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Acta Materialia 61 (2013) 7693–7704

Realization of high thermoelectric performance in p-typeunfilled ternary skutterudites FeSb2+xTe1�x via band

structure modification and significant point defect scattering

Gangjian Tan a, Wei Liu a,b, Hang Chi b, Xianli Su a, Shanyu Wang a, Yonggao Yan a,Xinfeng Tang a,⇑, Winnie Wong-Ng c, Ctirad Uher b

a State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology,

Wuhan 430070, People’s Republic of Chinab Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA

c Material Measurement Laboratory, Ceramics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

Received 2 July 2013; received in revised form 30 August 2013; accepted 5 September 2013Available online 28 September 2013

Abstract

FeSb2Te, a ternary derivative of binary CoSb3, displays anomalous electrical and thermal transport properties because of consider-able modifications in the band structure induced by Fe and significant mixed valence state (namely Fe2+ and Fe3+) scattering of phonons.The substitution of Te for Sb generates more holes without notably affecting the band structure, while markedly improving the electricalconductivity and retaining a high Seebeck coefficient due to the enhanced density of states, thereby leading to dramatically increasedpower factors. Furthermore, the heat carrying phonons are strongly scattered with increasing x value because of the formation of solidsolutions between two end members: hFeSb2Te and hFeSb3 (where h can be viewed as a vacancy). Consequently, high thermoelectricfigures of merit were achieved in the FeSb2+xTe1�x compounds, with the largest ZT value reaching �0.65 for the sample with x = 0.2.This is the highest value among all p-type unfilled skutterudites and is comparable with some filled compositions. Prospects for furtherimproving the performance of p-type FeSb2Te-based skutterudites are discussed.Crown Copyright � 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

Keywords: p-Type skutterudite; Thermoelectric; Band structure modification; Thermal conductivity; Point defect scattering

1. Introduction

Filled skutterudites have long been recognized aspotential materials for thermoelectric power generationapplications in the intermediate temperature range [1–3].Nonetheless, most of the fillers are sensitive to oxygen,making the preparation process quite complex and oftenrequiring operations under a protective gas [4–6]. In con-trast to filled skutterudites, many different preparationtechniques can be adopted to synthesize unfilled samples,

1359-6454/$36.00 Crown Copyright � 2013 Published by Elsevier Ltd. on beh

http://dx.doi.org/10.1016/j.actamat.2013.09.006

⇑ Corresponding author.E-mail address: tangxf@whut.edu.cn (X. Tang).

for instance chemical routes [7] and ball milling [8,9],besides the traditional melting method. If comparable ZT

values can be realized in unfilled compositions it wouldbe a great step forward towards actual production of thispromising material.

Indeed, relatively high ZTs have been achieved withn-type doped CoSb3. For example, the highest ZT reached�0.7 on Te doping of CoSb3 [10]. By following the chargecompensation principle the ZT values of Sn/Ge and Te co-doped series can be further increased to �1.1 [9,11] at800 K, which is encouraging. Unfortunately, the best ZT

value reported so far for p-type unfilled skutterudites fallsshort of this mark and hovers around a value of only 0.3in the Co1�xFexSb3 series [12–14]. The performance

alf of Acta Materialia Inc. All rights reserved.

7694 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

asymmetry between n- and p-type skutterudites has its ori-gins mainly in electrical transport [15], which is mainlydetermined by the unique band structure [16,17] of thematerial. For CoSb3-based skutterudites there is only onesingle light band in the vicinity of the top valence band,giving rise to smaller power factors in p-type doped CoSb3.Therefore, there is an opportunity to make favorable mod-ifications in the band structure details, especially in theregion of the top valence band, which would improve theelectrical transport of p-type unfilled skutterudites.

Recently Yang et al. [15] undertook a systematic inves-tigation of the influence of band structure on the propertiesof p-type fully filled skutterudites RFe4Sb12 (R denotes thefiller). They found that the heavy bands derived from Fe delectronic states also fall in the range of energies close tothe valence band edges in RFe4Sb12, which is quite differentfrom the single Sb-dominated light band in the valenceband edge of CoSb3. The alteration in band structure effec-tively enhances the density of states, leading to the largepower factors found in these RFe4Sb12 compounds. Mod-ifications of the band structure are mainly attributed to thesubstitution of Co by Fe. Therefore, it is reasonable toassume that analogous band alterations could occur inFeSb3, unfortunately such a structure does not exist. Nev-ertheless, isoelectronic analogs of binary CoSb3 providemany possibilities [18,19]. One such case is FeSb2Te, whichshows intrinsic p-type conduction and anomalous thermo-electric transport behavior. It seems that FeSb2Te is apotential candidate p-type unfilled skutterudite with highthermoelectric performance [18]. In this study we focuson exploration of the unusual electrical and thermal trans-port mechanisms in FeSb2Te-based ternary skutterudites.We also tried to improve the thermoelectric performanceby adjusting the electrical and thermal transport propertiesby changing the Sb/Te ratio.

