Thermal conductivity reduction by isoelectronic elements V and Ta for partial substitution of Nb in half-Heusler Nb_(1−x)/2V_(1−x)/2Ta_xCoSb

Abstract

Recently, we found a new n-type thermoelectric half-Heusler NbCoSb with a valence electron count of 19, different from the usual 18. In this paper, we focus on the effect of partial substitution of Nb by isoelectronic elements V and Ta on the reduction of the thermal conductivity of Nb_(1−x)/2V_(1−x)/2Ta_xCoSb. We found that the isoelectronic elements V and Ta for partial substitution of Nb can dramatically decrease the thermal conductivity from 7.0 W m⁻¹ K⁻¹ to 3.3 W m⁻¹ K⁻¹ at room temperature for Nb_0.44V_0.44Ta_0.12CoSb, but unfortunately a large power factor decrease also occurred. Consequently, a peak ZT of ∼0.5 is achieved at 700 °C for Nb_0.44V_0.44Ta_0.12CoSb, which is about 25% higher than the ∼0.4 reported earlier for NbCoSb.

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1. Introduction

Thermoelectric (TE) materials, which have potentials in waste heat recovery for electric power generation and refrigeration, could be an important part of solutions to today's energy crisis.^1,2 The performance of a TE material is characterized by the dimensionless figure of merit ZT = S²σT/(κ_e + κ_L), where S, σ, T, κ_e, and κ_L are the Seebeck coefficient, the electrical conductivity, the absolute temperature, and the electrical and lattice components of the total thermal conductivity, respectively.³ It is a longstanding challenge to achieve high ZT through optimizing these variables independently, because S, σ, κ_e are strongly coupled with each other via carrier concentration, scattering, and band structure.^4,5

Half-Heusler (HH) compounds with the general chemical formula XYZ usually form the cubic MgAgAs type of structure. In recent years, many HH compounds with valence electron count (VEC) of 18 have been identified as potential high temperature TE materials due to the small band gap and sharp slope of the density of states near the Fermi level.^6–9 Among the HH family with 18 VEC, MNiSn^10–17 and MCoSb^18–24 compounds (M = Hf, Zr, Ti) are the most widely investigated ones. Based on calculations,^25,26 the basic requirement for a HH compound to be thermoelectric materials is VEC = 18, otherwise, the Fermi level will enter the valence or conduction band and the compound will show either p-type or n-type metallic properties. The electronic structure calculations of many half-Heusler compounds showed that HHs with VEC = 19 such as VCoSb, NbCoSb, and TiNiSb are metallic, not suitable for semiconductor or thermoelectric applications.^27–29 However, to our surprise, we recently discovered that NbCoSb with VEC = 19 could be made into HH alloys with decent thermoelectric properties³⁰ and so is VCoSb.³¹

According to the definition of ZT = (S²σ/κ)T, there are usually two approaches to optimize the performance of a TE material: one is to optimize the power factor (S²σ) by band engineering, such as modification of electron states via resonant levels,^32–35 convergence of energy bands,^36–38 or weakening of scattering of the carriers.^39,40 And the other is to reduce the lattice thermal conductivity by alloying or nanostructuring to induce point defects,^41–43 or interfaces.⁴⁴ Forming solid solutions has been considered as an effective approach to enhance phonon scattering. To reduce the lattice thermal conductivity κ_L, the effectiveness of isoelectronic alloying on the M sublattice in HH compounds of MNiSn and MCoSb (M = Hf, Zr, Ti) has been successfully demonstrated.^{16,17,22,23,45–48} Point defect disorder caused by strain and mass differences between alloying atoms and host atoms acts as scattering centers for phonons, which reduces κ_L.

