Federico
Serrano-Sánchez
a,
Ting
Luo
b,
Junjie
Yu
c,
Wenjie
Xie
d,
Congcong
Le
a,
Gudrun
Auffermann
a,
Anke
Weidenkaff
d,
Tiejun
Zhu
c,
Xinbing
Zhao
c,
José A.
Alonso
e,
Baptiste
Gault
b,
Claudia
Felser
a and
Chenguang
Fu
*a
aMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany. E-mail: chenguang.fu@cpfs.mpg.de
bMax-Planck-Institut für Eisenforschung GmbH, Max-Planck Straße 1, 40237, Düsseldorf, Germany
cState Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, 310027 Hangzhou, China
dDepartment of Materials Science, Technical University of Darmstadt, 64287 Darmstadt, Germany
eInstituto de Ciencias de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain
First published on 14th July 2020
Half-Heusler compounds with a valence electron count of 18, including ZrNiSn, ZrCoSb, and NbFeSb, are good thermoelectric materials owing to favorable electronic structures. Previous computational studies had predicted a high electrical power factor in another half-Heusler compound NbCoSn, but it has not been extensively investigated experimentally. Herein, the synthesis, structural characterization, and thermoelectric properties of the heavy-element Pt-substituted NbCoSn compounds are reported. Pt is found to be an effective substitute enabling the optimization of electrical power factor and simultaneously leading to a strong point defect scattering of phonons and the suppression of lattice thermal conductivity. Post-annealing significantly improves the carrier mobility, which is ascribed to the decreased grain boundary scattering of electrons. As a result, a maximum power factor of ∼3.4 mW m−1 K−2 is obtained at 600 K. In conjunction with the reduced lattice thermal conductivity, a maximum figure of merit zT of ∼0.6 is achieved at 773 K for the post-annealed NbCo0.95Pt0.05Sn, an increase of 100% compared to that of NbCoSn. This work highlights the important roles that the dopant element and microstructure play in the thermoelectric properties of half-Heusler compounds.
NbCoSn is another half-Heusler alloy with a VEC of 18. The prediction of a large power factor (α2σ) in both n-type and p-type NbCoSn indicates its potential thermoelectric application.28,29 Particularly, for the p-type NbCoSn, the calculated α2σ is the largest among all studied half-Heusler alloys,28 which might originate from the high band degeneracy in the valence band edge.30 However, the preparation of a heavily hole-doped NbCoSn is experimentally challenging, and good thermoelectric performance has not been reported to date. Ti, Mo, and Hf were initially described as weak p-type acceptors for NbCoSn by Kawaharada et al.31,32 Later, Ferluccio et al.33 reported Zr- and Ti-doped NbCoSn with a positive Seebeck coefficient. Sc was also used as an acceptor for NbCoSn by Yan et al.34 However, the low electrical conductivities in these p-type NbCoSn samples suggested that the electrical power factors were not yet optimal, preventing the attainment of the predicted high performance. The interstitial Co, predicted to be the most stable intrinsic defect in NbCoSn by Bhattacharya and Madsen,29 was thought to be the possible ‘killer-defect’, hindering the realization of heavily hole-doped NbCoSn. Excess Co was found in the synthesized NbCoSn samples, despite being designed to have the nominal composition.34,35 A similar phenomenon was also observed in the ZrNiSn system, in which excess Ni significantly changes the electronic structure and transport properties.36,37 Therefore, further experimental understanding of the intrinsic defect in NbCoSn is necessary to optimize its p-type thermoelectric properties.
Meanwhile, n-type doping has been successfully achieved using Sb as a dopant.31,33,38 The alloys of NbCo1+xSn were prepared by optical floating zone method.39 Among these, NbCo1.05Sn showed the highest phase-purity and thermoelectric performance. He et al.40 reported an 80% enhancement of the power factor by improving the samples' phase purity, resulting in a maximum zT of 0.6 at 973 K in Sb-doped NbCoSn. Additionally, a material comprising the half-Heusler NbCoSn mixed with the full-Heusler NbCo2Sn was studied, and the antisite disorder was found to be suppressed by annealing.41 Generally, half-Heusler alloys require a high content of chemical doping to realize the optimal electrical power factor. Thus, the dopants could also generate significant suppression on phonon transport.13 A dopant element, which has large mass and radius differences with the host element, could enhance point defect scattering of phonons, thereby suppressing the lattice thermal conductivity.