2. Experiment

Samples with the nominal compositions FeSb2+xTe1�x

(x = 0, 0.05, 0.10, 0.15, 0.20 and 0.25) were prepared bythe traditional melting–annealing–spark plasma sinteringmethod as described below. Stoichiometric quantities ofthe constituent pure elements Fe (99.5%, shot), Sb(99.9999%, ingot) and Te (99.99%, ingot) were weighedaccording to their nominal compositions, loaded into aquartz tube, and then sealed under vacuum at a pressureof 10�3 Pa. The samples were slowly heated to 1373 Kand rested there for 24 h. They were then quenched in asaltwater base and annealed at 823–873 K for 168 h. Theresulting ingots were ground into fine powders and thensintered into dense bulk pellets with a diameter of 15 mmby spark plasma sintering (SPS) at 803–833 K for 5 minunder a pressure of 40 MPa.

The purities and chemical compositions of the bulk sam-ples were determined by powder X-ray diffraction (XRD)(PANalytical X’Pert Pro X-ray diffraction) using Cu Ka

radiation (k = 1.5406 A) and electron probe microanalysis(EPMA) (JXA-8230, JEOL). The morphologies of the bulkmaterials were analyzed by field emission scanning electronmicroscopy (FESEM) (Hitachi S-4800).

The pellets, 15 mm in diameter � 2 mm thick, weresliced into 8 � 8 � 1.5 mm square sheets and 3 � 2 �12 mm bars for measurement of their thermoelectric prop-erties. The electrical conductivity (r) and Seebeck coeffi-cient (a) were simultaneously measured using commercialequipment (ZEM-1, Ulvac Riko, Inc.) under a low pressureinert gas (He) atmosphere from 300 to 800 K. The thermalconductivity (j) was calculated from the measured thermaldiffusivity (D), specific heat (Cp), and density (d) using therelationship j = D � Cp � d. The thermal diffusivity wasmeasured by the laser flash diffusivity method using aNetzsch LFA 457 system and the specific heat (Cp) wasmeasured using a TA DSC Q20 instrument. All themeasurements were performed in the temperature range300–800 K. The densities of the bulk samples were mea-sured by the Archimedes method and the relative densitiesof all samples were higher than 97%. Uncertainties in theelectrical conductivity, Seebeck coefficient, and thermalconductivity were within 5%, 2%, and 5%, respectively, pri-marily originating from sample dimension measurements.

Hall effect measurements were performed in a cryostatequipped with a 5.5 T superconducting magnet. Hallmeasurements and low temperature thermal conductivityand Seebeck coefficient measurements were carried out inan in-house built apparatus at the University of Michi-gan. Procedures for these low temperature property mea-surements were as described elsewhere [20]. The roomtemperature sound velocity m was measured by an ultra-sonic pulse echo method (Panametrics 5072PR) with afundamental frequency of 20 MHz. The low temperatureheat capacity measurement was performed in a PhysicalProperties Measurement System (PPMS) (QuantumDesign). X-ray photoelectronic spectroscopy (XPS) anal-ysis was operated using the Kratos Axis Ultra XPS atthe Electron Microbeam Analysis Laboratory (EMAL),University of Michigan. Core level scans of Fe 2p andFe 3p for these FeSb2+xTe1�x samples were performedutilizing a monochromatized Al source (Al Ka =1486.6 eV) with an emission current of 8 mA and ananode voltage of 15 kV at a vacuum pressure of 10�8–10�9 torr, adopting a pass energy of 20 eV and a stepof 0.1 eV during the measurements. The analysis areafor this measurement was approximately 700 � 300 lmon the sample surface. The energies of all XPS spectrawere calibrated with respect to the non-functionalized ali-phatic carbon with a binding energy of 285.0 eV. Acharge neutralizer was employed to prevent samplecharging. The surface of these samples was cleaned byAr+ ion bombardment for 40 min before measurement.The data was peak fitted by applying the CasaXPS soft-ware from Casa Software Ltd., using a Lorentzian asy-metric lineshape (LA) model.

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3. Results and discussion

3.1. Phase composition and microstructure

Fig. 1a shows the powder XRD patterns for CoSb3 [21]and FeSb2+xTe1�x (x = 0–0.25). All samples display a sin-gle phase skutterudite structure (see JCPDS card 65-1791)when x is between 0.05 and 0.20. However, trace amountsof impurity phases, Sb2Te3 (JCPDS card 65-3678) and FeS-bTe (JCPDS card 42-1290) for the sample with x = 0, Sb(JCPDS card 01-0802) and FeSb2 (JCPDS card03-0717)for the sample with x = 0.25, can be detected when care-fully examining the XRD patterns. This could be furtherascertained from the EPMA results. Fig. 1b displays anenlarged view of the (13 6) diffraction peaks for all samples.A regular shift of the diffraction peaks to lower angles withincreasing Sb content (or x) until x = 0.20 can be observed,which is mainly attributed to the fact that Sb (1.53 A) has alarger atomic radius compared with Te (1.42 A). However,

Fig. 1. (a) Powder XRD patterns and (b) the enlarged (

Table 1The relative density, actual compositions determined by EPMA, room tempera(r), Seebeck coefficients (a) obtained from low temperature physical propeFeSb2+xTe1�x (x = 0–0.25) bulk samples.

