Achieving high power factor and output
power density in p-type half-Heuslers Nb
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He, Ran; Kraemer, Daniel; Mao, Jun; Zeng, Lingping; Jie, Qing;
Lan, Yucheng; Li, Chunhua, et al. “Achieving High Power Factor
and Output Power Density in p-Type Half-Heuslers Nb1-xTixFeSb.”
Proceedings of the National Academy of Sciences 113, no. 48
(November 2016): 13576–13581. © 2016 National Academy of
Sciences
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http://dx.doi.org/10.1073/pnas.1617663113
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National Academy of Sciences (U.S.)
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Final published version
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http://hdl.handle.net/1721.1/108823
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Achieving high power factor and output power density
in p-type half-Heuslers Nb
1-x
Ti
x
FeSb
Ran 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 and Engineering Physics, Morgan State University, Baltimore, MD 21251;eDepartment of Physics, Boston College, Chestnut Hill, MA 02467; andfLawrence Berkeley 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 past two decades have largely been based on decreasing the phonon thermal conductivity. Enhancing the power factor has been less successful in comparison. In this work, a peak power factor of ∼106 μW·cm−1·K−2is 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 power density of∼22 W·cm−2based on a single-leg device operating at between 293 K and 868 K. Such a high-output power density can be beneficial for large-scale power generation applications.
half-Heusler
|
thermoelectric|
power factor|
carrier mobility|
output power densityT
he majority of industrial energy input is lost as waste heat. Converting some of the waste heat into useful electrical power will lead to the reduction of fossil fuel consumption and CO2emission. Thermoelectric (TE) technologies are unique in converting heat into electricity due to their solid-state nature. The ideal device conversion efficiency of TE materials is usually characterized by (1)
η =TH− TC TH · ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1+ ZT p − 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1+ ZT p +TC TH , [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=PF
κtotT [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, electronic thermal 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 and consequently result in a much lower lattice thermal conductivity compared with that of the unmodified bulk counterpart (2). This approach works well for many inorganic TE materials, such as Bi2Te3 (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 the electron 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 widely studied (17–20). To the best of our knowledge, there is no the-oretical upper limit applied to the power factor. Additionally, the output power densityω of a device with hot side at THand cold
side at TCis 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 the reduction of length L, higher power factor favors higher power density 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 HH compounds, 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), and nontoxicity. Recently, the NbFeSb-based p-type materials were found to 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 works mark HH compounds among the most promising candidates for thermoelectric 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 mainly achieved by decreasing the thermal conductivity in many mate-rials. In comparison, there has been much less success in increasing the power factor. We report successful power factor enhance-ment by improving the carrier mobility. Our successful approach could suggest methods to improve the power factor in other materials. Using our approach, the highest power factor reaches ∼106 μW·cm−1·K−2 at room temperature. Such a high power
factor further yields a record output power density in a single-leg device tested between 293 K and 868 K, thus demonstrating the importance 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, or
zren@uh.edu.
This article contains supporting information online atwww.pnas.org/lookup/suppl/doi:10. 1073/pnas.1617663113/-/DCSupplemental.
Nb0.6Ti0.4FeSb0.95Sn0.05at 973 K. However, the composition with
40% Ti substitution strongly scatters the electrons as well. A subsequent work by Fu et al. (24) reported a higher power factor of ∼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 one sintering temperature at 1,123 K (12, 24). Because high-tempera-ture heat treatment for TE materials can be beneficial to TE performance (25), further optimization may be achieved in the NbFeSb system. Here we report the thermoelectric properties of the Nb1-xTixFeSb system with Ti substitution up to x= 0.3 prepared
by 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−2at 300 K in Nb
0.95Ti0.05FeSb. Such an unusually
high power factor has previously been observed only in metallic systems such as YbAl3 and constantan (26, 27). Furthermore, a
