent, n(⬃1/T n ), as a function of the inverse of the thermal conductivity peak, 1/ max , for all pentatelluride samples that were measured 共regardless of composition兲.
surfaces and the data must be averaged to estimate the cross sectional area. Uncertainty in measuring the sample dimensions leads to approximately 15%–20% uncertainty in the absolute value of the thermal conductivity. Accurate determination of sample dimensions is often an issue but is independent of the specific measurement technique used for the thermal conductivity. Thermal conductance measurements were performed in a commercial closed cycle cryocooler under automatic computer control and utilizing the PTC technique, which is described elsewhere.12 Briefly, the PTC technique consists of a preliminary measurement of the sample stage thermal conductance, which provides a base line. The total thermal conductance of the sample with the sample stage is then measured. By subtraction of the base line, the thermal conductance of the sample is then obtained. This technique was tested on several well-characterized materials including small Bi2Te3 type crystals and carbon fibers, demonstrating very good agreement with previous data. The PTC system provides an effective method for determining the thermal conductivity of most needle-like materials. Such samples are physically incapable of supporting a heater or thermocouples not to mention difficulties in determining heat losses and radiation effects. These effects, not associated with the sample, are accounted for utilizing the base line measurement with the PTC method. With a temperature gradient imposed on the sample, then to first order in ⌬T, radiation losses are proportional to T 3 , 共i.e., T 3 ⌬T). With the PTC technique the mean hot surface 共most important to radiation兲 is the heater and most of these associated radiation losses are included in the measurement of the base line. This is discussed in more detail in Ref. 12. The thermal conductivity of the pentatellurides, Hfx Zr1⫺x Te5 with 0⭐x⭐1, have been measured for several samples which are roughly of the same dimensions. This will allow the data to be averaged and better accuracy to be obtained. Figure 1 shows the thermal conductivity as a function
Zawilski, Littleton IV, and Tritt
of temperature for Hfx Zr1⫺x Te5 and its typical evolution with various nominal concentrations 共x兲 of Hf for Zr. In relation to the values at around room temperature, it can be seen that the parent ZrTe5 yields the highest thermal conductivity, as expected by the smaller mass of the Zr atoms. The substitution of Hf for Zr lowers the thermal conductivity with the parent HfTe5 being approximately a factor of 2 lower than that of ZrTe5 . The values for the mixed or doped pentatellurides, Hfx Zr1⫺x Te5 , lie roughly between these two curves. The temperature dependence appears to be that of a crystalline material, where roughly a 1/T temperature dependence is observed at higher temperatures. Also, a large peak is apparent at lower temperatures due to the depletion of umklapp phonon scattering and then at the lowest temperatures the thermal conductivity decreases rapidly with decreasing temperatures.15 There does appear to be a slight radiation tail at T⭓250 K in some of the samples and this effect is currently under investigation. This is not unexpected given the size of these samples. At lower temperatures, one of the main features of the addition of Hf is the lowering of the low-temperature peak with a minimum magnitude occurring at a nominal concentration x⬇0.25, likely due to alloy scattering. The values at or around room temperature are relatively close to each other. It is difficult to ascertain if there are real differences due to uncertainty in sample dimensions, except for the (ZrTe5 ) where the thermal conductivity is substantially larger, but as expected. These results show that the room temperature phonon scattering by umklapp process is most important and scattering due to mass fluctuation of the transition-metal atoms is less important. At lower temperatures, T⬍50 K, the magnitude of the lowtemperature peak depends on the lattice perfection as well as the lattice boundary scattering. According to this interpretation, it is natural to decrease the low temperature peak by introducing some imperfections in the lattice and to preserve the room temperature thermal conductivity magnitude due to umklapp scattering. The key parameter, relative to the thermal conductivity of the pentatellurides, seems to be the crystal quality. If size and composition of the mixed samples only slightly affect the room temperature magnitude, the low-temperature peak shows a variation by more than a factor of 2. In some materials, which are very pure, this peak can be orders of magnitude larger than the room temperature values. Impurities, imperfections, and sample quality can greatly affect this peak and any degradation is a direct consequence of the limit imposed by the lattice scattering on the low-temperature thermal conduction. The most important difficulty is then to measure or acquire a gauge of the ‘‘perfection’’ of each sample. To attempt to do this we first have investigated the temperature dependence of the thermal conductivity at the higher temperatures where ⬃1/T n . Of course for a very good crystalline material or single crystal where phonon scattering processes dominate the thermal conductivity, then the exponent, n, should be equal to 1 (n⫽1). 15 As well, the low-temperature maximum or peak ( max) should in some way also reflect the sample quality due to impurities and imperfections. The inset in Fig. 1 shows the slope, n, defined by the high temperature behavior of the thermal conductivity: ⬃1/T n , versus the inverse of the low-temperature
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Appl. Phys. Lett., Vol. 77, No. 15, 9 October 2000
FIG. 2. Thermal conductivity of HfTe5 for several cross-area values 共given in inset兲 as a function of temperature. The following designation is used: 䊊 共sample A兲, ⽧ 共sample B兲, 䉮 共sample C兲, and 䉱 共sample D兲.
