Thermoelectric properties of p -type half-Heusler alloys Zr 1 x Ti x Co Sn y Sb 1 y ( 0.0x 0.5 ; y = 0.15 and 0.3)V. Ponnambalam, Paola N. Alboni, J. Edwards, Terry M. Tritt, Slade R. Culp, and S. Joseph Poon

Citation: Journal of Applied Physics 103, 063716 (2008); doi: 10.1063/1.2896591 View online: http://dx.doi.org/10.1063/1.2896591 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/103/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Stress dependent magnetostriction in highly magnetostrictive Fe 100 x Ga x , 20 x 30 J. Appl. Phys. 105, 07A913 (2009); 10.1063/1.3058685 Magnetism in Zn 1 x Co x O ( 0 x 0.1 ) and Co 3 y Zn y O 4 ( y = 0 , 0.25, and 1) thin films J. Appl. Phys. 101, 09H118 (2007); 10.1063/1.2712305 Thermal and magnetic properties of La-doped Ce 1 y La y Ge 1.80 with 0 y 1.0 J. Appl. Phys. 99, 08F707 (2006); 10.1063/1.2167056 Magnetron sputter epitaxy of wurtzite Al 1 x In x N ( 0.1 x 0.9 ) by dual reactive dc magnetron sputter deposition J. Appl. Phys. 97, 083503 (2005); 10.1063/1.1870111 Epitaxial growth and properties of Mo O x ( 2 x 2.75 ) films J. Appl. Phys. 97, 083539 (2005); 10.1063/1.1868852

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Thermoelectric properties of p-type half-Heusler alloys Zr1−xTixCoSnySb1−y„0.0<x<0.5; y=0.15 and 0.3…

V. Ponnambalam,1,a� Paola N. Alboni,1 J. Edwards,1 Terry M. Tritt,1 Slade R. Culp,2 andS. Joseph Poon2

1Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634-0978, USA2Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA

�Received 21 October 2007; accepted 14 January 2008; published online 21 March 2008�

Half-Heusler alloys Zr1−xTixCoSnySb1−y �0.0�x�0.5; y=0.15 and 0.3� are investigated for theirpossible use as high temperature thermoelectric materials. In these p-type materials, the Zr site isprimarily substituted with Ti to reduce thermal conductivity ���, while the Sn content is varied tooptimize thermoelectric properties. For these compositions, these alloys exhibit moderate resistivity��� in the m� cm range and high positive thermopower ���, on the order of hundreds of �V /K.Measured Hall coefficients suggest that holes are dominant charge carriers. Calculated carriermobilities are rather low in the range of 0.8–1.5 cm2 /V s. Thermal conductivity ��� values as lowas �8.5–4.5 W m−1 K−1 are also measured. The calculated thermoelectric figure of merit ZT=�2T /�� is as high as 0.2 at T=1000 K, implying that these alloys could be potential p-typethermoelectric materials for energy conversion at high temperatures. © 2008 American Institute ofPhysics. �DOI: 10.1063/1.2896591�

I. INTRODUCTION

Half-Heusler �HH� alloys with valence electron count�VEC� 18 have received keen interest in recent times, mainlybecause these semiconductors �or semimetals� exhibit prom-ising thermoelectric properties.1–9 Many HH alloys withVEC 18 have been characterized with high thermoelectricfigure of merit ZT=�2T /��, where � is the Seebeck coeffi-cient or thermopower, � is the electrical resistivity, � is thethermal conductivity, and T is the absolute temperature. Inwell-optimized multicomponent n-type alloys, ZT can be ashigh as 0.8,1 a value very close to the values of the state-of-the-art materials used for energy conversion. However, it isto be noted that the HH alloys that exhibit good thermoelec-tric properties reported so far have been n type. Since energyconversion devices need both n- and p-type alloys with simi-lar thermoelectric properties as well as physical propertiessuch as thermal expansion, it is equally important to investi-gate possible promising p-type thermoelectric materials, par-ticularly multicomponent alloys with heavy elements, in thisfamily.