record 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 hardly changes within the range of grain sizes studied in this work. Thus, by using a higher HP temperature of 1,373 K and changing the Ti concentration, we have achieved higher power factor and ZT than the previously reported results for the same compositions (24). Materials and Methods
Synthesis. Fifteen grams of raw elements (Nb pieces, 99.9%, and Sb broken rods, 99.9%, Atlantic Metals & Alloy; Fe granules, 99.98%, and Ti foams, 99.9%, Alfa Aesar) are weighed according to stoichiometry. The elements are first arc melted multiple times to form uniform ingots. The ingots are ball milled (SPEX 8000M Mixer/Mill) for 3 h under Ar protection to produce nanopowders. The powders are then consolidated into disks via hot pressing at 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 to characterize the sample phases. Morphology and elemental ratios of the samples are characterized by a scanning electron microscope (SEM) (LEO 1525) and elec-tron probe microanalysis (EPMA) (JXA-8600), respectively. A transmission elecelec-tron microscope (TEM) (JEOL 2100F) is used to observe the detailed microstructures. Measurement. The thermal conductivity is calculated as a product of the thermal diffusivity, specific heat, and mass density that are measured by laser flash (LFA457; Netzsch), a differential scanning calorimeter (DSC 404 C; Netzsch), and an Archimedes’ kit, respectively. Bar-shaped samples with sizes around 2 mm × 2 mm× 10 mm are used for measuring the electrical conductivity and the Seebeck coefficient in a ZEM-3 (ULVAC). Hall concentrations (nH) are measured using the Van der Pauw method in a physical properties measurement system (PPMS) (Quantum Design) under±3 Tesla magnetic induction. The uncertainties for electrical conductivity, Seebeck coefficient, and thermal conductivity are 4%, 5%, and 12%, respectively. In particular, the thermal conductivity un-certainty comprises 4% for thermal diffusivity, 6% for specific heat, and 2% for mass density. As a result, the combined uncertainties for power factor and ZT are 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 Discussion
Enhanced Power Factor with Higher Hot Pressing Temperature.All of the compositions in this work possess pure half-Heusler phases (Fig. S1). Fig. 1 A–F shows the thermoelectric properties of Nb0.95Ti0.05FeSb 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 measurement
value in half-Heusler compounds. When the temperature is higher 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 electrical conductivity values converge and follow the T−3/2law, suggesting that acoustic phonons dominate carrier scattering (28). In con-trast, Fig. 1C shows that the Seebeck coefficient changes little regardless of the hot pressing temperature. The dashed line in Fig. 1C is the calculated Seebeck coefficient using the single parabolic band (SPB) model (29),
S= + kB e 2F1ðηÞ F0ðηÞ− η [6] FnðηÞ = Z∞ 0 χn 1+ eχ−ηdχ, [7]
whereη is related to nHthrough
nH= 4π 2mphkBT h2 3=2 4F2 0ðηÞ 3F−1=2ðηÞ, [8]
whereη, nH, mph, and kBare the reduced Fermi energy, the Hall
carrier 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 therther-mal conductivity, (F) bipolar therther-mal conductivity, (G) ZT, and (H) ZT with T from 300 K to 573 K. The green dashed lines in B and E represent the T−3/2and T−1relations, respectively. The magenta dashed line in C shows the calculated Seebeck coefficient using the SPB model.
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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) is obtained by fitting the Pisarenko relation (as is shown in TE Properties of p-Type Nb1-xTixFeSb). Fn(η) is the Fermi integral
of order n. The good agreement between the calculated result and experimental data shows the adequacy of the SPB model in describing the hole transport.
The total thermal conductivity is a multiplication of bulk density, thermal diffusivity, and specific heat (Fig. S2). The total thermal conductivity is slightly lower for samples hot pressed at lower temperature (Fig. 1D). This is mainly due to the difference in 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 theκefromκtot, we plot the sumκL+ κbipin
Fig. 1E. The sums of κL + κbipare barely affected by the hot
pressing temperature. Furthermore, at temperatures above 773 K, the thermal conductivity trend deviates slightly from the T−1 behavior, indicating some minor bipolar effects even though the Seebeck coefficient seems not to show such an effect. The κbip is calculated using a three-band model (Fig. 1F, Fig. S3,
andTable S1). The peakκbipreaches ∼0.4 W·m−1·K−1at 973
K, a small value compared with theκL.
Because of the enhanced power factor and the almost un-affected thermal conductivity, the ZT improves with elevated hot pressing temperatures (Fig. 1G). This is especially obvious at temperatures below 573 K, as shown in Fig. 1H, where the power factor shows larger differences (Fig. 1A).
SEM images show significant enlargement of the grains with higher hot pressing temperatures (Fig. 2 A–D). The average grain 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, and 1,373 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 K
over those pressed at 1,123 K. Because the lattice thermal con-ductivity changes little with the grain size (Fig. 1E), it is very interesting to investigate why the enlarged grain size affects the electron transport so differently.