Nominal composition

CoSb3 [21] x in FeSb2+xTe1�x

0 0.05 0

Actual composition CoSb2.995 FeSb2.030Te0.901 FeSb2.036Te0.885 FRelative density 98.7% 98.8% 99.1% 9a (lV K�1) 222.16 110.16 98.86 8r (104 S m�1) 2.10 3.24 4.05 5Np (1020 cm�3) 0.014 5.35 7.15 1lH (cm2 V�1 s�1) 937.5 3.79 3.54 2m� (me) 0.03 3.63 3.95 5

when x > 0.20 the position of the diffraction peak remainsalmost unchanged. The EPMA composition data, asshown in Table 1, reveal that the actual chemical composi-tion of the x = 0.20 and x = 0.25 (main phase) samples arevery close. Thus these results suggest that the solubility forTe/Sb substitutions is limited to around 0.8/2.2. Moreover,the similarity among all the powder XRD patterns suggeststhat neither the formation of ternary FeSb2Te nor Sb/Tesubstitutions in FeSb2+xTe1�x change the crystal structureof the skutterudite.

Fig. 2 displays FESEM images for the sample withx = 0.20. The grains are well crystallized and highly com-pacted. The average grain size is on the scale of 2–5 lm.The backscattering electron images (BSI) and correspond-ing X-ray elemental maps for the carefully polished samplewith x = 0.20 are shown in Fig. 3. All elements were homo-geneously distributed in the skutterudite matrix and noobvious aggregations were observed, at least on themicroscale.

136) peaks for FeSb2+xTe1�x (x = 0–0.25) samples.

ture Hall concentrations (Np), Hall motilities (lH), electrical conductivitiesrty measurements and calculated carrier effective masses m�/me of the

.1 0.15 0.2 0.25

eSb2.054Te0.847 FeSb2.094Te0.798 FeSb2.154Te0.765 FeSb2.157Te0.752

9.1% 98.9% 98.8% 99.8%6.37 78.67 85.21 84.33.95 6.67 8.85 9.902.52 21.46 33.82 23.75.97 1.94 1.64 2.61.01 6.54 9.60 7.51

Fig. 2. Typical FESEM images for the fractured surface of the FeSb2.2Te0.8 sample.

Fig. 3. (a) Backscattering images (BSI) and the corresponding elemental distributions, (b) Fe, (c) Sb and (d) Te, detected by wavelength dispersive X-rayspectrometry (WDS) for the carefully polished sample FeSb2.2Te0.8.

7696 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

3.2. Electrical transport properties

The high temperature electrical transport properties ofthe FeSb2+xTe1�x samples are shown in Fig. 4. For sampleswith x 6 0.05 the electrical conductivity (Fig. 4a) firstdecreased with increasing temperature and then tended toincrease at high temperatures due to the bipolar diffusioneffect. For samples with x P 0.10 the electrical conductivitydecreased with increasing temperature over the entire tem-perature range, typical of metallic conduction. Regardlessof temperature the electrical conductivity revealed a contin-uous improvement with increasing x (Sb content). The See-beck coefficient (Fig. 4b) for all samples was positive over

the whole temperature range, indicating p-type conduction.Moreover, the FeSb2Te compound displayed the highestSeebeck coefficient of �120 lV K�1 at room temperature.With increasing Sb content the Seebeck coefficientdecreased gradually while retaining a high value, probablydue to the greatly enhanced density of states, which will bediscussed below. The power factor (Fig. 4c) is greatlyenhanced by substituting Sb for Te, especially at elevatedtemperatures. The maximum power factor reaches2 � 10�3 W m�1 K�2 for the sample with x = 0.20, whichis about 2.5 times that of FeSb2Te and also much largerthan those of binary CoSb3 [21] as well as the optimizedCo1�xFexSb3 [12] and CoSb3�xSnx [22] series. For the

Fig. 4. High temperature electrical transport properties for FeSb2+xTe1�x (x = 0–0.25) samples: (a) electrical conductivity; (b) Seebeck coefficient; (c)power factor. For comparison the power factors for some optimized Co1�xFexSb3 [12] and CoSb3�xSnx [22] series are also included.

G. Tan et al. / Acta Materialia 61 (2013) 7693–7704 7697

sample with x = 0.25 the electrical performance was seri-ously degraded, probably due to the existence of the impu-rity phases Sb and FeSb2, as mentioned above.

To explore the origin of variations in the electrical con-ductivity and the Seebeck coefficient low temperature elec-trical transport properties and Hall efficient measurementswere carried out, as displayed in Fig. 5. As follows fromFig. 5a, low temperature electrical conductivities for allsamples exhibited excellent coincidence with the valuesobtained from high temperature measurements (within10% margin of error at room temperature). Fig. 5b plotsthe low temperature Seebeck coefficient as a function oftemperature for all FeSb2+xTe1�x samples. Similar to thehigh temperature data, the Seebeck coefficient generallydecreased with increasing x. For samples with the lowerSb content (x 6 0.05) the Seebeck coefficient was positivearound 3 K and increased almost linearly with increasing

Fig. 5. Low temperature electrical transport measurements and Hall data for Fcoefficient; (c) carrier concentration and (d) Hall mobility. The inset in (b) shoplotted in (d) predicts the lH–T�0.5 relationship.

temperature. However, for samples with the higher Sb con-tent (x P 0.10), the Seebeck coefficient was negativearound 3 K (see inset) and its absolute value increased withincreasing temperature, reaching the peak value between 30and 50 K and then starting to decline gradually, changingto positive around 100 K. Such a small valley in the lowtemperature a–T plot can be attributed to the so-calledphonon drag effect [23].