High value of the thermopower is rather a general fea-ture for n-type HH alloys satisfying VEC 18.1–9 However, forp-type doped HH alloys, the sign and magnitude of � can beunpredictable. For example, both positive �typically low+ve� as well as negative values of themopower have beenreported for Bi doped �p-type� ZrNiSn samples.4,9 On theother hand, large positive � values, �100 �V /K, have alsobeen reported upon appropriate doping in different HHalloys.10–12 In RE�Pd,Pt��Bi,Sb� �RE=rare earths�-type HHalloys, which are intrinsically p type, although high � �inhundreds of �V /K� and low thermal conductivity��3–3.5 W /m K� are possible, however, the figures of merit�ZT� for these alloys are still on the low side.13–16 In com-

parison to n-type HH alloys, so far, p-type materials are lesspromising in terms of their potential for thermoelectric ap-plications.

In the p-type alloy series TiCoSb1−xSnx, which is closelyrelated to the alloy series presented in this paper, a low ZT of�0.03 has been reported recently, despite high thermopowervalues; the main reason for the low ZT is high resistivity.17 Incontrast to this result, we have demonstrated in our earlierpaper,7 that ZrCoSb based multicomponent alloys do indeedshow the promise of being good p-type thermoelectrics. Inthis article, we mainly explore the influence of substitutionof elements on the electrical resistivity, thermopower, andthermal conductivity of multicomponent p-type alloys. Whilethe objective of substituting Ti was mainly to improve thethermal conductivity, Sn doping was carried out to achievean optimum carrier concentration. Our base system, ZrCoSb,is very resistive ���50 m� cm at 300 K�7 and we needed tosubstitute Sn as much as 15%–30%, in order to reduce theroom temperature resistivity values to ��1–2 m� cm, avalue more desirable for thermoelectric applications. We fur-ther substituted Ti at the Zr site in this system mainly inorder to reduce the thermal conductivity, which, for multi-component HHs, can be at least three times larger than thevalues known for the best thermoelectrics. Since HHs areessentially high temperature thermoelectric materials, wehave also measured the transport properties up to 1000 K.

II. EXPERIMENTAL METHODS

To prepare the alloys used in the present investigation,we employed the arc-melting method. This is the most con-venient way to obtain dense ingots close to 100% of theoret-ical density. In this method, appropriate amounts of elementsof purity �99.9% �for Zr and Hf the purity was about99.5%� were melted together on a water-cooled copperhearth by striking an electric arc using a 1% thoriated tung-a�Electronic mail: vponnam@clemson.edu.

JOURNAL OF APPLIED PHYSICS 103, 063716 �2008�

0021-8979/2008/103�6�/063716/5/$23.00 © 2008 American Institute of Physics103, 063716-1

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sten rod. To prevent oxidation of the melt, the chamber wascontinuously flushed with Ar gas. After each melting, theingot was flipped upside down and remelted two or threetimes to promote homogeneous mixing. In order to minimizethe evaporation of Sb, the ingots were melted at a powerlevel just enough to melt them. Then the ingots werewrapped in graphite foils and sealed in evacuated quartz am-poules to anneal at the temperature of 950 °C over night,followed by a long term annealing at 800 °C for a week.Rectangular bar shaped pieces were cut from the annealedingots for the transport measurements. Powder x-ray diffrac-tion was recorded to check the phase purity and all the alloyswere found to be single phase within the detection limit.Thermopower and resistivity were measured simultaneouslyover a temperature range of 10–1000 K, using the probesdescribed earlier.18,19 Hall coefficients were measured up to300 K in a Physical Property Measurement System �modelP670� by sweeping the magnetic field up to 1 T in bothpositive and negative directions. In order to compute thermalconductivity data above 300 K by a laser flash method, ther-mal diffusitvity �using Netzsch LFA457 microFlash System�and specific heat �using Netzsch Differential Scanning Calo-rimeter 404C Pegasus System� as well as density were alsomeasured.

III. RESULTS AND DISCUSSION

The resistivity behavior of the Zr1−xTixCoSn0.3Sb0.7 alloyseries as a function of temperature is shown in Fig. 1. Thetemperature variation of the resistivity ��T� as well as themagnitude is similar to what is expected for a semimetal orheavily doped �degenerate� semiconductor. The upturn in re-sistivity below T�50 K is probably a localization effect dueto a “substitution-induced” disorder. Above 60 K, invariablyfor all the samples, the resistivity monotonously increaseswith increasing temperature up to 700 K and then � tends tosaturate at higher temperature. The saturation behavior canbe explained as follows: since HHs are expected to have asmall band gap �0.1–0.4 eV�, one should expect the onset of