In this study, we have prepared heavy-element Pt-substituted NbCo1−xPtxSn (x = 0.00–0.15) samples using arc-melting and high-energy mechanical alloying, followed by a spark plasma sintering (SPS) process. After obtaining the sintered pellets, several samples are further annealed. Laboratory and synchrotron X-ray diffraction (XRD) measurements show that the obtained samples possess pure half-Heusler phase with negligible secondary phases. Heavy-element Pt substitution leads to the simultaneously improved power factor and suppressed lattice thermal conductivity. Post-annealing is effective in decreasing the grain boundary scattering of carriers and leads to high mobility in the annealed samples. As a result, a maximum zT of ∼0.6 is obtained at 773 K for the post-annealed NbCo0.95Pt0.05Sn, which is the highest value for this system at this temperature.40
XRD was performed at room temperature using an image-plate Huber G670 Guinier camera equipped with a Ge(111) monochromator and employing Co Kα1 radiation. Synchrotron XRD (SXRD) patterns were collected with an incident beam of 28 keV energy (λ = 0.4427 Å), in the high angular resolution mode (MAD set-up) on the MSPD-diffractometer at the ALBA synchrotron in Barcelona, Spain. The ground samples were analysed using quartz capillaries with 0.25 mm radius. Rietveld refinements of XRD and SXRD patterns were performed using FullProf program.42,43 A pseudo-Voigt function was employed for analyzing the shapes of the diffraction peaks. There were no excluded regions in the refinements. The final refinement of the synchrotron data was performed using parameters such as scale factor, set of background points, zero-point shift, pseudo-Voigt shape, and isotropic thermal displacement parameters of Nb, Co/Pt, and Sn.
Microstructural analysis of the samples was performed using scanning electron microscopy (SEM, Zeiss Merlin scanning electron microscope, Carl Zeiss AG, Oberkochen, Germany) in the backscattered mode, at an accelerating voltage of 30 kV and a beam current of 2 nA.
High-temperature measurements of the Seebeck coefficient and electrical resistivity were performed using an ULVAC-RICO ZEM-3 equipment. The thermal conductivity was calculated using the equation, κ = CpDρ, where Cp is the specific heat, D is the thermal diffusivity, and ρ is the sample density, employing thermal diffusivity values (Fig. S1, ESI†) measured by a LASER Flash (LFA 457, Netzsch). Cp (Fig. S2, ESI†) is calculated using the formula, Cp = Cph,H + CD, where Cph,H and CD are the contributions of the harmonic phonons and lattice dilation, respectively, which can be calculated by employing the sound velocity, thermal expansion coefficient, and density (Table S1†).24
The Hall effect measurements were performed in sample rods in a four-probe configuration using the resistivity option of the physical property measurement system (PPMS, Quantum Design). The measurements were symmetrized to eliminate the magnetoresistance contribution, and the carrier concentration was calculated using the formula, RH = −1/enH, where RH is the Hall coefficient, e is the free electron charge, and nH is the Hall carrier concentration.
Band structure calculations were performed using density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) code.44–46 The generalized-gradient approximation (GGA) for the exchange–correlation functional is used. The cut-off energy is set to be 500 eV for expanding the wave functions into plane-wave basis. In the calculation, the Brillouin zone (BZ) is sampled in the k space within Monkhorst–Pack scheme.47 On the basis of the equilibrium structure, the k mesh used is 12 × 12 × 12, and spin orbital coupling (SOC) is included in our calculation.