In this work, we focus on the effectiveness of isoelectronic alloying on reducing the thermal conductivity of the new half-Heusler NbCoSb with 19 VEC. According to our results, the isoelectronic substitution of Nb by V and Ta in NbCoSb can dramatically decrease the thermal conductivity from 7.0 W m⁻¹ K⁻¹ to 3.3 W m⁻¹ K⁻¹ for Nb_0.44V_0.44Ta_0.12CoSb at room temperature, but unfortunately a large power factor reduction also occurred. Consequently, a peak ZT of ∼0.5 is reached at 700 °C for Nb_0.44V_0.44Ta_0.12CoSb, which is about 25% higher than the ∼0.4 reported earlier for NbCoSb.³⁰

2. Experimental details

Samples were prepared by arc melting, ball milling and hot pressing. Compounds with nominal compositions Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, and Nb_0.88V_0.12CoSb were first prepared by arc melting of stoichiometric amounts of Ta (slug, 99.95%), Nb (slug, 99.99%), V (piece, 99.99%), Co (piece, 99.95%), and Sb with 5% excess (broken rod, 99.8%) under an argon atmosphere and flipped over for melting five times to ensure homogeneity. The obtained ingots were ball milled (SPEX 8000M Mixer/Mill) for 7 h to produce fine-grained powders of about 50 nm or less.^22,41 The powders were then hot pressed at 1000 °C for 2 min under a pressure of 77 MPa. The hot-pressed samples were used for measurements of thermal diffusivity, and then cut into rectangular bars for Seebeck coefficient and electrical conductivity measurements. Because of the small grain size and randomness of the crystal orientation, the properties of these compounds are isotropic.

The phase structures of the samples were studied by X-ray diffraction (XRD) on a PANalytical multipurpose diffractometer (PANalytical X'Pert Pro) using Cu K_α radiation (λ = 1.5406 Å). The microstructures were investigated by a scanning electron microscope (SEM, JEOL 6330F) and a high resolution transmission electron microscope (HRTEM, JEOL 2100F). The electrical conductivity (σ) and Seebeck coefficient (S) were simultaneously measured on a commercial system (ULVAC ZEM-3). The thermal conductivity κ was calculated using κ = ρDC_p, where ρ is the sample density measured by the Archimedes method, D the thermal diffusivity obtained on a laser flash apparatus (Netzsch LFA 457), and C_p the specific heat measured on a differential scanning calorimetry thermal analyzer (Netzsch DSC 404 C). Rectangular samples of ∼4 mm × ∼4 mm × ∼0.2 mm were prepared by polishing for Hall coefficient R_H measurements at room temperature using a PPMS (Quantum Design Physical Properties Measurement System) with a magnetic field sweeping between ±3.0 T and an electrical current of 8 mA. The Hall carrier concentration n_H and carrier mobility μ_H were calculated using n_H = 1/(eR_H), μ_H = σR_H, respectively, where σ is the electrical conductivity obtained from ZEM measurement.

In order to understand the band structures of TiCoSb with 18 VEC and NbCoSb with 19 VEC, calculations were carried out using density functional theory with the projector-augmented wave method as implemented in the Vienna ab initio simulation package (VASP). The generalized gradient approximation (GGA) function of Perdew, Burke and Ernzerhof (PBE) was adopted to treat the exchange and correlation potential in all calculations. A conventional cell with 12 atoms was used in pure TiCoSb and NbCoSb calculations. System relaxation was first carried out to find the equilibrium position, followed by self-consistent calculation (scf) with 5 × 5 × 5 k-points, and non-self-consistent calculation (nscf) with 15 × 15 × 15 k-points. The density of states (DOS) of the pure TiCoSb and NbCoSb were then obtained.

3. Results and discussion

A schematic representation of the structure of a typical half-Heusler compound is given in Fig. 1. HH consists of XYZ, where X is a transition metal, or a noble metal, or a rare-earth element, Y is a transition metal or a noble metal, and Z is a main group element. In a primitive unit cell, elements X and Z form a rock salt structure and Y is located at one of the two body diagonal positions (1/4, 1/4, 1/4) in the cell, leaving the other one (3/4, 3/4, 3/4) unoccupied. In this paper, we focus on two HH compounds, i.e., TiCoSb and NbCoSb.

Fig. 1 The cubic crystallographic unit cell of a typical HH compound XYZ.

