Band engineering of high performance p-type FeNbSb based half-Heusler thermoelectric materials for figure of merit zT > 1

Abstract

We report new p-type FeNb_1−xTi_xSb (0.04 ≤ x ≤ 0.24) half-Heusler thermoelectric materials with a maximum zT of 1.1 at 1100 K, which is twice that of the ZrCoSb half-Heusler alloys. The electrical properties are optimized by a tradeoff between the band effective mass and mobility via a band engineering approach. A high content of Ti up to x = 0.2 optimizes the power factor and reduces the lattice thermal conductivity. In view of abundantly available elements, good stability and high zT, FeNb_1−xTi_xSb alloys could be promising materials for high temperature power generation.

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Broader context

Thermoelectric materials enable heat to be directly converted into electricity. However, the relatively poor efficiency, low stability and high cost of these materials have limited their potential as a practical alternative to conventional power generation technologies. For thermoelectric conversion, a large temperature difference across the devices and a high dimensionless figure of merit zT of thermoelectric materials will result in enhanced conversion efficiency. In recent years, half-Heusler (HH) thermoelectric materials have attracted much attention due to their high temperature stability and potential for high temperature power generation. However, developing high performance p-type HH compounds is a big challenge. In this work, we report a new kind of p-type FeNb_1−xTi_xSb HH thermoelectric material with a maximum zT of 1.1 at 1100 K, and the thermoelectric properties are optimized by a band engineering approach via the tradeoff between the band effective mass and carrier mobility. In view of abundantly available elements, good stability and high zT, FeNb_1−xTi_xSb HH alloys could be promising materials for high temperature power generation.

Thermoelectric (TE) materials allow for direct thermal-to-electric energy conversion without hazardous liquids, moving parts, or greenhouse emissions. The demand for new sustainable energy technology, the environmental concern for the use of fossil fuels, and the ubiquitous heat source have consistently driven the pursuit of higher performance TE materials.¹ The conversion efficiency of a TE device strongly depends on the materials' dimensionless figure of merit zT, zT = α²σT/(κ_e + κ_L), where α, σ, T, κ_e and κ_L are respectively the Seebeck coefficient, the electrical conductivity, the absolute temperature, and the electron and lattice components of total thermal conductivity κ.² Developing bulk materials with high zT is the central theme for the large scale application of TE technology. To date, Bi₂Te₃-based materials are the most efficient for refrigeration near room temperature,³ PbTe, filled skutterudites and Mg₂(Si, Sn) are promising for mid-temperature power generation,^4–7 and SiGe and Yb₁₄MnSb₁₁ are known for high-temperature TE application.^8,9

Half-Heusler (HH) compounds, with a valence electron count of 8 or 18, have recently been identified as one of the most promising TE materials for high temperature power generation due to their excellent electrical and mechanical properties and high temperature stability.^10–14 The n-type (Zr, Hf)NiSn based HH compounds have exhibited the maximum zT as high as ∼1.0 at 1000 K, which exceeds the industry benchmark set by SiGe high temperature alloys (zT ∼ 0.8 for n-type and 0.6 for p-type).^10–14 However, the typical p-type HH compounds, (Zr, Hf)CoSb, have the reproducible highest zT of only ∼0.5.^10,14 Therefore, developing high performance p-type HH compounds is imperative to achieve high efficiency high temperature TE devices based on HH compounds, because the practical systems require both n- and p-type materials with similar properties.¹⁰

FeVSb based HH compounds with abundantly available constituent elements, despite the high power factor α²σ (∼4.5 × 10⁻³ W m⁻¹ K⁻² at 300 K), have been paid less attention due to their high lattice thermal conductivity (∼10 W m⁻¹ K⁻¹ at 300 K) and low zT (∼0.3 for n-type).^15,16 In our previous study, a significantly reduced thermal conductivity of 5.5 W m⁻¹ K⁻¹ at 300 K was obtained for the FeV_0.6Nb_0.4Sb solid solutions by the enhanced point defect scattering of phonons.¹⁶ Fe(V, Nb)Sb solid solutions can be promising p-type TE materials due to their high band degeneracy and reduced lattice thermal conductivity. However, there are two factors hindering the further improvement of the alloys' TE performance: one is that the optimal carrier concentration cannot be reached due to the limited solubility of the Ti dopant on V/Nb sites; the other is that the low carrier mobility leads to a relatively low power factor (∼3.0 × 10⁻³ W m⁻¹ K⁻² at 900 K).¹⁵