intrinsic conduction at higher temperatures around 650 K.This can give rise to weak temperature dependent resistivityas we see in the resistivity plots. In contrast to expectations,the Ti substitution seems to have profound influence on themagnitude of the resistivity, however, the temperature depen-dence did not change significantly. Although the change inresistivity is small up to 15% of Ti, 30% and 50% Ti substi-tuted samples showed a dramatic increase in the resistivity.The room temperature � values are in �0.9–2.5 m� cmrange, depending on the Ti content. At 1000 K, the valuesspread out further over a range of �1.5–3 m� cm as the Ticontent is varied from x=0.0 to 0.5. We can attribute thisbehavior to the increased carrier scattering caused by the Tisubstitution. It appears that Ti acts as a point defect, probablydue to its smaller size, and this may be the reason for theobserved resistivity increase with increasing Ti content.However, it is to be noted that similar substitution in n-typeHH alloys4,9 does not seem to affect the resistivity to thisextent. Thus, it appears for some reason that the holes aremore effectively scattered than electrons by the substituted Tiat the Zr sites. The sample doped with 15% Sn shows higherresistivity values which is presumably due to lesser amountof doping. For the 15% Sn sample, � at 1000 K is�4.7 m� cm, a value too high for thermoelectric applica-tions. Therefore, we did not pursue 15% Sn doped samplesfurther by varying the Ti content.

The thermopower ��� behavior of the various alloys as afunction of temperature is shown in Fig. 2. The most strikingobservation, especially at higher temperatures, is the largepositive thermopower values, suggesting that these alloyscould successfully be doped to give high � values while theresistivity values could be around the m� cm range. Thelarge values of the thermopower can be attributed to a higheffective mass m*. The calculated m* values are given in alatter paragraph of this article. Large effective mass valueswere reported for n-type HHs as well.9

Unlike the variation of the resistivity ���T��, � is almostcomposition independent for the alloys doped with 30% ofSn. A rapid increase, followed by a moderate increase of �

FIG. 1. �Color online� Resistivity variation as a function of T for Ti substi-tuted alloys Zr1−xTixCoSn0.3Sb0.7 and Zr0.5Ti0.5CoSn0.15Sb0.85 in the tempera-ture range of 10–1000 K.

FIG. 2. �Color online� Thermopower variation as a function of T for the Ticontent varied Zr1−xTixCoSn0.3Sb0.7 series and the Sn content reducedZr0.5Ti0.5CoSn0.15Sb0.85 alloy. The temperature range is 10–−1000 K.

063716-2 Ponnambalam et al. J. Appl. Phys. 103, 063716 �2008�

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above 450 K, is the common feature for all the alloys stud-ied. Again the moderate increase in � at higher T can beattributed to the onset of intrinsic conduction. At 100 K, ir-respective of composition, these values are around�35 �V /K, steadily increasing to �90 �V /K at �300 K,and finally reach a maximum value of �170 �V /K at1000 K. A similar trend is observed for the less dopedZr0.5Ti0.5CoSn0.15Sb0.85 alloy. However, the thermopowervalues are on the higher side ���200 �V /K�, which is notsurprising, because this alloy is expected to have a smallerconcentration of charge carriers. The measured Hall coeffi-cient �RH� is indeed larger, suggesting a low carrier concen-tration �Table I� for the 15% Sn doped alloy. Basically, theseSn doped alloys demonstrate that high positive thermopoweris possible in the multicomponent HH alloys. This is veryencouraging, since high themopower values are critically im-portant, as they indicate the maximum possible ZT �Ref. 20�in any material. For example, for � of 170 �V /K, the ZTmax

will be �1.2, if lattice part of thermal conductivity is as-sumed to be zero. However, in a real material, ZT will al-ways be lower due to a finite lattice thermal conductivity.

For compositions with x�0.15, i.e., alloys substitutedwith a smaller amount of Ti, the Hall resistance Rxy �perpen-dicular to magnetic field� varies nonlinearly with magneticfield over the entire temperature range of 10–300 K. Thissuggests possible multicarrier contribution to Rxy. However,in the same temperature range, for alloys with x0.3, theHall resistance is positive and varies linearly with magneticfield, suggesting the charge carriers are holes and Rxy is es-sentially determined by these holes. In Fig. 3, we presentHall coefficient RH �panel A� and carrier mobility �H �panelB� for the alloys with x0.3. In a single carrier model, theHall coefficient can be given by RH=1 / pe, where p is thecarrier concentration and e is the electronic charge. FromFig. 3, it is obvious that the carrier concentration is almosttemperature independent, and for 15% Sn doped sample, p ison the higher side as expected. The calculated carrier con-centration �Table I� is around n�1021 cm−3, presumably dueto the large amount of doping with Sn. This would indicatethat the samples should indeed exhibit semimetal or degen-erate semiconductor behavior, as shown from the resistivityin Fig. 1.