Effect of Grain Size on Lattice Thermal Conductivity and Carrier Mobility.The lattice thermal conductivity (κL) of sample pressed
at 1,373 K is obtained by subtracting κe and κbip from κtot. To
describe 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 are given 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 hot
pressing temperatures Composition and hot pressing
temperature nH, 1020cm−3 μH, cm2·V−1·s−1 Edef, eV
Relative
density, % EPMA composition x= 0.04, 1,373 K 6.3 25.2 12.5 99.1 Nb0.95Ti0.04Fe1.03Sb0.98 x= 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 Nb0.94Ti0.05Fe1.01Sb0.99 x= 0.06, 1,373 K 9.3 27.3 11.6 99.3 Nb0.93Ti0.06Fe1.01Sb0.99 x= 0.07, 1,373 K 10.7 26.7 11.6 98.9 Nb0.92Ti0.07Fe0.99Sb1.01 x= 0.10, 1,373 K 15.2 24.0 12.7 99.3 Nb0.89Ti0.1Fe1.00Sb0.99 x= 0.20, 1,373 K 25.7 15.2 13.7 99.1 Nb0.8Ti0.2Fe1.02Sb0.99 x= 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) 1,173 K, (C) 1,273 K, and (D) 1,373 K.
Fig. 3. Effect of grain size on (A)κLand (B)μH(= σRH,300K). The symbols are obtained from the measurements and the lines are fitted using the transport models. The error bars in A and B show 12% and 4% relative error, respectively.
results combining 3P, GB, PD, and EP are shown in TE Properties of p-Type Nb1-xTixFeSb. Here, in Fig. 3A, we show only the effect
of GB scattering. Clearly, the calculated reduction in the lattice thermal 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 phonon transport to the grain size may indicate that the dominant thermal MFPs that contribute to the thermal conductivity of Nb0.95Ti
0.05-FeSb may be less than 0.3μm. We are currently in the process of measuring the phonon MFP (31–36) distributions for Nb0.95Ti0.05FeSb and some preliminary measurement data at
room temperature are included inSupporting Information(Fig. S5). The results suggest that the dominant phonon MFPs of Nb0.95Ti0.05FeSb are in the range of a few tens to a few hundreds
of nanometers. This supports our experimental observation of the insensitivity of the thermal conductivity to the grain size because 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 nHfrom room temperature through
573 K. This assumption is reasonable within the temperature region where the bipolar effect is small and weakly temperature dependent (Fig. 1F). This effect was experimentally observed in another half-Heusler system (29). Thus, the carrier mobility,μH=
σRHfrom room temperature up to 573 K can be approximated by
the measured quantityσRH,300K,
μH= σRH,300K= σ
qnH,300K−1, [10]
where q is the carrier charge, and RH,300Kand nH,300Kare the
Hall 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=2F1=2ðηÞF0ðηÞ 2 ffiffiffi 2 p eπZ4 3ðkBTÞ3=2 v2 ldðNvÞ 5=3 E2 def mph5=2, [11] where vlis the longitudinal phonon velocity and calculated from
the elastic constants (37), d is the mass density, and Nvis the
valley degeneracy. Edef is the deformation potential that is
obtained by extrapolating the high-temperature mobility back to room temperature, using the T−3/2 law. Edef is found to be
∼12 eV for Nb0.95Ti0.05FeSb, a relatively small value compared with
other 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 1 2πmp bkBT 1=2 exp −EB kBT , [12]
where D is the grain size and EBis a commonly fitted barrier energy
of the GB. Combining the two scattering mechanisms according to Matthiessen’s rule yields the expression for Hall mobility:
μ−1
H = μ−1AP+ μ−1GB. [13]
The calculated mobility (μH) with EB∼ 0.1 eV and the measured
quantity σRH,300Kare shown in Fig. 3B. The good fitting
demon-strates the importance of the grain boundaries in scattering carriers below 573 K. At temperatures higher than 573 K the charge carriers are mainly scattered by the acoustic phonons, and thus the mobility curves converge. In addition, Fig. 3B shows that the GB scattering becomes stronger when the grain size is smaller: For decreasing size from 0.5μm to 0.3 μm, the mobility decreases by ∼30%, but for decreasing size from 4.5μm 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. The electrical conductivity (σ) of undoped NbFeSb (i.e., x = 0) in-creases with temperature, consistent with typical semiconductor behavior (Fig. 4A, Inset). For the highly doped samples,σ obeys the T−3/2law, suggesting the dominant acoustic phonon scattering of charge carriers (28). Meanwhile,σ increases with increasing x up to 0.2 because of the increased nH; upon further increase of x to
Fig. 4. Thermoelectric property dependence on temperature for Nb1-xTixFeSb with 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) lattice and bipolar thermal conductivity, and (F) ZT. In A, the purple dashed line and Inset show the∼T−3/2relation and the measured conductivity of undoped NbFeSb, respectively.