If acoustic phonon scattering dominates the carrier transport, zT ∝ N_v/m^*_bκ_L,¹⁷ where N_v is the number of degenerate valleys and m^*_b is the band effective mass. This suggests that multiple degenerate valleys with low band effective mass and low lattice thermal conductivity are beneficial for high zT.^4,5,18,19 In fact, most of the recent studies on enhancing zT have focused on two strategies: one is to reduce the lattice thermal conductivity κ_L by alloying or nanostructuring to enhance phonon scattering;^1,5,20,21 the other is to improve the electrical properties by band engineering, such as band convergence^4,22 or resonant states.²³

p-type Fe(V, Nb)Sb HH solid solutions have high band degeneracy and relatively low lattice thermal conductivity.¹⁵ Therefore, further enhancement of zT may be realized by reducing the band effective mass to improve the mobility. Generally, the heavier band gives a larger band effective mass. Electronic band calculations show that the valence band maxima (VBM) of both FeVSb and FeNbSb locate at the L point with twofold orbital degeneracy,^24,25 and the valence band of FeVSb is flatter than that of FeNbSb.²⁴ Therefore, increasing the Nb content in the Fe(V_1−yNb_y)Sb solid solutions may achieve a lower valence band effective mass and consequently higher carrier mobility. Moreover, the decrease in band effective mass can lead to the decrease in optimal carrier concentration,¹⁸ which is favorable for p-type Fe(V, Nb)_1−xTi_xSb due to the limited solubility of Ti.¹⁵ Furthermore, FeNbSb has a larger band gap E_g (∼0.54 eV) than that of FeVSb (∼0.34 eV),^15,25 and increasing the Nb content in Fe(V_1−yNb_y)_1−xTi_xSb will prevent the degradation of the TE performance at high temperatures due to the thermally activated minority carriers.

In this work, we indeed obtain a high zT of 1.1 at 1100 K for FeNb_1−xTi_xSb without V substitution, which is the highest reported value for p-type HH compounds. The decreased band effective mass and the increased band gap with increasing Nb content in Fe(V_1−yNb_y)_1−xTi_xSb lead to the enhanced carrier mobility and diminished bipolar conduction at high temperature, respectively, and a high content of Ti doping not only optimizes the carrier concentration but also guarantees the reduced lattice thermal conductivity in FeNb_1−xTi_xSb (0.04 ≤ x ≤ 0.24), which all contribute to high zT, demonstrating that p-type FeNb_1−xTi_xSb alloys are promising TE materials for high temperature power generation.

Electronic band structures of FeVSb and FeNbSb have been investigated by the first principles calculations (Fig. S1, ESI†) and our results are similar to those previously reported.^24,25 The valence band of FeVSb is flatter than that of FeNbSb, indicating that increasing the Nb content in Fe(V_1−yNb_y)_1−xTi_xSb will lead to a lower band effective mass (Table S1, ESI†).

The carrier concentration dependence of the Seebeck coefficient for Fe(V_1−yNb_y)_1−xTi_xSb samples at room temperature is shown in Fig. 1(a), which agrees well with the calculated curves using a single parabolic band (SPB) model.¹² A distinct decrease of band effective mass m^*_b can be found with increasing Nb content y, varying from 2.5m_e for p-type Fe(V_0.6Nb_0.4)_1−xTi_xSb to 1.6m_e for FeNb_1−xTi_xSb. The unchanged band effective mass with increasing Ti content in Fe(V_1−yNb_y)_1−xTi_xSb samples indicates that substituting Ti at V/Nb sites has no effect on the valence band structure. This can be understood from the fact that the valence band structure is dominated by the electronic character of the Fe element (Fig. S1, ESI†), and is also consistent with the previous results by Jodin et al.²⁵

Fig. 1 (a) Seebeck coefficient versus the Hall carrier concentration for Fe(V_1−yNb_y)_1−xTi_xSb samples at 300 K. (b) Mobility versus carrier concentration for the samples at 300 K. (c) Carrier concentration dependence of power factor at 900 K. The inset in (c) shows schematic representation of valence and conduction band structures of FeVSb (red solid line) and FeNbSb (blue dotted line). (d) Temperature dependence of zT of FeNb_1−xTi_xSb samples. The theoretical curves (solid lines) were calculated by the SPB model.