Lattice parameters (Fig. 1d) were determined using Rietveld refinements of the XRD patterns in the F3m space group, displaying an excellent match with the literature data.33 The lattice parameter increases almost linearly with increasing Pt content, which indicates the efficiency of Pt as a donor for NbCoSn. Carrier concentration measurements allow the assessment of the effectiveness of Pt substitution in terms of the electron transfer to the half-Heusler structure. Fig. 1d shows that the carrier concentration follows an approximately linear behaviour with increasing Pt content. Using a simple assumption of one added electron per Pt atom, the estimated carrier concentrations (red dashed line in Fig. 1d) are consistent with the experimental values. The calculated carrier concentration is 9.42 × 1020 cm−3 for x = 0.05, which is close to the experimental value. The results indicate that Pt is a highly effective dopant for this system.
The temperature-dependence of the electrical conductivity σ for NbCo1−xPtxSn (x = 0.00–0.15) samples is shown in Fig. 2a. An increasing trend is observed for the pristine NbCoSn sample, indicating a semiconducting behaviour. After substituting with Pt, the σ shows a noticeable increase in the complete temperature range, with a decreasing trend at temperatures above 500 K, suggesting a degenerate semiconductor behaviour. Interestingly, the sample with x = 0.05, which was post-annealed, shows a higher σ compared to that of the sample with x = 0.06, despite the higher carrier concentration of the latter. A similar phenomenon is also observed for another post-annealed sample with x = 0.10, whose σ value at room temperature is higher than that of the sample with x = 0.12. Thereafter, the carrier mobilities of the samples were calculated (Fig. 2b). Overall, the two post-annealed samples with x = 0.05 and x = 0.10 have higher carrier mobilities than those of the others, suggesting an annealing-induced change in the microstructure. Therefore, the backscattered electron imaging was performed for samples with x = 0.05 and x = 0.06, as shown in Fig. 2c and d, respectively. This analysis shows that the sample with x = 0.05, with post-annealing after SPS, has a grain size of a few micrometres, which is almost ten times larger than that of the sample with x = 0.06. Grain boundary scattering has recently been found to hinder the mobilities and conductivities (particularly near room temperature) of Mg3Sb2,48 half-Heusler Nb1−xTixFeSb49 and (Zr,Hf)CoSb,50 and elemental Te.51,52 Herein, an increase in the grain size in post-annealed samples can support their high electrical conductivities and carrier mobilities. The confirmation of the influence of grain boundary processes will be the focus of a separate study.
The temperature dependence of the Seebeck coefficient (Fig. 3a) of Pt-substituted NbCoSn shows an approximately linear increase with rising temperature, which is a typical behaviour of a degenerate semiconductor, as expected from the Mott equation.2,53 The absolute Seebeck coefficient increases in the complete temperature range with no observable contribution from bipolar conduction. In contrast, the pristine NbCoSn shows an increase in the absolute Seebeck coefficient up to 600 K, when a small bump is observed. Similar data have been previously reported for the pristine compound.33,39 As expected according to the Pisarenko relationship,9 the absolute Seebeck coefficient decreases with an increase of Pt content due to the increased electron concentration.
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Fig. 3 (a) Temperature dependence of Seebeck coefficient for NbCo1−xPtxSn (x = 0.00–0.15). (b) Pisarenko plot at room temperature for several n-type half-Heusler compounds including NbCoSn,40 (Zr,Hf)CoSb,24,50,54 and (Zr,Hf)NiSn.20,55 (c) Temperature dependence of power factor for NbCo1−xPtxSn (x = 0.00–0.15). (d) Power factor as a function of Pt content at 300 K (![]() ![]() |
A Pisarenko plot using the single parabolic band model24 (Fig. 3b) was used to better assess the electrical properties of n-type NbCoSn. The density of states (DOS) effective mass m* is linked to the single-valley effective mass via the expression,
, where Nv is the number of degenerate valleys.9 A m* of 6.5 me is derived for the Pt-substituted NbCoSn samples. Notably, this m* value is close to that of the n-type (Zr,Hf)CoSb,24,50,54 but more than two times higher than that of n-type (Zr,Hf)NiSn.20,55