Fig. 2a and c shows the density of states (DOS) of compound TiCoSb with 18 valence electrons compared with NbCoSb with 19 VEC. As shown in Fig. 2a, TiCoSb shows a semiconducting band structure, a band gap of 1.0 eV is found at the Fermi edge, and the Fermi level is located at the top of the valence band, which is consistent with Frederick's calculation.²⁶ The DOS of NbCoSb in Fig. 2c shows a band gap of also about 1.0 eV, but the Fermi level is into the conduction band. The gap width in the XYZ compounds is correlated with the electronegativity difference between the Y and Z element.⁴⁹ TiCoSb and NbCoSb has almost the same gap width because of the same Co and Sb element in the Y and Z positions, respectively. However, the Fermi levels of the two compounds are very different: for TiCoSb, it is above the valence band edge, but for NbCoSb it is in the conduction band, meaning that NbCoSb should show more metallic or semi-metallic behavior, very different from TiCoSb. The calculated detailed band structures of TiCoSb and NbCoSb are displayed in Fig. 2b and d, consistent with the results of DOS.

Fig. 2 (a and c) Density of states, and (b and d) calculated band structures of compound TiCoSb with VEC = 18 and NbCoSb with VEC = 19.

The XRD patterns of Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, and Nb_0.88V_0.12CoSb are presented in Fig. 3. All samples could be indexed to the half-Heusler phase of NbCoSb with a cubic MgAgAs-type crystal structure (JCPDS 51-1247, a = 0.5897 nm). A small amount of secondary phases like Nb₃Sb or Nb₅Sb₄ are also identified, which are resulted from peritectic reactions during the cooling process of arc-melting. As shown in Table 1, lattice constants of these samples are all consistent with that of the JCPDS card. The theoretical density of the samples can be calculated by ρ_cal = ∑n_iM_i/(a³N_A), where n_i is the number of atoms of Nb, Co, and Sb per unit cell, M_i is the corresponding atomic mass of each element, a is the lattice constant, and N_A is the Avogadro constant (6.023 × 10²³ mol⁻¹). The relative densities of these samples are found to be ∼96 ± 1%, as shown in Table 1.

Fig. 3 XRD patterns of n-type half-Heusler compounds. (a) Nb_0.44V_0.44Ta_0.12CoSb, (b) Nb_0.375V_0.375Ta_0.25CoSb, (c) Nb_0.333V_0.333Ta_0.333CoSb, (d) Nb_0.88Ta_0.12CoSb, (e) Nb_0.88V_0.12CoSb, and (f) NbCoSb.

Table 1 Lattice constant, theoretical, experimental, and relative density of half-Heusler compounds Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, and Nb_0.88V_0.12CoSb

Nominal composition	Lattice constant (nm)	Density (g cm^−3)		Relative density (%)
		Theoretical	Experimental
Nb0.44V0.44Ta0.12CoSb	0.5895	8.613	8.244	95.71
Nb0.375V0.375Ta0.25CoSb	0.5896	9.069	8.845	97.53
Nb0.333V0.333Ta0.333CoSb	0.5888	9.397	8.953	95.27
Nb0.88Ta0.12CoSb	0.5895	9.212	8.787	95.39
Nb0.88V0.12CoSb	0.5891	8.725	8.365	95.87

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The SEM image of the freshly fractured surface of the hot pressed sample Nb_0.44V_0.44Ta_0.12CoSb shows that the sample is dense and consists of grains with several hundreds of nanometers (Fig. 4a). The TEM study also reveals the sample is densely packed polycrystalline and consists of grains with sizes of around 200–600 nm, as shown in Fig. 4b. Furthermore, some nano inclusions of 10–20 nm were observed in Fig. 4b, and also identified in the HRTEM image in Fig. 4d. Such image contrast are most likely due to the slight composition difference with the single crystalline grain matrix, similar to the Ge-doped Mg₂Sn⁵⁰ and Sn/Te-codoped CoSb₃.⁵¹ These nano inclusions are the active phonon-scattering centers. Currently, we have not yet fully understood the real formation mechanism of these nano inclusions. It is difficult to find out whether these nano inclusions are Nb₃Sb or Nb₅Sb₄ as shown in the XRD patterns because of the difficult on measuring the compositions of such small areas. The HRTEM image in Fig. 4c shows a three grains adjacent sharing a triple junction and clearly indicates that individual grains are highly crystalline and the grain boundaries are clean. A fast Fourier transform (FFT) image from one of the grains is shown in Fig. 4e. All of the spots in the pattern can be successfully indexed as the [114] zone axis according to an ideal F4̄3m half-Huesler structure. The lattice spacing measured from the crystal grain is about 0.21 nm, which corresponds to the (220) interplanar spacing of half-Huesler. Fig. 4f shows crystal defects embedded inside the grains along the grain boundary (indicated by white arrows), which are beneficial to lower the thermal conductivity.