The decrease in m^*_b is beneficial for the increase of carrier mobility. As shown in Fig. 1(b), the carrier mobility of FeNb_1−xTi_xSb is twice as high as that of Fe(V_0.6Nb_0.4)_1−xTi_xSb. The room temperature carrier mobility of FeNb_1−xTi_xSb is about 15–25 cm² V⁻¹ s⁻¹, which is higher than that of other Fe-containing p-type TE materials.^26,27 For example, the carrier mobility of p-type FeVSb is about 1–4 cm² V⁻¹ s⁻¹,²⁶ while p-type Fe-based skutterudites have a carrier mobility of ≤10 cm² V⁻¹ s⁻¹.²⁷ The low mobility in these Fe-containing p-type TE materials is due to the heavy band mass resulting from the spatially localized nature of transition metal 3d orbitals.²⁸ In addition to the decrease in m^*_b, the reduced alloy scattering of carriers should also contribute to the increased carrier mobility in p-type FeNb_1−xTi_xSb, compared to Fe(V_0.6Nb_0.4)_1−xTi_xSb solid solutions.

The decreased m^*_b leads to the low Seebeck coefficient but contributes more to the enhanced carrier mobility. As a result, the optimal power factor distinctly increases with decreasing m^*_b (Fig. 1(c)), while the optimal carrier concentration p_opt decreases with the decreased m^*_b. For the FeNb_1−xTi_xSb system, the p_opt is ∼2.6 × 10²¹ cm⁻³, lower than that of the Fe(V_1−yNb_y)_1−xTi_xSb solid solutions. In Fe(V_0.6Nb_0.4)_1−xTi_xSb, the experimentally obtained maximum carrier concentration is only ∼1.5 × 10²¹ cm⁻³ due to the limited solubility of Ti, far below the p_opt of ∼6 × 10²¹ cm⁻³.¹⁵ Decreasing m^*_b makes it possible to achieve the optimal power factor at a lower carrier concentration in the FeNb_1−xTi_xSb system. A similar phenomenon is also found in the high performance PbTe system.¹⁸

Therefore, the TE properties of p-type Ti doped FeNb_1−xTi_xSb (x = 0.04–0.24) alloys were systematically investigated. Fig. 1(d) indeed shows that the zT of FeNb_1−xTi_xSb samples increases with increasing Ti content and a very high zT of 1.1 is reached at 1100 K for FeNb_0.8Ti_0.2Sb, which is the highest reported value for p-type HH compounds.

The transport features of FeNb_1−xTi_xSb will be discussed in detail below. The electrical conductivity of FeNb_1−xTi_xSb samples decreases rapidly above room temperature and follows a temperature dependence of T^−1.5 (Fig. 2(a)), implying that the acoustic phonon scattering dominated charge transport,²⁹ since the hole concentration is almost independent of temperature before intrinsic excitation for heavily doped semiconductors¹⁵ (Fig. S2, ESI†). The calculated Seebeck coefficient α by the SPB model, in Fig. 2(b), agrees well with the experimental data before the intrinsic excitation of charge carriers. All the FeNb_1−xTi_xSb samples have high power factors (PFs) (Fig. S3, ESI†), and the PF of p-type FeNb_0.8Ti_0.2Sb is about 4.5 × 10⁻³ W m⁻¹ K⁻² at 1100 K, comparable with that of the optimized n-type (Hf, Zr)NiSn based HH compounds,¹¹ and about twice as high as that of the most widely used p-type SiGe alloys for high temperature power generation.³⁰

Fig. 2 Temperature dependence of electrical conductivity (a) and Seebeck coefficient (b) for FeNb_1−xTi_xSb samples. The theoretical curves in (b) were calculated using the SPB model.