We calculated the carrier mobility using the relation�H=RH /�. As apparent in panel B of Fig. 3, these data arealso essentially temperature independent. The temperaturedependence of the carrier mobility can be used to identify thepredominant scattering mechanisms that are operative in

these materials. For example, while �H�T3/2 dependencesuggests acoustic phonon scattering, temperature indepen-dent mobility is suggestive of neutral impurity scattering.Alloy scattering can give rise to weak temperature dependentmobility of the form �H�T1/2 for a nondegenerate case.21

Our alloys are heavily substituted with Ti, which can poten-tially act as alloy scattering centers. This is evident from thelow temperature resistivity data which increase systemati-cally with Ti content. As mentioned previously, the carrierconcentration is high for these alloys ��1021 cm−3� and forsuch a degenerate semiconductor, then the mobility shouldbe temperature independent.22 Our experimental mobilitydata show a weak temperature dependence, suggesting thatdifferent scattering mechanisms are simultaneously operativein these alloys up to 300 K. The Hall mobility values �H arearound �0.8–1.45 cm2 V−1 s−1 only. These values are sur-prisingly low. High carrier concentration may be part of thereason. It is to be noted that for a low carrier concentration of�1020 cm−3, an order of magnitude larger mobility��10–40 cm2 V−1 s−1� is known for n-type HH alloys.9

A reasonable estimation of the effective mass m* can beachieved by assuming a single parabolic band with scatteringdominated by acoustic phonons around room temperature.For such a simplified model, in terms of Fermi–Dirac inte-grals, the thermopower � can be given21

TABLE I. Room temperature carrier concentration �p�, Hall coefficient �RH�, electrical resistivity ���, Hallmobility ��H�, thermopower ���, and thermal conductivity ��� of various compositions in the seriesZr1−xTixCoSnySb1−y

Samplep

�1021 /cm3�RH

�10−9 m3 /C��

�m� cm��H

�cm2 /V s��

��V /K��

�W m−1 K−1�

Zr0.95Ti0.05CoSn0.3Sb0.7 ¯ ¯ 0.96 ¯ 82.9 ¯

Zr0.85Ti0.15CoSn0.3Sb0.7 ¯ ¯ 1.16 ¯ 85.9 10.2Zr0.7Ti0.3CoSn0.3Sb0.7 2.2 2.83 1.92 1.45 89.5 5.34Zr0.5Ti0.5CoSn0.3Sb0.7 3.0 2.05 2.54 0.81 82.1 4.44Zr0.5Ti0.5CoSn0.15Sb0.85 1.0 6.12 4.20 1.44 140.2 4.83

FIG. 3. �Color online� Hall coefficient �RH� and carrier mobility ��� varia-tions for the samples Zr0.5Ti0.5CoSn0.15Sb0.85 ���, Zr0.5Ti0.3CoSn0.3Sb0.7, ���and Zr0.5Ti0.5CoSn0.3Sb0.7 ��� up to 300 K.

063716-3 Ponnambalam et al. J. Appl. Phys. 103, 063716 �2008�

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� = �kB

e�2F1���

F0���− �� , �1�

where kB is the Boltzmann constant, e is the electronicchange, and Fx is the Fermi integral of order x. �= �EF /kBT� is the reduced Fermi energy measured from theband edges. The carrier concentration �p /n� is given by

p/n =4

� 2 m*kBT

h2 3/2

F1/2��� . �2�

By combining Eqs. �1� and �2�, the effective mass can becalculated from the experimentally measured Hall and ther-mopower data. The m* values thus calculated are �7me �me

is the free electron mass� for these alloys doped with 15% aswell as 30% Sn. These m* values are larger than the 2–3me

reported for n-type HH alloys.9

Among many different classes of thermoelectric materi-als, the HHs are somewhat novel with respect to their ther-moelectric power factors. In particular, for n-type materials,these values are larger than the best values known for thestate-of-the-art thermoelectrics. In Fig. 4, we show powerfactor trends for many compositions that exhibit high posi-tive �. The power factor PF=�2T /� increases rapidly with T,mainly due to the increase of thermopower with increasingT. Although the highest value PF�2.0 W m−1 K−1 observedat 1000 K is low compared to 4.5 W m−1 K−1 known forn-type HH materials,6 it is still comparable to the valuesknown for the best thermoelectrics. High PFs at higher tem-peratures certainly make them candidate materials for ther-moelectric energy conversion around 1000 K.

