Achieving high power factor and output power densityin p-type half-Heuslers Nb1-xTixFeSbRan Hea,b, Daniel Kraemerc, Jun Maoa,b, Lingping Zengc, Qing Jiea,b, Yucheng Land, Chunhua Lie, Jing Shuaia,b,Hee Seok Kima,b, Yuan Liua,b, David Broidoe, Ching-Wu Chua,b,f,1, Gang Chenc,1, and Zhifeng Rena,b,1

aDepartment of Physics, University of Houston, Houston, TX 77204; bTexas Center for Superconductivity at the University of Houston, University of Houston,Houston, TX 77204; cDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; dDepartment of Physics andEngineering Physics, Morgan State University, Baltimore, MD 21251; eDepartment of Physics, Boston College, Chestnut Hill, MA 02467; and fLawrenceBerkeley National Laboratory, Berkeley, CA 94720

Contributed by Ching-Wu Chu, October 24, 2016 (sent for review September 7, 2016; reviewed by Jing-Feng Li and Silke Paschen)

Improvements in thermoelectric material performance over the pasttwo decades have largely been based on decreasing the phononthermal conductivity. Enhancing the power factor has been lesssuccessful in comparison. In this work, a peak power factor of∼106 μW·cm−1·K−2 is achieved by increasing the hot pressing tem-perature up to 1,373 K in the p-type half-Heusler Nb0.95Ti0.05FeSb.The high power factor subsequently yields a record output powerdensity of ∼22 W·cm−2 based on a single-leg device operating atbetween 293 K and 868 K. Such a high-output power density can bebeneficial for large-scale power generation applications.

half-Heusler | thermoelectric | power factor | carrier mobility |output power density

The majority of industrial energy input is lost as waste heat.Converting some of the waste heat into useful electrical powerwill lead to the reduction of fossil fuel consumption and CO2emission. Thermoelectric (TE) technologies are unique in convertingheat into electricity due to their solid-state nature. The ideal deviceconversion efficiency of TE materials is usually characterized by (1)

η=TH −TC

TH·

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1+ZT

p− 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1+ZTp

+ TCTH, [1]

where ZT is the average thermoelectric figure of merit (ZT)between the hot side temperature (TH) and the cold side tem-perature (TC) of a TE material and is defined as

ZT =PFκtot

T [2]

PF = S2σ [3]

κtot = κL + κe + κbip, [4]

where PF, T, κtot, S, σ, κL, κe, and κbip are the power factor,absolute temperature, total thermal conductivity, Seebeck coeffi-cient, electrical conductivity, lattice thermal conductivity, electronicthermal conductivity, and bipolar thermal conductivity, respec-tively. Higher ZT corresponds to higher conversion efficiency.One effective approach to enhance ZT is through nano-

structuring that can significantly enhance phonon scattering andconsequently result in a much lower lattice thermal conductivitycompared with that of the unmodified bulk counterpart (2). Thisapproach works well for many inorganic TE materials, such asBi2Te3 (2), IV–VI semiconductor compounds (3, 4), lead–anti-mony–silver–tellurium (LAST) (5), skutterudites (6), clathrates(7), CuSe2 (8), Zintl phases (9), half-Heuslers (10–12), MgAgSb(13, 14), Mg2(Si, Ge, Sn) (15, 16), and others.However, nanostructuring is effective only when the grain size

is comparable to or smaller than the phonon mean free path(MFP). In compounds with a phonon MFP shorter than the

nanosized grain diameters, nanostructuring might impair theelectron transport more than the phonon transport, thus po-tentially decreasing the power factor and ZT. In contrast, im-proving ZT by boosting the power factor has not yet been widelystudied (17–20). To the best of our knowledge, there is no the-oretical upper limit applied to the power factor. Additionally, theoutput power density ω of a device with hot side at TH and coldside at TC is directly related to the power factor by (21)

ω=ðTH −TCÞ

4L

2

PF, [5]

where L is the leg length of the TE material and PF is the aver-aged power factor over the leg. As contact resistance limits thereduction of length L, higher power factor favors higher powerdensity when heat can be efficiently supplied and removed.One group of thermoelectric materials that may have high power

factor is half-Heusler (HH) compounds. Among the various HHcompounds, ZrNiSn-based n-type and ZrCoSb-based p-type mate-rials have been widely studied due to their satisfactory ZT ∼ 1 at 873–1,073 K (10), low cost (11), excellent mechanical properties (22), andnontoxicity. Recently, the NbFeSb-based p-type materials were foundto possess good TE properties. Joshi et al. (23) and Fu et al. (24)reported ZT ∼ 1 with Ti substitution. Moreover, a record-high ZT ∼1.5 at 1,200 K was reported with Hf substitution (12). These worksmark HH compounds among the most promising candidates forthermoelectric conversion in the mid-to-high temperature range.As reported by Joshi et al. (23), a high power factor of

∼38 μW·cm−1·K−2 was realized in the p-type half-Heusler

Significance

Thermoelectric technology can boost energy consumption effi-ciency by converting some of the waste heat into useful electricity.Heat-to-power conversion efficiency optimization is mainlyachieved by decreasing the thermal conductivity in many mate-rials. In comparison, there has beenmuch less success in increasingthe power factor. We report successful power factor enhance-ment by improving the carrier mobility. Our successful approachcould suggest methods to improve the power factor in othermaterials. Using our approach, the highest power factor reaches∼106 μW·cm−1·K−2 at room temperature. Such a high powerfactor further yields a record output power density in a single-legdevice tested between 293 K and 868 K, thus demonstrating theimportance of high power factor for power generation applications.