The temperature dependence of thermal conductivity κ and lattice thermal conductivity κ_L of FeNb_1−xTi_xSb alloys is shown in Fig. 3. The lattice thermal conductivity was obtained by subtracting the electronic component κ_e from the total thermal conductivity κ. κ_e was calculated via κ_e = LσT, where L is the Lorenz number and can be calculated using the SPB model with reasonable approximation.¹² The total thermal conductivity at room temperature decreases from 15 W m⁻¹ K⁻¹ at x = 0.04 to 7.5 W m⁻¹ K⁻¹ at x = 0.2, mainly resulting from the significant decrease in the lattice thermal conductivity (Fig. 3(b)). The κ_L decreases rapidly with increasing Ti content over the measured temperature, indicating that the substitution of Ti at Nb sites is an effective way to reduce the κ_L of FeNbSb. The lattice thermal conductivity of all FeNb_1−xTi_xSb samples follows a κ_L ∼ T^s behavior with the exponent −0.5 ≤ s < −1, indicating that strong point defect scattering is present.³¹

Fig. 3 Thermal conductivity κ (a) and lattice thermal conductivity κ_L (b) of FeNb_1−xTi_xSb samples. The solid lines in (a) and (b) show the κ and κ_L of Fe(V_0.6Nb_0.4)_0.8Ti_0.2Sb for comparison.

Although p-type FeNb_1−xTi_xSb compounds have the largest power factor among Fe(V_1−yNb_y)_1−xTi_xSb alloys, they have the higher lattice thermal conductivity compared with the V substituted solid solutions due to the stronger point defect scattering of phonons in the latter.¹⁶ However, the room temperature κ_L of FeNb_1−xTi_xSb samples rapidly decreases with increasing Ti content (Fig. S4a, ESI†), and are only ∼30% higher than the Fe(V_0.6Nb_0.4)_1−xTi_xSb solid solutions at high Ti contents (x ≥ 0.2). At higher temperatures, due to the strong phonon–phonon scattering, the difference in κ_L between FeNb_0.8Ti_0.2Sb and Fe(V_0.6Nb_0.4)_0.8Ti_0.2Sb is even smaller, only ∼15% at 800 K (Fig. S4b, ESI†). Calculations of the phonon relaxation time using the Callaway model reveal that in FeNb_0.8Ti_0.2Sb the Umklapp process is dominant at 400 K (Fig. S5, ESI†).³² Although it was previously reported that the low content Ti could improve the electrical conductivity in FeNb_0.95Ti_0.05Sb,²⁴ our work shows for the first time that high content Ti doping at Nb sites not only optimizes the carrier concentration but also enhances the point defect scattering of phonons to suppress the lattice thermal conductivity.

It is noteworthy that the band gap of FeNb_1−xTi_xSb (∼0.54 eV) is larger than that of Fe(V_0.6Nb_0.4)_1−xTi_xSb (∼0.42 eV), which is beneficial to inhibit the intrinsic excitation of minority carrier and leads to the maximum Seebeck coefficient at higher temperature (Fig. S6, ESI†). The thermal conductivity of Fe(V_0.6Nb_0.4)_0.8Ti_0.2Sb begins to increase above 800 K due to the bipolar conduction, whereas in FeNb_1−xTi_xSb it is above 1100 K (Fig. (3)). Therefore, the increased band gap and suppressed bipolar conduction also contribute to the high zT at high temperature in FeNb_1−xTi_xSb.

As shown in Fig. 1(d), FeNb_1−xTi_xSb alloys exhibit a maximum zT of 1.1 at x = 0.2. Compared with other good p-type high temperature TE materials (Fig. 4), FeNb_0.8Ti_0.2Sb is more competitive in high temperature power generation. Especially, the maximum zT of the FeNb_0.8Ti_0.2Sb half-Heusler alloy is almost twice as high as that of the most widely used p-type SiGe TE materials.³⁰ At high temperatures (>900 K) the p-type FeNb_0.8Ti_0.2Sb displays superior TE performance to the optimized n-type (Hf, Zr)NiSn compound, which makes it possible to achieve a high efficiency TE device based on half-Heusler alloys. The good experimental repeatability and high temperature stability of FeNb_0.8Ti_0.2Sb have also been confirmed (Fig. S7 and S8, ESI†).

Fig. 4 zT comparison of typical high temperature p-type TE materials. TE performance of FeNb_0.8Ti_0.2Sb superior to other advanced high temperature p-type materials (solid line)^9,14,15,30 and the optimized n-type (Hf, Zr)NiSn¹¹ based HH compound (dashed line).