The Hall carrier concentration Np was determined fromthe Hall coefficient RH using Np = 1/eRH, where e is theelectron charge, assuming a scattering factor equal to 1and a single carrier model, and is shown in Fig. 5c. The signof the Hall coefficient was positive, consistent with the signof the Seebeck coefficient. The resulting carrier density wasnearly temperature independent between 10 and 300 K,suggesting a heavily doped metal-like behavior. Withincreasing Sb/Te ratio (or x) the room temperature hole

eSb2+xTe1�x (x = 0–0.25) samples: (a) electrical conductivity; (b) Seebeckws details of the Seebeck coefficient between 0 and 100 K. The dashed line

Fig. 6. Room temperature Seebeck coefficient as a function of carrierconcentration for FeSb2+xTe1�x (x = 0–0.25) samples. For comparisonthe data for Co1�xFexSb3 [24], CoSb3�xSnx [25] and some pure iron-basedskutterudites [26–28] are also included.

7698 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

concentration increased gradually from 5.4 � 1020 cm�3 forthe sample with x = 0 to 3.4 � 1021 cm�3 for the samplewith x = 0.20, in full accord with the expected electronacceptor role of Sb substituting for Te. The x = 0.25 sampleshowed a reduced hole concentration with respect to thesample with x = 0.2, probably due to the emergence ofimpurity phases. It is worthy of note that although binaryCoSb3 is isoelectronic, ternary FeSb2Te shows a threeorders of magnitude higher hole density (see Table 1), whichlikely arises from the high density of lattice vacancies at theanionic sites of FeSb2Te, as can be seen from the EPMAresults shown in Table 1. To extract more informationabout the scattering process the Hall mobility l wasdetermined from the electrical conductivity r and theHall coefficient RH using the relation l = rRH. Thetemperature-dependent Hall mobility is plotted in Fig. 5d.All samples possessed low carrier mobilities (<10 cm2

V�1 s�1) that were substantially constant until about50 K. Above this temperature the mobilities started todecline rapidly with increasing temperature, roughly obey-ing the rule l � T�1/2 near room temperature, typical ofalloy scattering behavior. Generally, hole mobilitydecreased with increasing x because of increased degener-acy, except for the sample with the largest x value due tothe emergence of secondary phases, as described above.The low temperature electrical conductivity and Hall datameasurements confirmed that the enhancement of electricalconductivity and decrease in Seebeck coefficient withincreasing x can be mainly attributed to the increased holeconcentration due to Sb/Te substitutions. It should benoted that ternary compounds possess seriously diminishedhole mobilities with respect to the mobility of p-type CoSb3

(�1000 cm2 V�1 s�1) [21], probably due to the significantcharge transfer scattering (Fe2+ and Fe3+) [18] andenhanced point defect scattering (including alloy scatteringand vacancies, etc.), and perhaps also related to theincreased effective mass (modification of the bandstructure), which will be discussed below in detail.

Fig. 6 shows the Seebeck coefficient at room temperatureas a function of the carrier concentration for FeSb2+xTe1�x

samples. For comparison data for other p-type unfilledskutterudites [24,25] and pure iron-based filled skutteru-dites [26–28] are also included. The FeSb2+xTe1�x samplesshowed comparable hole densities (�1021 cm�3) to thoseof pure iron-based filled skutterudites [26–28], which aremuch larger than those in Co1�xFexSb3 [24] and CoSb3�x-

Snx [25] (�1019 cm�3) materials. However, these pureiron-based skutterudites display much larger Seebeck coef-ficients than the Co-based skutterudites (see Fig. 6). This isa bit surprising because from the classic physics perspectivesamples having a lower carrier density should have a largerSeebeck coefficient given a fixed band structure. The greatlyenhanced Seebeck coefficients of the ternary FeSb2+xTe1�x

skutterudites in comparison with the Co-based skutteru-dites suggest a considerable enhancement of the effectivemass in the ternary system. To reach this conclusion weestimated the effective mass by assuming a single parabolic

band model with a scattering factor r = –1/2 for alloydisorder scattering. In this model the Seebeck coefficient afor a p-type semiconductor can be expressed as [29,30]:

a ¼ kB

e2

F 1ðgÞF 0ðgÞ

� g

� �ð1Þ

where kB is the Boltzmann’s constant, g is the reduced Fer-mi energy and Fx is a Fermi integral of order x. The holeconcentration Np can be written as [29,30]:

Np ¼ 4p2m�kBT

h2

� �3=2

F 1=2ðgÞ ð2Þ

where m� is the density of states effective mass and h isPlanck’s constant. Using experimental Seebeck coefficientsand Hall carrier concentration values based on Eqs. (1) and(2) one can obtain the effective masses at room temperaturefor the FeSb2+xTe1�x samples, which range from 3.6 to 9.6me (me is the mass of a free electron), much larger thanthose of pure CoSb3 (0.03 me) [21], Co1�xFexSb3 (0.071–0.3 me) [24] and CoSb3�xSnx (0.1–0.2 me) [25]. Moreover,the effective mass increases with increasing hole concentra-tion, which is possibly related to the non-parabolic natureof the skutterudite band structure [4]. In fact, based on thequasilinear valence band model proposed by Singh et al.,the p-type skutterudite has quite a different doping depen-dence than one would expect for a material with the usualparabolic band, and the degenerate form of its Seebeckcoefficient within the constant relaxation time approxima-tion is given by [17,31,32]:

a ¼ � 2pk2BT

3exp

3N p

� �1=3

ð3Þ

where kB is the Boltzmann constant, e is the electron chargeand x is the slope of the linearly dispersing band. We found

G. Tan et al. / Acta Materialia 61 (2013) 7693–7704 7699

that the a–Np plot for the FeSb2+xTe1�x series agrees wellwith the a–(Np)�1/3 relation (red solid line), confirmingquasilinear dispersion of the valence band in skutteruditesand indicating that substitution of Te by Sb has little influ-ence on the band structure of FeSb2Te. The fitted x valueis �0.46 eV A for FeSb2+xTe1�x compounds, while theabsolute value is much lower than that of binary CoSb3

(�3.10 eV A) [17]. This means that the top of the valenceband in FeSb2Te is flatter compared with CoSb3. Thisresult suggests a significant band structure modificationof FeSb2Te with respect to CoSb3. Interestingly, the datafor pure iron-based filled skutterudites [26–28] also scatteraround the theoretical line for the FeSb2+xTe1�x series,confirming the similarity in band structure betweenFeSb2Te and RFe4Sb12. This might be expected becausefillers have a weak influence on the band structure whilethe modification in band structure of FeSb2Te and RFe4-

Sb12 with respect to CoSb3 has its origin mainly in thepresence of Fe.

To validate this conjecture the electronic band structureand density of states (DOS) for CoSb3 and FeSb2Te werecalculated from first principles using the Vienna ab initiosimulation package (VASP) [33] within the Perdew–Burke–Ernzerhof (PBE) parameterization of the general-ized gradient approximation (GGA) for exchange and cor-relation [34] and using the projector augmented wave(PAW) method [35,36], as shown in Fig. 7. Both com-pounds have a direct band gap at the C point equal to�0.43 eV for FeSb2Te (close to the band gaps for RFe4-

Sb12, i.e. 0.49 eV for BaFe4Sb12 [15]) and �0.16 eV forCoSb3, quite close to the value of �0.17 eV reported bySofo et al. [16] and Yang et al. [15] using the same GGAmethod for CoSb3). Similar band gaps for FeSb2Te and

Fig. 7. Electronic band structure and density of states (DOS) of CoSb3

(top) and FeSb2Te (bottom) calculated from first principles.

RFe4Sb12 again demonstrate that band modification is gen-erally caused by Fe. The much larger band gap implies thatthe influence of the bipolar effect on p-type electrical trans-port will be negligible in ternary FeSb2Te-based skutteru-dites at achievable temperatures if a reasonable carrierconcentration is maintained. The valence band of CoSb3

shows a gap crossing light band with a quasilinear disper-sion around the C point, similar to prior studies [16,17].The light band possesses a stronger Sb character, althoughit also hybridizes with Co states. Several heavy bands withlarge Co projections (the spatially localized nature of 3dorbitals is the reason for the large effective masses of theseheavy bands) are located too deep in the valence band,contributing little to electrical transport. Therefore, inCo-based skutterudites hole transport is dominated bythe light band, giving rise to a low effective mass. However,for FeSb2Te there are several heavy bands with a mostly Fecharacter that make up the region near the valence bandmaximum. These heavy bands are so flat that the Fermilevel is almost pinned by them. This is the reason why higheffective hole masses are observed in p-type ternaryFeSb2+xTe1�x skutterudites. This modification in bandstructure is crucially important in enhancement of the elec-trical performance of p-type skutterudites because thepower factor can be simply evaluated by the weighedmobility U = (m�)3/2l [37]. Larger effective masses arefavorable in obtaining a higher Seebeck coefficient. How-ever, although the optimized power factors in FeSb2+x

Te1�x compounds are much larger than those of any otherp-type unfilled skutterudites, they are still lower than thoseof p-type filled skutterudites RFe4Sb12 [6,28] because oftheir much smaller carrier mobility l due to lattice distor-tion at the anion sites, as discussed previously. Futureattempts aimed at further improving the power factorsshould focus on increasing the carrier mobility.