Author contributions: R.H. and Z.R. designed research; R.H. performed research; D.K., L.Z.,Y. Lan, C.L., J.S., H.S.K., Y. Liu, and D.B. contributed new reagents/analytic tools; R.H., J.M., Q.J.,G.C., and Z.R. analyzed data; and R.H., D.K., L.Z., D.B., C.-W.C., G.C., and Z.R. wrote the paper.

Reviewers: J.-F.L., Tsinghua University; and S.P., Vienna University of Technology.

The authors declare no conflict of interest.1To whom correspondence may be addressed. Email: cwchu@uh.edu, gchen2@mit.edu, orzren@uh.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental.

13576–13581 | PNAS | November 29, 2016 | vol. 113 | no. 48 www.pnas.org/cgi/doi/10.1073/pnas.1617663113

Dow

nloa

ded

by g

uest

on

July

3, 2

021

http://crossmark.crossref.org/dialog/?doi=10.1073/pnas.1617663113&domain=pdfmailto:cwchu@uh.edumailto:gchen2@mit.edumailto:zren@uh.eduhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplementalwww.pnas.org/cgi/doi/10.1073/pnas.1617663113

Nb0.6Ti0.4FeSb0.95Sn0.05 at 973 K. However, the composition with40% Ti substitution strongly scatters the electrons as well. Asubsequent work by Fu et al. (24) reported a higher power factorof ∼62 μW·cm−1·K−2 at 400 K in Nb0.92Ti0.08FeSb that was at-tributed to less electron scattering. However, they studied only onesintering temperature at 1,123 K (12, 24). Because high-tempera-ture heat treatment for TE materials can be beneficial to TEperformance (25), further optimization may be achieved in theNbFeSb system. Here we report the thermoelectric properties ofthe Nb1-xTixFeSb system with Ti substitution up to x = 0.3 preparedby using arc melting, ball milling, and hot pressing (HP) at 1,123 K,1,173 K, 1,273 K, and 1,373 K. We find that higher HP tempera-ture enhances the carrier mobility, leading to a high power factor of∼106 μW·cm−1·K−2 at 300 K in Nb0.95Ti0.05FeSb. Such an unusuallyhigh power factor has previously been observed only in metallicsystems such as YbAl3 and constantan (26, 27). Furthermore, arecord output power density of ∼22 W·cm−2 with a leg length∼2 mm is experimentally obtained with TC = 293 K and TH =

868 K. We also observe that the lattice thermal conductivity hardlychanges within the range of grain sizes studied in this work. Thus,by using a higher HP temperature of 1,373 K and changing the Ticoncentration, we have achieved higher power factor and ZT thanthe previously reported results for the same compositions (24).

Materials and MethodsSynthesis. Fifteen grams of raw elements (Nb pieces, 99.9%, and Sb brokenrods, 99.9%, Atlantic Metals & Alloy; Fe granules, 99.98%, and Ti foams,99.9%, Alfa Aesar) are weighed according to stoichiometry. The elementsare first arc melted multiple times to form uniform ingots. The ingots areball milled (SPEX 8000M Mixer/Mill) for 3 h under Ar protection to producenanopowders. The powders are then consolidated into disks via hot pressingat 80 MPa for 2 min at 1,123 K, 1,173 K, 1,273 K, or 1,373 K with an in-creasing temperature rate of ∼100 K/min.

Characterization. An X-ray diffraction machine (PANalytical X’Pert Pro) is used tocharacterize the sample phases. Morphology and elemental ratios of the samplesare characterized by a scanning electron microscope (SEM) (LEO 1525) and elec-tron probe microanalysis (EPMA) (JXA-8600), respectively. A transmission electronmicroscope (TEM) (JEOL 2100F) is used to observe the detailed microstructures.

Measurement. The thermal conductivity is calculated as a product of the thermaldiffusivity, specific heat, and mass density that are measured by laser flash(LFA457; Netzsch), a differential scanning calorimeter (DSC 404 C; Netzsch), andan Archimedes’ kit, respectively. Bar-shaped samples with sizes around 2 mm ×2 mm × 10 mm are used for measuring the electrical conductivity and theSeebeck coefficient in a ZEM-3 (ULVAC). Hall concentrations (nH) are measuredusing the Van der Pauw method in a physical properties measurement system(PPMS) (Quantum Design) under ±3 Tesla magnetic induction. The uncertaintiesfor electrical conductivity, Seebeck coefficient, and thermal conductivity are4%, 5%, and 12%, respectively. In particular, the thermal conductivity un-certainty comprises 4% for thermal diffusivity, 6% for specific heat, and 2% formass density. As a result, the combined uncertainties for power factor and ZTare 10% and 20%, respectively. To increase the readability of the figures pre-sented, we add error bars only to some of the curves (Figs. 3 and 5B).