Fig. 5. (A) Pisarenko plot at 300 K, with DOS effective mass m*h= 7.5m0for
holes, 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 EP processes are shown. For GB, the grain size is set at 4.5μm. The error bars show 12% relative error.
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0.3,σ decreases due to the decreased μHbecause of the stronger
alloy scattering (Table 1). The Seebeck coefficient varies with nH
in good agreement with the Pisarenko relation using a DOS ef-fective mass mph= 7.5 m0at 300 K (Fig. 5A) (43),
S=8πk 2 B 3eh2 m p hT π 3nH 2=3 . [14]
The power factors of the p-type Nb1-xTixFeSb are very high at
a wide temperature range (Fig. 4C). These values are much higher than those reported by Fu et al. (24), where a temperature of 1,123 K was used for sintering. As shown in Fig. 6A, higher pressing 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 probable reason being the higher sample densities (∼99%) in the current work 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 reaches 1.1 for Nb0.8Ti0.2FeSb (Fig. 4F) at 973 K with a linear upward
trend 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 fitting parameters are listed inSupporting Information (Table S2). As shown in Fig. 5B, the GB scattering is much weaker compared with the other scattering processes. Note that the EP interaction is quite important in this system. Similar results were also reported 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 factors of at least 100μW·cm−1·K−2. It should be noted that YbAl3and
constantan are essentially metals where the anomalous Seebeck coefficients are due to Kondo resonance (44) and virtual bound states (45), respectively. To the best of our knowledge, such high power 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 much lower than Nb0.95Ti0.05FeSb.
Power Output. Due to the higher power factor, higher power output is expected. Following the approach of Kim et al. (46), the output power density (ω) and efficiency (ηmax) under a large
temperature gradient are calculated. With TC= 293 K and a leg
length L= 2 mm, the calculated ω and ηmaxare∼28 W·cm−2and
8.8%, respectively, for Nb0.95Ti0.05FeSb when THis 868 K (Fig. 7
A and B). The corresponding experimental measured values are ∼22 W·cm−2 and 5.6%, respectively, which are lower than the
calculated results, probably due to imperfect device fabrication and possible parasitic heat losses during device measurement (seeSupporting Informationfor details,Fig. S6). To the best of our knowledge, this work obtains the highest power density for bulk thermoelectric materials, which can be important for power generation 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 heat is supplied. However, maintaining the cold side temperature at 293 K could be challenging, and it would be more practical to maintain the cold side temperature at around∼320–340 K by convection heat removal. Thus, we calculate the cold side tem-perature (TC)-dependent output power density (ω) and
effi-ciency (ηmax) with fixed THat 873 K, as shown in Fig. 7 C and D,
respectively. Clearly, the cold side temperature is very important to both the output power density and conversion efficiency.
Fig. 6. TE property comparison. (A) Power factor and (B) ZT of the Nb1-xTixFeSb systems from different reports (23, 24). (C) Power factor and (D) ZT among Nb0.95Ti0.05FeSb, constantan (27), and YbAl3(26), with peak power factor ex-ceeding 100μW·cm−1·K−2.
Fig. 7. Calculated (dotted lines) and measured (symbols) (A) output power density and (B) conversion efficiency of Nb1-xTixFeSb (x= 0.05 and 0.2) samples with 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 leg length∼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.
However, the calculated output power density for Nb0.95Ti0.05FeSb
remains 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 and
E, higher power factor leads to higher output power density with the same leg length. Similarly, higher ZT results in higher effi-ciency, as shown in Fig. 7 B and F.
Conclusions
A higher hot pressing temperature up to 1,373 K is found to be beneficial for higher carrier mobility due to larger grain size. The resulting 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 record
output power density of∼22 W·cm−2is experimentally achieved, which can be important for power generation applications.
ACKNOWLEDGMENTS. This work is funded in part by the US Department of Energy 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 of Energy, Office of Science, Office of Basic Energy Science under Award DE-SC0001299 (output power density measurement), as well as by US Air Force Office 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 through the Texas Center for Superconductivity at the University of Houston.
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