In summary, new high performance p-type FeNb_1−xTi_xSb half-Heusler thermoelectric alloys were developed via a band engineering approach through a tradeoff between the band effective mass and carrier mobility. A high zT value of 1.1 at 1100 K was achieved for FeNb_0.8Ti_0.2Sb. The high content of Ti doping at Nb sites not only optimizes the power factor but also enhances point defect scattering of phonons. The increased band gap of FeNb_1−xTi_xSb, compared to Fe(V_0.6Nb_0.4)_1−xTi_xSb, leads to the suppressed intrinsic excitation at high temperatures. Considering the competitive cost, good stability and high TE properties, FeNb_1−xTi_xSb alloys exhibit high potential for high temperature TE power generation.

Methods

Synthesis

The ingots (∼20 g) with nominal composition Fe(V_1−yNb_y)_1−xTi_xSb (x = 0–0.24 and y = 0.4–1.0) were prepared by levitation melting of stoichiometric amounts of Fe (piece, 99.97%), V (piece, 99.97%), Nb (foil, 99.98%), Ti (rod, 99.99%) and Sb (block, 99.999%) under an argon atmosphere for 3 minutes. The ingots were remelted three times to ensure homogeneity. The obtained ingots were mechanically milled (Mixer Mill MM200, Retsch) for 4 h under argon protection. The obtained powders were loaded into the graphite die and compacted by spark plasma sintering (SPS-1050, Sumitomo Coal Mining Co.) at 1123 K for 10 min under 65 MPa in a vacuum. The as-sintered samples, of which the relative densities were found to be ∼95%, were annealed at 1023 K for 2 days.

Structural characterization

Phase structures of the samples were investigated by X-ray diffraction (XRD) on a RigakuD/MAX-2550PC diffractometer using Cu K_α radiation (λ₀ = 1.5406 Å) and the chemical compositions were checked by electron probe microanalysis (EPMA, JEOL, JXA-8100). The XRD patterns of Fe(V_1−yNb_y)_1−xTi_xSb show a single phase that can be indexed to the HH phase with a cubic MgAgAs-type crystal structure (space group, F4̄3m),¹⁵ and the XRD patterns of FeNb_1−xTi_xSb (x = 0–0.24) samples are shown in Fig. S9a.† The lattice parameters of FeNb_1−xTi_xSb were calculated via Bragg's law using Jade® codes, which decrease almost linearly with the nominal Ti content (Fig. S9b, ESI†) since the covalent radius of Ti is smaller than that of Nb. The fairly good linearity is consistent with Vegard's law. The microstructure and homogeneity of FeNb_0.8Ti_0.2Sb were investigated by EPMA (Fig. S10, ESI†). The EPMA results (Table S2, ESI†) show that the actual compositions are close to the nominal ones.

TE property measurement

The low temperature electrical conductivity and Hall coefficients from 10 K to 300 K were measured using a Mini Cryogen Free Measurement System (Cryogenic Limited, UK). The carrier concentration p_H was calculated by p_H = 1/eR_H, where e is the unit charge and R_H is the Hall coefficient. The carrier mobility μ_H was calculated by μ_H = σR_H. The Seebeck coefficient and electrical conductivity from 300–1100 K were measured on a commercial Linseis LSR-3 system using a differential voltage/temperature technique and a DC four-probe method. The thermal conductivity κ was calculated using κ = DρC_p, where ρ is the sample density estimated by the Archimedes method. The thermal diffusivity D and specific heat C_p were measured by a laser flash method on a Netzsch LFA457 instrument with a Pyroceram standard (Fig. S11, ESI†). The accuracy is ±3% and ±5%, respectively.

Acknowledgements

This work was supported by the National Basic Research Program of China (2013CB632503), the Nature Science Foundation of China (51171171), the Program for New Century Excellent Talents in University (NCET-12-0495), the Program for Innovative Research Team in the University of Ministry of Education of China (IRT13037), and the Ph.D. program Foundation of Ministry of Education of China (no. 20120101110082).

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Footnote

† Electronic supplementary information (ESI) available: Band structure calculation, electrical and thermal properties, thermogravimetric analysis, reproducibility, XRD patterns, and electron probe microanalysis. See DOI: 10.1039/c4ee03042g

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