Results and DiscussionEnhanced Power Factor with Higher Hot Pressing Temperature.All ofthe compositions in this work possess pure half-Heusler phases(Fig. S1). Fig. 1 A–F shows the thermoelectric properties ofNb0.95Ti0.05FeSb with hot pressing temperatures of 1,123 K, 1,173 K,1,273 K, and 1,373 K. As shown in Fig. 1A, the power factor (PF)improves significantly at below 573 K. The peak value reaches∼106 μW·cm−1·K−2 at 300 K and is the highest measurementvalue in half-Heusler compounds. When the temperature ishigher than 873 K, the power factor values converge.Fig. 1B shows that the high power factor is mainly due to the

improved electrical conductivity. Above 673 K, the electricalconductivity values converge and follow the T −3/2 law, suggestingthat acoustic phonons dominate carrier scattering (28). In con-trast, Fig. 1C shows that the Seebeck coefficient changes littleregardless of the hot pressing temperature. The dashed line inFig. 1C is the calculated Seebeck coefficient using the singleparabolic band (SPB) model (29),

S=+�kBe

��2F1ðηÞF0ðηÞ − η

�[6]

FnðηÞ=Z∞

0

χn

1+ eχ−ηdχ, [7]

where η is related to nH through

nH = 4π�2mphkBT

h2

�3=2 4F20ðηÞ3F−1=2ðηÞ

, [8]

where η, nH, mph, and kB are the reduced Fermi energy, the Hallcarrier concentration, the density of states (DOS) effective mass

Fig. 1. Thermoelectric property dependence on temperature for the half-Heusler Nb0.95Ti0.05FeSb hot pressed at 1,123 K, 1,173 K, 1,273 K, and 1,373 K.(A) Power factor, (B) electrical conductivity, (C) Seebeck coefficient, (D) total ther-mal conductivity, (E) lattice plus bipolar thermal conductivity, (F) bipolar thermalconductivity, (G) ZT, and (H) ZTwith T from 300 K to 573 K. The green dashed linesin B and E represent the T −3/2 and T −1 relations, respectively. Themagenta dashedline in C shows the calculated Seebeck coefficient using the SPB model.

He et al. PNAS | November 29, 2016 | vol. 113 | no. 48 | 13577

APP

LIED

PHYS

ICAL

SCIENCE

S

Dow

nloa

ded

by g

uest

on

July

3, 2

021

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF1

of holes, and the Boltzmann constant, respectively. The nH val-ues are obtained through the Hall measurement and are pre-sented in Table 1. The DOS hole effective mass (mph) isobtained by fitting the Pisarenko relation (as is shown in TEProperties of p-Type Nb1-xTixFeSb). Fn(η) is the Fermi integralof order n. The good agreement between the calculated resultand experimental data shows the adequacy of the SPB model indescribing the hole transport.The total thermal conductivity is a multiplication of bulk

density, thermal diffusivity, and specific heat (Fig. S2). The totalthermal conductivity is slightly lower for samples hot pressed atlower temperature (Fig. 1D). This is mainly due to the differencein the electronic thermal conductivity originating from the dif-ference in the electrical conductivity

κe =LσT, [9]

where L is the Lorenz number evaluated using the SPB model(29). By subtracting the κe from κtot, we plot the sum κL + κbip in

Fig. 1E. The sums of κL + κbip are barely affected by the hotpressing temperature. Furthermore, at temperatures above 773 K,the thermal conductivity trend deviates slightly from the T −1

behavior, indicating some minor bipolar effects even thoughthe Seebeck coefficient seems not to show such an effect. Theκbip is calculated using a three-band model (Fig. 1F, Fig. S3,and Table S1). The peak κbip reaches ∼0.4 W·m−1·K−1 at 973K, a small value compared with the κL.Because of the enhanced power factor and the almost un-

affected thermal conductivity, the ZT improves with elevated hotpressing temperatures (Fig. 1G). This is especially obvious attemperatures below 573 K, as shown in Fig. 1H, where the powerfactor shows larger differences (Fig. 1A).SEM images show significant enlargement of the grains with

higher hot pressing temperatures (Fig. 2 A–D). The averagegrain sizes are found to be ∼0.3 μm, ∼0.5 μm, ∼3.0 μm, and∼4.5 μm for samples pressed at 1,123 K, 1,173 K, 1,273 K, and1,373 K, respectively (Fig. S4). Meanwhile, the room tempera-ture (RT) Hall measurement (Table 1) shows an ∼73% en-hancement of Hall mobility (μH) of samples pressed at 1,373 Kover those pressed at 1,123 K. Because the lattice thermal con-ductivity changes little with the grain size (Fig. 1E), it is veryinteresting to investigate why the enlarged grain size affects theelectron transport so differently.