maximal thermal conductivity magnitude max . This data represents all the samples regardless of composition that we have measured. A relatively good fit may be given by a linear relation n⫽n 0 ⫺4/ max . If we assume an absolutely perfect crystal which would show an ‘‘infinite or very large’’ thermal conductivity then we can extrapolate 1/ max to 0 and find that n 0 ⫽0.86. Of course, from the classical model for a perfect crystalline material, n 0 ⫽1, so this gives us some concept of the crystalline quality of these materials, which is relatively good agreement given this crude analysis. There is no apparent evidence of any anomaly in the thermal transport which might correspond to the resistivity and the Seebeck anomalies that are reported in these materials.11 This point, as well as previous heat capacity measurements, confirms that the observed anomalies seemingly result from an electronic evolution rather than from a phase transition. Due to the reduced dimensions of the samples, size effects may also occur. For this reason several samples of the same composition but with different crosssectional area have been measured. Figure 2 shows the thermal conductivity as a function of temperature of several samples (HfTe5 ) with different cross sectional area as indicated in the figure. All these samples were of comparable length 共2.5–4 mm兲. As expected, the most important size effect is observed on the low-temperature peak magnitude, which decreases with increasing area. We can interpret it as evidence of enhanced sample quality with reduced cross area resulting from improved homogeneity of the sample. Variations of the magnitude of the room temperature thermal conductivity are relatively small remaining close to a mean value of approximately 6 W/m K. However, for thermoelectric applications, it is desired that the thermal conductivity be much smaller, ⬍2 W/m K. In this letter we present, direct thermal conductivity measurements of the transition-metal pentatellurides,
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Hfx Zr1⫺x Te5 . The variation in the characteristics of the thermal conductivity due to different cross-sectional area is also presented. Our measurements show the importance of the sample composition and quality 共purity as well as homogeneity兲 for the low-temperature maximum max , while a stable magnitude exists for the room temperature thermal conductivity, 300 K . In order to minimize the thermal conductivity for thermoelectric considerations, substitution共s兲 on the Te sites should also be studied, since doping on the Te sites typically have yielded higher power factors.11 Preliminary measurements on some Hfx Thx Te5 samples 共Th⫽232 amu兲 have shown a very low thermal conductivity 300 K ⬇2 W/m K giving even more promise in reducing the thermal conductivity. Further substitutions on both the metal site and the Te site 共induced defect兲 may yield lower thermal conductivity, which should compliment the high power factor for these materials and make their potential for thermoelectric applications even greater. Also, the ability to measure other crystals of many other materials of similar size may prove very important not only for thermoelectrics but in our general understanding of thermal conductivity and thermal transport in many of these comparable low-dimensional materials. The authors would like to acknowledge financial support from an ARO/DARPA 共Grant No. DAAG55-97-1-0267兲 for the research funds provided for this work. The authors would like to also acknowledge Dr. G. Mahan, for his encouragement to perform these very difficult measurements. The author also acknowledge collaborations with Dr. J. W. Kolis and Dr. D. R. Ketchum who provided the samples in this study. 1
S. Furuseth, L. Brattas, and A. Kjekshus, Acta Chem. Scand. 27, 2367 共1973兲. 2 T. Sambongi, K. Biljakovic, A. Smontara, and L. Guemas, Synth. Met. 10, 161 共1985兲. 3 S. Okada, T. Sambongi, and M. Ido, J. Phys. Soc. Jpn. 49, 839 共1980兲. 4 S. Okada, T. Sambongi, M. Ido, Y. Tazuke, R. Aoki, and O. Fujita, J. Phys. Soc. Jpn. 51, 460 共1982兲. 5 T. E. Jones, W. W. Fuller, T. J. Wieting, and F. Levy, Solid State Commun. 42, 793 共1982兲. 6 M. Izumi, K. Uchinokura, S. Harada, R. Yochizaki, and E. Matsuura, Solid State Commun. 42, 793 共1982兲. 7 F. J. DiSalvo, R. M. Fleming, and J. V. Waszczak, Phys. Rev. B 24, 2935 共1981兲. 8 M. Izumi, K. Uchinokura, and E. Matsuura, Solid State Commun. 37, 641 共1981兲. 9 R. Shavin, E. F. Westrum, Jr., H. Fjellvag, and A. Kjekshus, J. Solid State Chem. 81, 103 共1989兲. 10 M. Rubinstein, Phys. Rev. B 60, 1627 共1999兲. 11 R. T. Littleton IV, T. M. Tritt, J. W. Kolis, and D. R. Ketchum, Phys. Rev. B 60, 13453 共1999兲. 12 B. M. Zawilski, R. T. Littleton IV, and T. M. Tritt 共unpublished兲. 13 L. Brattas and A. Kjeskshus, Acta Chem. Scand. 25, 2783 共1971兲. 14 R. T. Littleton IV, T. M. Tritt, J. W. Kolis, and D. R. Ketchum 共unpublished兲. 15 C. Kittel, Introduction to Solid State Physics, 7th ed. 共Wiley, New York, 1976兲, p. 133.
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