Fig. 4 (a) Representative SEM image; (b) low magnification TEM image; (c) HRTEM images showing triple grain boundary; (d) HRTEM image showing nano inclusion inside the individual grain; (e) the corresponding fast Fourier transform; (f) HRTEM image showing crystal defect of hot pressed sample Nb_0.44V_0.44Ta_0.12CoSb.

Fig. 5 shows the thermal transport properties of Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, Nb_0.88V_0.12CoSb, and NbCoSb. The thermal diffusivities are plotted in Fig. 5a, obviously, the thermal diffusivity is reduced a lot after partially substituting Nb with V or Ta. Furthermore, the thermal diffusivity could be further reduced significantly by co-substitution of Nb by V and Ta. Specific heat capacity (C_p) is also measured, as plotted in Fig. 5b. C_p increases a little bit after substitution of Nb by V and Ta. The total thermal conductivity (κ) is then obtained by multiplying the measured density, specific heat capacity, and thermal diffusivity of each sample. As shown in Fig. 5c, the samples containing V and Ta show the lowest total thermal conductivity. It is clear that the room temperature κ of sample Nb_0.44V_0.44Ta_0.12CoSb decreased by ∼50% comparing with that of NbCoSb. The thermal conductivity is typically the sum of electronic, lattice and bipolar contributions: κ = κ_L + κ_e + κ_bi. The Wiedemann–Franz relation permits an estimation of the electronic component, κ_e = LσT, where L is the Lorenz number and can be calculated by the single parabolic band approximation.^52–54 The calculated Lorenz constant for Nb_0.44V_0.44Ta_0.12CoSb compound is in the range of 1.69 × 10⁻⁸ W Ω K⁻² to 2.06 × 10⁻⁸ W Ω K⁻², lower than the metallic limit L₀ of 2.45 × 10⁻⁸ W Ω K⁻². The κ_e of Nb_0.44V_0.44Ta_0.12CoSb increased from 0.49 W m⁻¹ K⁻¹ to 0.93 W m⁻¹ K⁻¹ within the range of 25–700 °C and contributes ∼15% to the total thermal conductivity at room temperature. The calculated electronic thermal conductivity is subtracted from the measured total thermal conductivity to obtain the lattice thermal conductivity, and the bipolar thermal conductivity is assumed to be negligibly small because the temperature dependent Seebeck coefficient shows a linear increase up to 700 °C. As shown in Fig. 5d, the lattice thermal conductivity decreased a little bit below 500 °C for samples partially substituting of Nb by just V or Ta, but the κ_L is largely reduced for samples containing both V and Ta in the whole measured temperature range, almost 40% reduction at room temperature for sample Nb_0.44V_0.44Ta_0.12CoSb in comparison with NbCoSb. The large reduction of lattice thermal conductivity of samples containing both V and Ta is related to the significant phonon scattering effect owing to the additional mass difference and point defects caused by isoelectronic substitution, as shown in high resolution TEM spectrum (Fig. 4d and f).

Fig. 5 Temperature dependence of (a) thermal diffusivity, (b) specific heat capacity, (c) thermal conductivity, and (d) lattice thermal conductivity for half-Heusler compounds Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, Nb_0.88V_0.12CoSb, and NbCoSb.

The measured electrical conductivity σ, Seebeck coefficient S, power factor S²σ, and ZT are shown in Fig. 6 as a function of temperature. The electrical conductivity of NbCoSb and Nb_0.88Ta_0.12CoSb declines rapidly with increasing temperature, while the descending trend of σ for samples containing V and Ta is not significant. It is generally observed that co-substitution by V and Ta produces lower electrical conductivity. There is no obvious change of σ with increasing temperature when varying the ratio of Ta, Nb, and V. The monotonically increasing Seebeck coefficient and resistivity with increasing temperature allow the assumption of single band conduction behavior. All measured Seebeck coefficients are negative, indicating n-type transport behavior. The maximum is not reached even at 700 °C, which makes NbCoSb based compounds possible for even higher temperature applications. It is seen that V and Ta co-substitution results in higher Seebeck coefficient than the un-doped ones, and among them Nb_0.44V_0.44Ta_0.12CoSb displays the highest S. Consequently, the power factor is calculated and presented in Fig. 6c. The V and Ta co-substituted samples show lower power factor, despite of the increased Seebeck coefficient. Among all the co-substituted samples, Nb_0.44V_0.44Ta_0.12CoSb showed the highest power factor of ∼16.3 μW cm⁻¹ K⁻² at 700 °C.