Effect of Grain Size on Lattice Thermal Conductivity and CarrierMobility. The lattice thermal conductivity (κL) of sample pressedat 1,373 K is obtained by subtracting κe and κbip from κtot. Todescribe the lattice thermal conductivity, we use the Klemens (30)model and split the phonon scattering into four different sources:three-phonon (3P) processes, grain boundary (GB) scattering,point defects (PD) scattering, and electron–phonon (EP) in-teraction. The calculation details and the fitting parameters aregiven in Supporting Information, Klemens Model. The complete

Table 1. RT Hall carrier concentration (nH), Hall mobility (μH), deformation potential (Edef),relative density, and EPMA composition of Nb1-xTixFeSb at different Ti concentrations and hotpressing temperatures

Composition andhot pressingtemperature nH, 10

20 cm−3 μH, cm2·V−1·s−1 Edef, eV

Relativedensity, % EPMA composition

x = 0.04, 1,373 K 6.3 25.2 12.5 99.1 Nb0.95Ti0.04Fe1.03Sb0.98x = 0.05, 1,123 K 7.2 15.2 —* 99.4 —x = 0.05, 1,173 K 7.7 20.2 —* 98.9 —x = 0.05, 1,273 K 7.7 24.3 11.8 98.6 —x = 0.05, 1,373 K 8.1 26.3 11.5 99.0 Nb0.94Ti0.05Fe1.01Sb0.99x = 0.06, 1,373 K 9.3 27.3 11.6 99.3 Nb0.93Ti0.06Fe1.01Sb0.99x = 0.07, 1,373 K 10.7 26.7 11.6 98.9 Nb0.92Ti0.07Fe0.99Sb1.01x = 0.10, 1,373 K 15.2 24.0 12.7 99.3 Nb0.89Ti0.1Fe1.00Sb0.99x = 0.20, 1,373 K 25.7 15.2 13.7 99.1 Nb0.8Ti0.2Fe1.02Sb0.99x = 0.30, 1,373 K 30.3 9.3 17.6 98.9 Nb0.69Ti0.3Fe1.02Sb0.98

*Data are not shown because the mobility is strongly affected by GB scattering.

Fig. 2. SEM images of Nb0.95Ti0.05FeSb hot pressed at (A) 1,123 K, (B) 1,173K, (C) 1,273 K, and (D) 1,373 K.

Fig. 3. Effect of grain size on (A) κL and (B) μH (= σRH,300K). The symbols areobtained from the measurements and the lines are fitted using the transportmodels. The error bars in A and B show 12% and 4% relative error, respectively.

13578 | www.pnas.org/cgi/doi/10.1073/pnas.1617663113 He et al.

Dow

nloa

ded

by g

uest

on

July

3, 2

021

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF2http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=ST1http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF4http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=STXThttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=STXTwww.pnas.org/cgi/doi/10.1073/pnas.1617663113

results combining 3P, GB, PD, and EP are shown in TE Propertiesof p-Type Nb1-xTixFeSb. Here, in Fig. 3A, we show only the effectof GB scattering. Clearly, the calculated reduction in the latticethermal conductivity is small with decreasing grain size, only ∼9%when the grain size decreases by more than one order of magni-tude from 4.5 μm to 0.3 μm. The insensitivity of the phonontransport to the grain size may indicate that the dominant thermalMFPs that contribute to the thermal conductivity of Nb0.95Ti0.05-FeSb may be less than 0.3 μm. We are currently in the processof measuring the phonon MFP (31–36) distributions forNb0.95Ti0.05FeSb and some preliminary measurement data atroom temperature are included in Supporting Information (Fig.S5). The results suggest that the dominant phonon MFPs ofNb0.95Ti0.05FeSb are in the range of a few tens to a few hundredsof nanometers. This supports our experimental observation ofthe insensitivity of the thermal conductivity to the grain sizebecause the grain sizes in our measurement range are signifi-cantly larger than the dominant phonon MFPs.To analyze the measured carrier mobility, we assume a weak

temperature dependence of nH from room temperature through573 K. This assumption is reasonable within the temperatureregion where the bipolar effect is small and weakly temperaturedependent (Fig. 1F). This effect was experimentally observed inanother half-Heusler system (29). Thus, the carrier mobility, μH =σRH from room temperature up to 573 K can be approximated bythe measured quantity σRH,300K,

μH = σRH,300K = σ�qnH,300K

�−1, [10]where q is the carrier charge, and RH,300K and nH,300K are theHall coefficient and carrier concentration at 300 K, respectively.At high temperatures, the dominant electron scattering is from

acoustic phonons (AP), and thus the mobility is expressed as

μAP =F0ðηÞ

2F1=2ðηÞ2

ffiffiffi2

peπZ4

3ðkBTÞ3=2v2l dðNvÞ5=3E2def

�mph

�5=2, [11]

where vl is the longitudinal phonon velocity and calculated fromthe elastic constants (37), d is the mass density, and Nv is thevalley degeneracy. Edef is the deformation potential that isobtained by extrapolating the high-temperature mobility back toroom temperature, using the T −3/2 law. Edef is found to be∼12 eV for Nb0.95Ti0.05FeSb, a relatively small value compared withother TE systems like InSb (∼33 eV) (38), PbTe (∼22.5 eV) (39),and Bi2Te3 (∼20 eV) (40), suggesting a weaker EP in the HH systems(29) that can benefit the electron transport and the power factor.The mobility with the GB scattering is written as (41, 42)