The thermal conductivity is another key parameter thatdetermines the usefulness of a thermoelectric material. Al-though multicomponent HH alloys exhibit lower � in therange of 3.5–3.1 W m−1 K−1,7,8 it is still higher than the val-ues �1.5–2 W m−1 K−1� known for the best thermoelectricmaterials. As we show in Fig. 5, �1000 K values of the alloyswe studied are in the range of 8–4.5 W m−1 K−1 dependingon the composition and very comparable to the values knownalready for HH alloys substituted with heavier elements.1,8

For the sample substituted with 15% Ti �x=0.15�, � is

weakly temperature dependent, and this suggests an appre-ciable contribution from phonon-phonon scattering �Um-klapp processes�. In addition, we see that the � values de-crease with increasing Ti content and are almost temperatureindependent for samples with higher Ti content. The atomicsize of Ti �1.45 � is smaller than the size of Zr �1.59 �.Also Ti is lighter than Zr. These can cause strong mass andstrain field fluctuations in the lattice. These fluctuations canbe the predominant phonon scattering centers and thereforemay be the reason for the reduced and temperature indepen-dent thermal conductivity observed in the samples of higherTi content.

Finally, we present thermoelectric figure of merit ZT inFig. 6, by combining � with �2T /�. Our maximum ZT valuesare �0.2 and are comparable to the values known for thep-type HH alloy HfPtSn.23 This is a very significant resultsince not many p-type materials, except Si–Ge alloys, areknown for energy conversion at these temperatures.24 Veryrecently, high ZT�1.0 at 1200 K has been reported for thep-type Yb14MnSb11 Zintl phase, mainly due to its signifi-

FIG. 4. �Color online� Power factor �2T /� vs T plots in the temperaturerange of 10–1000 K.

FIG. 5. �Color online� High temperature thermal conductivity data for thealloy series Zr1−xTixCoSn0.3Sb0.7 �x=0.15–0.5� and 15% Sn dopedZr0.5Ti0.5CoSn0.15Sb0.85 sample as a function of temperature �T�. The tem-perature range is 300–1000 K.

FIG. 6. �Color online� Dimensionless figure of merit ZT vs T plots forselected compositions.

063716-4 Ponnambalam et al. J. Appl. Phys. 103, 063716 �2008�

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cantly low � of �0.7 W m−1 K−1.25 Among other p-type ma-terials, the well-studied SiGe alloys exhibit ZTmax�0.5 at1100 K,25 whereas Chevrel phase Cu4Mo6Se8 is known forsometime with ZTmax�0.6 at 1150 K.26 Although our valuesare low, HH alloys offer the advantage of composition flex-ibility and thermal stability. Unlike many thermoelectrics,HH is relatively a larger alloy system with many composi-tions known to be semimetallic �or semiconducting� and alsoquite amenable for substitution with elements of differentsizes, masses, and atomic numbers. This means that there isa tremendous potential for this system to be tailored furtherfor better � as well as ZT values.

IV. SUMMARY

In summary, we have studied a multicomponentZr1−xTixCoSn0.3Sb0.7 alloy series as well as a less-dopedZr0.5Ti0.5CoSn0.15Sb0.85 alloy with an objective of evaluatingthem as p-type thermoelectric materials for energy conver-sion at higher temperatures, where Si–Ge alloys are currentlybeing used. Based on our measurements, we conclude thathigh thermopower in excess of � 170 �V /K along with theresistivity of few m� cm is possible around 1000 K. Ther-mal conductivity can also be reduced to a value of�4.5 W m−1 K−1 in this alloy series. Our ZT values at1000 K are around 0.2, which is low compared to valuesknown for Si–Ge alloys. This is mainly due to low carriermobility.

ACKNOWLEDGMENTS

We acknowledge the financial support from DOE �DE-FG02-04ER-46139� and SC EPSCoR/Clemson UniversityCost Share.

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