Fig. 6 Temperature dependence of (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor, and (d) ZT value for half-Heusler compounds Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, Nb_0.88V_0.12CoSb, and NbCoSb.

The temperature dependent figure of merit ZT was calculated and shown in Fig. 6d. A maximum ZT of ∼0.5 was obtained at 700 °C for samples Nb_0.44V_0.44Ta_0.12CoSb, an increase of ∼25% compared with NbCoSb. The improved ZT of Nb_0.44V_0.44Ta_0.12CoSb is mainly due to the largely reduced thermal conductivity, implying that the alloy disorder is beneficial.

Table 2 summarizes the transport properties of all the samples at room temperature. Hall coefficients have negative values for all the samples, indicating n-type conduction with electrons as the major carriers, in agreement with the Seebeck measurement by transport method using ZEM-3. The carrier concentration is obviously increased when both V and Ta are used to partially substitute Nb in NbCoSb, implying that even isoelectronic substitution could significantly change the carrier concentration, which is probably due to the differences of the detailed electronic structures of these elements. Meanwhile, the mobility of the co-substituted samples is largely decreased, which is resulted from the enhanced alloy scattering caused by additional disorder.

Table 2 The resistivity, carrier concentration, Hall mobility and effective mass at room temperature of half-Heusler compounds Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33), Nb_0.88Ta_0.12CoSb, Nb_0.88V_0.12CoSb, and NbCoSb

Nominal composition	Resistivity (10^−5 Ω m)	Carrier concentration (10^21 cm^−3)	Hall mobility (cm^2 V^−1 s^−1)
Nb0.44V0.44Ta0.12CoSb	1.272	10.416	0.472
Nb0.375V0.375Ta0.25CoSb	1.446	14.536	0.297
Nb0.333V0.333Ta0.333CoSb	1.673	10.235	0.365
Nb0.88Ta0.12CoSb	0.427	4.775	3.065
Nb0.88V0.12CoSb	0.846	4.218	1.752
NbCoSb	0.285	6.113	3.582

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Compared with NbCoSb we reported before, Nb_0.44V_0.44Ta_0.12CoSb has lower thermal conductivity, higher Seebeck coefficient and higher ZT. Therefore, it is clear that the thermoelectric properties of NbCoSb could be improved through proper composition tuning. It is necessary to point out that these samples still have a small amount of impurities. These impurities are very detrimental to the individual thermoelectric properties because they affect the thermal and electrical conductivities in a detrimental way. We believe it is highly possible to double the ZT when all the impurities are completely eliminated, which requires lots of composition tuning or even a totally different preparing method.

4. Conclusions

We found that partial co-substitution of V and Ta for Nb strongly affect the thermoelectric properties of Nb_(1−x)/2V_(1−x)/2Ta_xCoSb (x = 0.12, 0.25, and 0.33). V and Ta co-substitution for Nb in NbCoSb is proved effective in suppressing thermal conductivity, ∼50% reduction at room temperature and 40% reduction at 700 °C. A maximum ZT value of ∼0.5 is obtained at 700 °C for sample Nb_0.44V_0.44Ta_0.12CoSb due to the lower thermal conductivity, ∼25% increase compared with that of NbCoSb.

Acknowledgements

The work performed at Xihua University is supported by the Chunhui Program from Education Ministry of China (No. Z2014042), the Key Scientific Research Fund Project of Xihua University (No. Z1322332), Research Project of Education Department of Sichuan Province (No. 14ZB0133), Open Research Fund of Key Laboratory of High-performance Materials and Forming Technology in Xihua University (No. SZJJ2013-034), Natural Science Foundation of China (No. 51372208, No. 51472207, and No. 51572226), and that at the University of Houston is supported by “Solid State Solar Thermal Energy Conversion Center (S³TEC)”, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science under award number DE-SC0001299.

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