μGB =De�

12πmpbkBT

�1=2exp

�−EBkBT

�, [12]

whereD is the grain size and EB is a commonly fitted barrier energyof the GB. Combining the two scattering mechanisms according toMatthiessen’s rule yields the expression for Hall mobility:

μ−1H = μ−1AP + μ

−1GB. [13]

The calculated mobility (μH) with EB ∼ 0.1 eV and the measuredquantity σRH,300K are shown in Fig. 3B. The good fitting demon-strates the importance of the grain boundaries in scattering carriersbelow 573 K. At temperatures higher than 573 K the charge carriersare mainly scattered by the acoustic phonons, and thus the mobilitycurves converge. In addition, Fig. 3B shows that the GB scatteringbecomes stronger when the grain size is smaller: For decreasing sizefrom 0.5 μm to 0.3 μm, the mobility decreases by ∼30%, but fordecreasing size from 4.5 μm to 3.0 μm, the mobility drops by only 5%.

TE Properties of p-Type Nb1-xTixFeSb. Fig. 4 shows the TE proper-ties of Nb1-xTixFeSb pressed at 1,373 K with x = 0, 0.04, 0.05,0.06, 0.07, 0.1, 0.2, and 0.3 as a function of temperature. Theelectrical conductivity (σ) of undoped NbFeSb (i.e., x = 0) in-creases with temperature, consistent with typical semiconductorbehavior (Fig. 4A, Inset). For the highly doped samples, σ obeysthe T −3/2 law, suggesting the dominant acoustic phonon scatteringof charge carriers (28). Meanwhile, σ increases with increasing xup to 0.2 because of the increased nH; upon further increase of x to

Fig. 4. Thermoelectric property dependence on temperature for Nb1-xTixFeSbwith x = 0, 0.04, 0.05, 0.06, 0.07, 0.1, 0.2, and 0.3. (A) Electrical conductivity, (B)Seebeck coefficient, (C) power factor, (D) total thermal conductivity, (E) latticeand bipolar thermal conductivity, and (F) ZT. In A, the purple dashed line andInset show the ∼T−3/2 relation and the measured conductivity of undopedNbFeSb, respectively.

Fig. 5. (A) Pisarenko plot at 300 K, with DOS effective mass m*h = 7.5m0 forholes, showing the validity of the SPB model in describing hole transport.(B) The contribution of different phonon scattering mechanisms to the lat-tice thermal conductivity of Nb1-xTixFeSb at RT. The 3P, GB, PD, and EPprocesses are shown. For GB, the grain size is set at 4.5 μm. The error barsshow 12% relative error.

He et al. PNAS | November 29, 2016 | vol. 113 | no. 48 | 13579

APP

LIED

PHYS

ICAL

SCIENCE

S

Dow

nloa

ded

by g

uest

on

July

3, 2

021

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=STXThttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF5http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF5

0.3, σ decreases due to the decreased μH because of the strongeralloy scattering (Table 1). The Seebeck coefficient varies with nHin good agreement with the Pisarenko relation using a DOS ef-fective mass mph = 7.5 m0 at 300 K (Fig. 5A) (43),

S=8πk2B3eh2

 mphT�

π

3nH

�2=3. [14]

The power factors of the p-type Nb1-xTixFeSb are very high ata wide temperature range (Fig. 4C). These values are muchhigher than those reported by Fu et al. (24), where a temperatureof 1,123 K was used for sintering. As shown in Fig. 6A, higherpressing temperature accounts for the higher power factor.Moreover, even when comparing the samples pressed at 1,123 K,our work also shows higher power factor, with the probablereason being the higher sample densities (∼99%) in the currentwork compared with those reported by Fu et al. (24) (∼95%).The total thermal conductivities (κtot) are shown in Fig. 4D.

With increased Ti doping, the lattice thermal conductivity de-creases significantly (Fig. 4E). As a result, the peak ZT reaches1.1 for Nb0.8Ti0.2FeSb (Fig. 4F) at 973 K with a linear upwardtrend suggesting even higher ZT at higher operating tempera-tures (Figs. 4F and 6B).To analyze the RT lattice thermal conductivity, we use the

Klemens model incorporating the 3P, GB, PD, and EP pro-cesses, as mentioned in the previous section (30). The fittingparameters are listed in Supporting Information (Table S2). Asshown in Fig. 5B, the GB scattering is much weaker comparedwith the other scattering processes. Note that the EP interactionis quite important in this system. Similar results were alsoreported by Fu et al. (12) with Zr and Hf doping.Fig. 6 C and D compares the power factor and ZT, re-

spectively, of a few materials with very high power factor, in-cluding YbAl3 single crystal (26), Nb0.95Ti0.05FeSb (this work),and constantan (27). These materials possess peak power factorsof at least 100 μW·cm−1·K−2. It should be noted that YbAl3 andconstantan are essentially metals where the anomalous Seebeckcoefficients are due to Kondo resonance (44) and virtual boundstates (45), respectively. To the best of our knowledge, such highpower factor above RT has never been realized before in semi-conductor-based TE materials. Despite similar power factors,the other two materials possess very high thermal conductivity

because they are essentially metals, and thus their ZT are muchlower than Nb0.95Ti0.05FeSb.