3.3. Thermal transport properties

Fig. 8 plots the high temperature thermal conductivityas a function of temperature for all FeSb2+xTe1�x samples.As shown in Fig. 8a, all samples display much smaller ther-mal conductivities compared with binary CoSb3 [21] (insetin Fig. 8a), �10 W mK�1 for CoSb3 but only�3.1 W mK�1 for the FeSb2Te compound. Moreover, thethermal conductivity was further decreased on increasingthe Sb/Te ratio, in spite of continuously improving electri-cal conductivity. The lattice thermal conductivity jL isinferred from jL = j–jC, where jC is the carrier contribu-tion to thermal conductivity calculated according to theWiedemann–Franz law jC = LrT, with L being the Lorenznumber and r the measured electrical conductivity. TheLorenz number can be obtained within the degenerateapproximation using the equation [38]:

L ¼ kB

e

� �2 3F 0ðgÞF 2ðgÞ � 4F 21ðgÞ

F 20ðgÞ

� �ð4Þ

Fig. 8. Thermal conductivity of FeSb2+xTe1�x (x = 0–0.25) samples and CoSb3 [21]: (a) high temperature thermal conductivity; (b) calculated Lorenznumber; (c) high temperature lattice thermal conductivity. Lattice thermal conductivities for other p-type unfilled skutterudites (Fe2Pd2Sb12 [39],CoSb3�xSnx [25] and Co1�xFexSb3 [12]) are also included in (c) for comparison.

Fig. 9. High resolution spectra from the Fe 2p transition for FeSb2+x-

Te1�x samples with x = 0 and 0.25.

7700 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

The calculated L values and jL as a function of temper-ature are plotted in Fig. 8b and c, respectively. Forcomparison, the lattice thermal conductivity data for otherp-type unfilled skutterudites are included in Fig. 8c. Com-pared with CoSb3 the room temperature lattice thermalconductivity for FeSb2Te shows a 70% reduction, and isalso much lower than those of other p-type heavily dopedskutterudites [12,25,39], which can be largely attributed tothe anionic lattice distortion in FeSb2Te. It has beenreported (without any experimental evidence) that Feshows mixed valence states (namely Fe2+ and Fe3+) inFeSb2Te, and electron transfer between the two statesmight significantly scatter phonons [18]. Moreover, specificcharge transfer scattering of phonons depends on the pres-ence of both charge states [40]. The phonon scatteringprobability and, hence, the thermal resistivity should varyas a product of c(Fe2+)c(Fe3+), where c is the concentrationin atoms per unit volume. It is evident that c(Fe2+)c(Fe3+)reaches a maximum when c(Fe2+) = c(Fe3+) = 0.5. We car-ried out XPS measurements on two selected samples toexamine the valence states of Fe and quantitatively deter-mined their respective content in the compounds in orderto reveal more detail of the mixed valence scattering (orcharge transfer scattering) mechanism.

Fig. 9 shows the high resolution Fe 2p spin orbit doublespectra for FeSb2+xTe1�x samples with x = 0 and 0.25. TheFe 2p3/2 spectra of FeSb2+xTe1�x with x = 0 and 0.25 showsharp peaks with a maximum of �707.5 eV, while thepeaks for Fe 2p1/2 are somewhat broadened. Meanwhile,an obvious chemical shift of the Fe 2p1/2 and Fe 2p3/2 spec-tra was found on varying the Te content. Specifically, theFe 2p1/2 and Fe 2p3/2 spectra moved towards the higherenergy region, �0.7 eV, as x was increased from 0 to0.25. This implies the existence of both Fe2+ and Fe3+ cat-ions as well as an increasing Fe3+/Fe2+ ratio with increas-ing x value. So mixed charge transfer scattering between

Fe2+ and Fe3+ may be another important factor that leadsto the extremely low lattice thermal conductivity inFeSb2Te, in addition to anionic lattice distortion.

In order to quantify the valence state of iron inFeSb2+xTe1�x we recorded the Fe 3p XPS spectrum in rela-tion to the Te content. As shown in Fig. 10, the Fe 3p spec-trum of FeSb2+xTe1�x with x = 0 and 0.25 was resolved intotwo separate components with different full width half max-ima (FWHM) using the LA fitting model noted in the exper-imental section. The lower energy component in the fittingwas considered to be due to Fe2+, as labeled by the blue line,while the higher energy component was ascribed toFe3+, displayed as the red line. The integral area ratio ofFe3+/Fe2+ was about 49/51 at x = 0, which means that thephonon scattering probability reached a peak in FeSb2Te,which could explain its extremely low lattice thermal

Fig. 10. Fitted Fe 3p spectrum for FeSb2+xTe1�x samples with (a) x = 0 and (b) x = 0.25. The dark line shows experimental data while the fittedcomponents are represented by the red (Fe3+) and blue (Fe2+) lines. (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

G. Tan et al. / Acta Materialia 61 (2013) 7693–7704 7701

conductivity compared with CoSb3. When x was increasedto 0.25 the integral area ratio of Fe3+/Fe2+ was close to78/22, indicating an increasing content of Fe3+. This inves-tigation also confirmed that most Fe existed in the formFe3+ in FeSb2.25Te0.75, which coincides with the appearanceof FeSb2 secondary phase when x exceeded 0.2 due to chargeimbalance in FeSb2+xTe1�x-based materials (see XRD anal-ysis). Moreover, based on the charge compensation rule, weconcluded that the relative content of Fe3+ increases regu-larly with increasing x and thus the probability of phononscattering and, hence, the thermal resistivity due to mixedvalency scattering should decrease gradually with increasingx. However, experimentally we found that the lattice ther-mal conductivity decreased gradually with increasing x internary FeSb2+xTe1�x skutterudites and the minimum lat-tice thermal conductivity attained a value close to that offilled skutterudites [6]. This result suggests that scatteringmechanisms other than mixed valency scattering must beresponsible for the significant reduction in the lattice ther-mal conductivity of FeSb2+xTe1�x compounds with increas-ing x value, which we will discuss below.