Power Output. Due to the higher power factor, higher poweroutput is expected. Following the approach of Kim et al. (46),the output power density (ω) and efficiency (ηmax) under a largetemperature gradient are calculated. With TC = 293 K and a leglength L = 2 mm, the calculated ω and ηmax are ∼28 W·cm−2 and8.8%, respectively, for Nb0.95Ti0.05FeSb when TH is 868 K (Fig. 7A and B). The corresponding experimental measured values are∼22 W·cm−2 and 5.6%, respectively, which are lower than thecalculated results, probably due to imperfect device fabricationand possible parasitic heat losses during device measurement(see Supporting Information for details, Fig. S6). To the best ofour knowledge, this work obtains the highest power density forbulk thermoelectric materials, which can be important for powergeneration applications (12, 23, 47, 48).For power generation applications, the hot side temperature

could be easily maintained at about 873 K as long as enough heatis supplied. However, maintaining the cold side temperature at293 K could be challenging, and it would be more practical tomaintain the cold side temperature at around ∼320–340 K byconvection heat removal. Thus, we calculate the cold side tem-perature (TC)-dependent output power density (ω) and effi-ciency (ηmax) with fixed TH at 873 K, as shown in Fig. 7 C and D,respectively. Clearly, the cold side temperature is very importantto both the output power density and conversion efficiency.

Fig. 6. TE property comparison. (A) Power factor and (B) ZT of the Nb1-xTixFeSbsystems from different reports (23, 24). (C) Power factor and (D) ZT amongNb0.95Ti0.05FeSb, constantan (27), and YbAl3 (26), with peak power factor ex-ceeding 100 μW·cm−1·K−2.

Fig. 7. Calculated (dotted lines) and measured (symbols) (A) output powerdensity and (B) conversion efficiency of Nb1-xTixFeSb (x = 0.05 and 0.2) sampleswith the cold side temperature at ∼293 K and the leg length ∼2 mm, calcu-lated (C) output power density and (D) conversation efficiency of Nb1-xTixFeSb(x = 0.05 and 0.2) samples with hot side temperature at ∼873 K and the leglength ∼2 mm but varying the cold side temperature, and comparison of (E)power factor and (F) ZT of Nb0.95Ti0.05FeSb and Nb0.8Ti0.2FeSb.

13580 | www.pnas.org/cgi/doi/10.1073/pnas.1617663113 He et al.

Dow

nloa

ded

by g

uest

on

July

3, 2

021

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=STXThttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=ST2http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=STXThttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617663113/-/DCSupplemental/pnas.201617663SI.pdf?targetid=nameddest=SF6www.pnas.org/cgi/doi/10.1073/pnas.1617663113

However, the calculated output power density for Nb0.95Ti0.05FeSbremains quite high (∼25 W·cm−2) under more attainable temper-ature boundaries (TC = 330 K and TH = 873 K).Fig. 7 E and F shows the power factor and ZT, respectively, of

Nb0.95Ti0.05FeSb and Nb0.8Ti0.2FeSb. Clearly, from Fig. 7 A andE, higher power factor leads to higher output power density withthe same leg length. Similarly, higher ZT results in higher effi-ciency, as shown in Fig. 7 B and F.

ConclusionsA higher hot pressing temperature up to 1,373 K is found to bebeneficial for higher carrier mobility due to larger grain size. Theresulting increase in electrical conductivity leads to a much

higher power factor of ∼106 μW·cm−1·K−2 in the p-type half-Heusler Nb0.95Ti0.05FeSb. With the high power factor, a recordoutput power density of ∼22 W·cm−2 is experimentally achieved,which can be important for power generation applications.

ACKNOWLEDGMENTS. This work is funded in part by the US Department ofEnergy under Contract DE-SC0010831 (materials synthesis and characteriza-tions) and in part by the “Solid State Solar Thermal Energy Conversion Cen-ter,” an Energy Frontier Research Center funded by the US Department ofEnergy, Office of Science, Office of Basic Energy Science under Award DE-SC0001299 (output power density measurement), as well as by US Air ForceOffice of Scientific Research Grant FA9550-15-1-0236, T. L. L. Temple Founda-tion, John J. and Rebecca Moores Endowment, and the State of Texas throughthe Texas Center for Superconductivity at the University of Houston.

1. Ioffe AF (1957) Semiconductor Thermoelements and Thermoelectric Cooling (In-fosearch, London).

2. Poudel B, et al. (2008) High-thermoelectric performance of nanostructured bismuthantimony telluride bulk alloys. Science 320(5876):634–638.

3. Zhao LD, et al. (2014) Ultralow thermal conductivity and high thermoelectric figure ofmerit in SnSe crystals. Nature 508(7496):373–377.

4. Zhang Q, et al. (2013) High thermoelectric performance by resonant dopant indium innanostructured SnTe. Proc Natl Acad Sci USA 110(33):13261–13266.

5. Hsu KF, et al. (2004) Cubic AgPbmSbTe2+m: Bulk thermoelectric materials with highfigure of merit. Science 303(5659):818–821.