We performed theoretical fits of the low temperature lat-tice thermal conductivity (Fig. 11) for the entire series ofFeSb2+xTe1�x samples using the expression [41]:

jL ¼kB

2p2mkBT

�h

� �3 Z D=T

0

sCðy; T Þy4ey

ðey � 1Þ2dy ð5Þ

where y = ⁄x/kBT, ⁄ is the reduced Planck constant, x isthe phonon frequency, kB is the Boltzmann constant, hD

is the Debye temperature, m is the velocity of sound, andsC is the combined relaxation time. Generally the phononscattering rate s�1

C can be written as [38]:

s�1C ¼ s�1

B þ s�1PD þ s�1

U þ s�1ep

¼ tLþ A-4 þ B-2T exp � hD

3T

� �þ C-2 ð6Þ

Here L is the grain size and the coefficients A, B, and C

are fitting parameters related to point defect scattering,phonon–phonon Umklapp scattering and electron–phononscattering, respectively. The velocity of sound was mea-sured by an ultrasonic pulse echo method, and the resultsare summarized in Table 2. hD was obtained from low tem-perature (2–8 K) heat capacity measurements, as shown inFig. 12. At low temperatures the heat capacity Cp can beexpressed as [42]:

Cp ¼ aT þ bT 3 ð7ÞHere the first term on the right side represents the elec-

tronic contribution, and the second term the lattice contri-bution. When T is low enough (i.e. 2–8 K), Cp/T isproportional to T2. By plotting Cp/T as a function of T2

(shown in the inset in Fig. 12) one can obtain b values bymeasuring the slope. The results are shown in Table 2.Then the fitted parameter b was used to calculate theDebye temperature hD through the formula:

hD ¼12p4NR

5b

� �1=3

ð8Þ

where N and R denote the number of atoms in the com-pound formula and the gas constant, respectively. The cal-culated hD is also listed in Table 2. The fitting plots andcoefficients of low temperature lattice thermal conductivityare displayed in Fig. 11 and Table 2, respectively. The dis-crepancy between the data and fits at T > 100 K may bedue to a variety of reasons: radiation losses, temperaturedependence of the Lorenz number, and deviation of thethermal conductivity from the assumed 1/T temperaturedependence at high temperatures [20]. The fitted samplegrain size varies from about 5 to 12 lm with no obvioustrend among the samples, which is in good agreement withthe FESEM observations. Little variation in grain size re-veals that grain boundary scattering contributes little to

Fig. 11. Low temperature lattice thermal conductivity as a function of temperature for FeSb2+xTe1�x (x = 0–0.25) samples: (a) x = 0; (b) x = 0.05, (c)x = 0.10, (d) x = 0.15; (e) x = 0.20; (f) x = 0.25. The red solid line represents the fitted data. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

Table 2The measured room temperature transverse sound velocity mT, longitudinal sound velocity mL and the calculated sound velocity m according to the relationof m = (2mT + mL)/3, as well as some calculated or fitted physical parameters obtained from the low temperature heat capacity and thermal conductivitymeasurements for CoSb3 and FeSb2+xTe1�x (x = 0–0.25) bulk samples.

Composition

CoSb3 x in FeSb2+xTe1�x

0 0.05 0.1 0.15 0.2 0.25

mT (m s�1) 2735 2589 2446 2451 2512 2533 2499mL (m s�1) 4586 4360 4124 4203 4155 4142 4110m (m s�1) 3352 3179 3005 3035 3060 3069 3036b (mJ mol�1 K�4) 0.24 0.28 0.33 0.31 0.32 0.32 0.34hD (K) 319 303 286 293 289 289 284jL (W mK�1) 9.82 2.89 2.72 2.58 2.46 2.18 1.91L (lm) 11.03 12.05 10.92 5.34 12.00 6.20A (10�42 s3) 4.09 3.96 5.17 9.27 12.85 15.51B (10�18 s K�1) 9.11 7.72 9.47 12.38 18.73 21.27

7702 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

the lattice thermal conductivity reduction in theseFeSb2+xTe1�x samples. Importantly, the fitting resultscould not yield positive C values, indicating that elec-tron–phonon interaction in these p-type skutterudites isnot a significant factor, consistent with a previous study[20]. Umklapp phonon scattering should not depend signif-icantly on whether Te is substituted by Sb or not. More-over, the Debye temperature is a crucial parameter that

determines the Umklapp scattering rate. The Debye tem-perature derived from low temperature heat capacity mea-surements in this research indeed does not varysignificantly among the FeSb2+xT1�x samples. Our fittedB coefficients also do not vary greatly when x < 0.20, sup-porting the argument. The larger B value when x = 0.25may be related to the discrepancy between the data andthe fits at high temperatures where Umklapp scattering

Fig. 12. Low temperature (2–10 K) heat capacity data for the FeSb2+x-

Te1�x (x = 0–0.25) samples and CoSb3. The inset plots Cp/T as a functionof T2 in the temperature range 3–7 K.