6. Shi X, et al. (2011) Multiple-filled skutterudites: High thermoelectric figure of meritthrough separately optimizing electrical and thermal transports. J Am Chem Soc133(20):7837–7846.

7. Saramat A, et al. (2006) Large thermoelectric figure of merit at high temperature inCzochralski-grown clathrate Ba8Ga16Ge30. J Appl Phys 99(2):023708.

8. Liu H, et al. (2012) Copper ion liquid-like thermoelectrics. Nat Mater 11(5):422–425.9. Shuai J, et al. (2016) Higher thermoelectric performance of Zintl phases (Eu0.5Yb0.5)1-xCaxMg2Bi2

by band engineering and strain fluctuation. Proc Natl Acad Sci USA 113(29):E4125–E4132.

10. Chen S, Ren ZF (2013) Recent progress of half-Heusler for moderate temperaturethermoelectric applications. Mater Today 16(10):387–395.

11. He R, et al. (2014) Investigating the thermoelectric properties of p-type half-HeuslerHfx(ZrTi)1-xCoSb0.8Sn0.2 by reducing Hf concentration for power generation. RSCAdvances 4(110):64711–64716.

12. Fu C, et al. (2015) Realizing high figure of merit in heavy-band p-type half-Heuslerthermoelectric materials. Nat Commun 6:8144.

13. Zhao HZ, et al. (2014) High thermoelectric performance of MgAgSb-based materials.Nano Energy 7:97–103.

14. Kraemer D, et al. (2015) High thermoelectric conversion efficiency of MgAgSb-basedmaterial with hot-pressed contacts. Energy Environ Sci 8(4):1299–1308.

15. Liu W, et al. (2015) n-type thermoelectric material Mg2Sn0.75Ge0.25 for high powergeneration. Proc Natl Acad Sci USA 112(11):3269–3274.

16. Liu W, et al. (2012) Convergence of conduction bands as a means of enhancing thermo-electric performance of n-type Mg2Si(1-x)Sn(x) solid solutions. Phys Rev Lett 108(16):166601.

17. Pei Y, et al. (2011) Convergence of electronic bands for high performance bulkthermoelectrics. Nature 473(7345):66–69.

18. Heremans JP, et al. (2008) Enhancement of thermoelectric efficiency in PbTe by dis-tortion of the electronic density of states. Science 321(5888):554–557.

19. Yu B, et al. (2012) Enhancement of thermoelectric properties by modulation-dopingin silicon germanium alloy nanocomposites. Nano Lett 12(4):2077–2082.

20. Jie Q, et al. (2012) Electronic thermoelectric power factor and metal-insulator tran-sition in FeSb2. Phys Rev B 86(11):115121.

21. Narducci D (2011) Do we really need high thermoelectric figures of merit? A criticalappraisal to the power conversion efficiency of thermoelectric materials. Appl PhysLett 99(10):102104.

22. He R, et al. (2015) Studies on mechanical properties of thermoelectric materials bynanoindentation. Phys Status Solidi A Appl Mater Sci 212(10):2191–2195.

23. Joshi G, et al. (2014) NbFeSb-based p-type half-Heuslers for power generation ap-plications. Energy Environ Sci 7(12):4070–4076.

24. Fu CG, Zhu TJ, Liu YT, Xie HH, Zhao XB (2015) Band engineering of high performancep-type FeNbSb based half-Heusler thermoelectric materials for figure of merit ZT > 1.Energy Environ Sci 8(1):216–220.

25. Chen L, et al. (2015) Uncovering high thermoelectric figure of merit in (Hf,Zr)NiSnhalf-Heusler alloys. Appl Phys Lett 107(4):041902.

26. Rowe DM, Kuznetsov VL, Kuznetsova LA, Min G (2002) Electrical and thermal trans-port properties of intermediate-valence YbAl3. J Phys D Appl Phys 35(17):2183–2186.

27. Mao J, et al. (2015) High thermoelectric power factor in Cu-Ni alloy originate frompotential barrier scattering of twin boundaries. Nano Energy 17:279–289.

28. Brooks H (1955) Advances in Electronics and Electron Physics (Academic, New York).29. Xie HH, et al. (2013) Beneficial contribution of alloy disorder to electron and phonon

transport in half-Heusler thermoelectric materials. Adv Funct Mater 23(41):5123–5130.30. Klemens P (1951) The thermal conductivity of dielectric solids at low temperatures.

Proc R Soc Lond A Math Phys Sci 208(1092):108–133.31. Chiloyan V, et al. (2016) Variational approach to extracting the phonon mean free path dis-

tribution from the spectral phonon Boltzmann transport equation. Phys Rev B 93(15):155201.32. Chiloyan V, et al. (2016) Variational approach to solving the spectral Boltzmann trans-

port equation in transient thermal grating for thin films. J Appl Phys 120(2):025103.

33. Hu Y, Zeng L, Minnich AJ, Dresselhaus MS, Chen G (2015) Spectral mapping of thermalconductivity through nanoscale ballistic transport. Nat Nanotechnol 10(8):701–706.

34. Zeng L, et al. (2015) Measuring phonon mean free path distributions by probingquasiballistic phonon transport in grating nanostructures. Sci Rep 5:17131.