Fig. 13. Variation in the experimental and calculated lattice thermalconductivities of (hFeSb2Te)1�x(hFeSb3)x (x = 0–0.25) solid solutions at300 K.

Fig. 14. Calculated ZT values for the FeSb2+xTe1�x (x = 0–0.25) samples.For comparison, some other p-type skutterudites (Co1�xFexSb3 [14],CoSb3�xSnx [22], Yb0.6Fe2Co2Sb12 [47] and Ce0.1La0.2FeCo3Sb12 [48]) arealso included.

G. Tan et al. / Acta Materialia 61 (2013) 7693–7704 7703

dominates, especially for samples with high x values, asshown in Fig. 11. By far the greatest effect on the latticethermal conductivity is due to enhanced point defect scat-tering (parameter A) as x increases. The results can be quitenicely understood if the compounds studied here arethought of as solid solutions of hFeSb2Te and hFeSb3,where h indicates a vacancy, although FeSb3 does not existin itself based on the phase diagram because of the chargeimbalance. (However, in FeSb2+xTe1�x solid solution thesituation may be different. As mentioned above, chargetransfer occurs between Fe2+ and Fe3+, and such a transferprocess would probably stabilize the FeSb3 phase giventhat its content is relatively low.)

To quantify this approach we compared the measuredthermal resistivity with that predicted based on point defectscattering. For high defect concentrations, such as is thecase in a solid solution, the lattice thermal conductivity isgiven by jL = kB/[4pm(A�DT)1/2] [43–46]. Here DT is therelaxation time for phonon–phonon scattering (where D

is a constant and T is the temperature). The phonon–phonon relaxation time can be determined from themeasured thermal conductivity of FeSb2Te at 300 K usingjL ¼ k2

BhD=ðpmhDT Þ ¼ 2:89 W mK�1. This yields DT =3.02 � 10�15 s. The lattice thermal conductivity due tosolid solution formation is thus solved and we can compareit with the experimental data, as illustrated in Fig. 13. Thecalculated lattice thermal conductivity agrees reasonablywell with the experimental values, which suggests that theformation of solid solutions is a plausible explanation forthe decreasing lattice thermal conductivity with increasingx in FeSb2+xTe1�x.

3.4. ZT value

The dimensionless figure of merit ZT for FeSb2+xTe1�x

compounds is calculated based on the measured values of

a, r and j and is shown in Fig. 14. For comparison theZT values for binary CoSb3, the optimized Co1�xFexSb3

[14] and CoSb3�xSnx [22] series, as well as some typicalp-type filled compositions Yb0.6Fe2Co2Sb12 [47] andCe0.1La0.2FeCo3Sb12 [48] are plotted in Fig. 14. It isapparent that ternary FeSb2+xTe1�x compounds show thehighest thermoelectric performance among all unfilledp-type skutterudites. The largest ZT value of �0.65 around800 K is obtained for the sample with x = 0.20, which isabout four times larger than the ZT value of CoSb3 andis comparable with some filled p-type skutterudites. How-ever, this value is still lower than the best ZT value ofthe optimized p-type filled skutterudites (�0.9) because ofthe reduced hole mobility in the ternary FeSb2+xTe1�x

7704 G. Tan et al. / Acta Materialia 61 (2013) 7693–7704

compounds. Future work should focus on finding ways tomaintain a reasonably high mobility in ternaryskutterudites.

4. Conclusions

In summary, we have made a comprehensive study ofthe thermoelectric transport properties of p-type unfilledternary skutterudites FeSb2+xTe1�x (x = 0–0.25). A purephase compound can be obtained when x varies from0.05 to 0.20. The band structure calculation confirms thatthe valence band maximum in ternary FeSb2Te is signifi-cantly broadened compared with CoSb3. This modificationin the band structure gives rise to a large effective mass and,therefore, the high power factors found in these ternarycompounds. XPS analysis confirmed that Fe appears as amixed valence state (namely Fe2+ and Fe3+) in FeSb2Te,and charge transfer scattering between the two states givesrise to a much reduced lattice thermal conductivity com-pared with CoSb3. Meanwhile, the heat carrying phononsare strongly scattered by the formation of a solid solutionbetween the two end members, hFeSb2Te and hFeSb3,where h represents a vacancy, thus leading to a furtherreduction in the lattice thermal conductivity with increas-ing x in FeSb2+xTe1�x. The ZT value is thereby muchimproved, reaching �0.65 around 800 K for the sampleFeSb2.2Te0.8.

Acknowledgements

This work was partially supported by the National BasicResearch Program of China (grant 2013CB632502), theNatural Science Foundation of China (grants nos.51172174 and 51002112) and the International Scienceand Technology Cooperation Program of China (grant2011DFB60150), along with the 111 Project (grantB07040). The work at the University of Michigan (low tem-perature transport measurements, the high temperatureHall effect, and the XPS analysis) is supported by the Cen-ter for Solar and Thermal Energy Research, an EnergyFrontier Research Center funded by the US Departmentof Energy, Office of Science, Office of Basic Energy Sci-ences under award DE-SC0000957.

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