35. Zeng LP, Chen G (2014) Disparate quasiballistic heat conduction regimes from peri-odic heat sources on a substrate. J Appl Phys 116(6):064307.

36. Zeng LP, et al. (2016) Monte Carlo study of non-diffusive relaxation of a transientthermal grating in thin membranes. Appl Phys Lett 108(6):063107.

37. Hong AJ, et al. (2016) Full-scale computation for all the thermoelectric property pa-rameters of half-Heusler compounds. Sci Rep 6:22778.

38. Tukioka K (1991) The determination of the deformation potential constant of theconduction band in InSb by the electron mobility in the intrinsic range. Jpn J ApplPhys 30(2):212–217.

39. Pei YZ, et al. (2014) Optimum carrier concentration in n-type PbTe thermoelectrics.Adv Energy Mater 4(13):1400486.

40. Koumoto K, Mori T (2013) Thermoelectric Nanomaterials (Springer, Berlin).41. Seto J (1975) The electrical properties of polycrystalline silicon films. J Appl Phys

46(12):5247–5254.42. de Boor J, et al. (2014) Microstructural effects on thermoelectric efficiency: A case

study on magnesium silicide. Acta Mater 77:68–75.43. Cutler M, Fitzpatrick RL, Leavy JF (1963) The conduction band of cerium sulfide

Ce3-xS4. J Phys Chem Solids 24(2):319–327.44. Walter U, Holland-Moritz E, Fisk Z (1991) Kondo resonance in the neutron spectra of

intermediate-valent YbAl3. Phys Rev B Condens Matter 43(1):320–325.45. Foiles CL (1968) Thermoelectric power of dilute Cu-Ni alloys in a magnetic field. Phys

Rev 169(3):471–476.46. Kim HS, Liu W, Chen G, Chu CW, Ren Z (2015) Relationship between thermoelectric

figure of merit and energy conversion efficiency. Proc Natl Acad Sci USA 112(27):8205–8210.

47. Hu X, et al. (2016) Power generation from nanostructured PbTe-based thermoelectrics:Comprehensive development frommaterials to modules. Energy Environ Sci 9(2):517–529.

48. Salvador JR, et al. (2014) Conversion efficiency of skutterudite-based thermoelectricmodules. Phys Chem Chem Phys 16(24):12510–12520.

49. Aukerman L, Willardson R (1960) High temperature Hall coefficient in GaAs. J ApplPhys 31(5):939–940.

50. Liu WS, et al. (2016) New insight into the material parameter B to understand theenhanced thermoelectric performance of Mg2Sn1-x-yGexSby. Energy Environ Sci 9(2):530–539.

51. Tang Y, et al. (2015) Convergence of multi-valley bands as the electronic origin of highthermoelectric performance in CoSb3 skutterudites. Nat Mater 14(12):1223–1228.

52. Minnich AJ, et al. (2011) Thermal conductivity spectroscopy technique to measurephonon mean free paths. Phys Rev Lett 107(9):095901.

53. Minnich AJ (2012) Determining phonon mean free paths from observations of qua-siballistic thermal transport. Phys Rev Lett 109(20):205901.

54. Chen G (1996) Nonlocal and nonequilibrium heat conduction in the vicinity ofnanoparticles. J Heat Transfer 118(3):539–545.

55. Kang K, Koh YK, Chiritescu C, Zheng X, Cahill DG (2008) Two-tint pump-probemeasurements using a femtosecond laser oscillator and sharp-edged optical filters.Rev Sci Instrum 79(11):114901.

56. Schmidt AJ, Chen X, Chen G (2008) Pulse accumulation, radial heat conduction, andanisotropic thermal conductivity in pump-probe transient thermoreflectance. Rev SciInstrum 79(11):114902.

57. Ashcroft N, Mermin N (1976) Solid State Physics (Saunders College, Philadelphia).58. Klemens P (1955) The scattering of low-frequency lattice waves by static imperfec-

tions. Proc Phys Soc A 68(12):1113–1128.59. Abeles B (1963) Lattice thermal conductivity of disordered semiconductor alloys at

high temperatures. Phys Rev 131(5):1906–1911.60. Slack G (1962) Thermal conductivity of MgO, Al2O3, MgAl2O4, and Fe3O4 crystals from

3 to 300 °K. Phys Rev 126(2):427–441.61. Roufosse M, Klemens P (1973) Thermal conductivity of complex dielectric crystals.

Phys Rev B 7(12):5379–5386.62. Geng H, Meng X, Zhang H, Zhang J (2014) Lattice thermal conductivity of nano-

grained half-Heusler solid solutions. Appl Phys Lett 104(20):202104.63. Shi X, Pei Y, Snyder GJ, Chen L (2011) Optimized thermoelectric properties of Mo3Sb7-xTex

with significant phonon scattering by electrons. Energy Environ Sci 4(10):4086–4095.64. Rogl G, et al. (2016) Mechanical properties of half-Heusler alloys. Acta Mater 107:

178–195.

He et al. PNAS | November 29, 2016 | vol. 113 | no. 48 | 13581

APP

LIED

PHYS

ICAL

SCIENCE

S

Dow

nloa

ded

by g

uest

on

July

3, 2

021