The variation in calculated power factor is shown in Fig. 3c. It follows an increasing trend with an increase in temperature because of the increase in the absolute Seebeck coefficient up to 600–700 K and then saturates at high temperatures. Pt-substituted NbCoSn samples exhibit noticeably higher power factors than that of the undoped NbCoSn, suggesting the optimization of electrical properties. The Pt content dependence of the power factor at 300 and 765 K is shown in Fig. 3d. The second set of samples with x = 0.05 and x = 0.10, which have larger grain sizes, show overall higher power factors than those of the first set of samples. This is attributed to the decreased grain scattering and thus improved carrier mobility. Electrical conductivity and Seebeck coefficient of Pt-substituted NbCoSn samples show clear trends resulting from the carrier concentration evolution, but this is not the case for the power factor, which displays a non-monotonous change with increasing Pt content. A maximum power factor of ∼3.4 mW m−1 K−2 is obtained at 600 K for the post-annealed sample with x = 0.05, which is comparable to that of NbCoSn0.9Sb0.1 at 900 K.40
Complementary to the above electrical transport analysis, the calculated band structure and DOS are shown in Fig. 4. As previously reported by He et al.,40 at the conduction band bottom (CBB), there are two bands (denoted as X1 and X2) which converge at the X point. Considering the symmetry of the X point in the Brillouin zone, a high Nv of 6 is found for the CBB of NbCoSn. In contrast, for (Zr,Hf)NiSn30,37 and (Zr,Hf)CoSb,24 there is only one band at the CBB, giving a smaller Nv of 3. Therefore, different from n-type (Zr,Hf)CoSb, the similar m* (Fig. 3b) of NbCoSn should also have a contribution from its larger Nv, indicating a smaller . Moreover, Fig. 4 shows also the orbital weighted contribution of each element to the band structure and DOS. The electronic states in the CBB are dominated by the Nb-d orbitals, with additional contribution from the d orbitals of Co. In contrast, the valence band top is dominated by the d orbitals of Co, with additional contributions from both the d orbitals of Nb and the p orbitals of Sn.
The change in the total thermal conductivity κ of NbCo1−xPtxSn with temperature is shown in Fig. 5a. A decrease in the κ value of Pt-substituted samples is observed near room temperature. To further understand this behaviour, κe and κL were calculated using the equations, κe = LσT and κL = κ − κe, where L is the Lorenz number (Fig. S3a, ESI†), which was calculated using the single parabolic band model.24 As shown in Fig. 5b, a notable decrease in κL is observed upon Pt substitution and a maximum reduction of 45% is obtained for x = 0.15, indicating that heavy element substitution is effective in enhancing the phonon scattering by introducing strong mass and strain field fluctuations.13Fig. 5c shows a monotonic reduction of κL as a function of Pt content, regardless of the grain size distribution of the samples, suggesting that point defect scattering dominates the phonon transport.
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Fig. 5 Temperature evolution of (a) total thermal conductivity and (b) lattice thermal conductivity. (c) Variation of κ, κe, and κL with an increase in Pt content at room temperature. (d) Figure of merit zT for NbCo1−xPtxSn (x = 0.00–0.15) as a function of temperature. zT for the optimized NbCoSn0.9Sb0.1 is also shown (dashed line).40 |
Table S3† displays the disorder scattering parameters, which were calculated as described in the ESI.† The slight differences between experimental Γexp and mass fluctuation ΓM parameter indicate that large mass difference between Co and Pt atoms dominates the reduction in the κL. This description agrees with the monotonic evolution of κL upon Pt substitution, as the governing mass fluctuation scattering mechanism would depend directly on the amount of Pt in NbCo1−xPtxSn. Moreover, in spite of the increased grain size of x = 0.05 and x = 0.10 samples, κL shows no deviation from this trend. This could be explained as grain boundary scattering acting on a different length scale within the grain size range observed in these samples. At a high Pt content, κL shows values down to 4.0–3.2 W m−1 K−1 for x = 0.10–0.15, lower than those previously reported for this system, typically in the range of 5–10 W m−1 K−1 at room temperature.33,40,41 In addition, an increase in κe (Fig. S3b†) is observed with increasing Pt content due to the evolution of the electrical conductivity. Compared to Sb doping,40 Pt substitution is more effective at suppressing the κL of NbCoSn, thereby contributing to the decrease in κ. These values are comparable and even lower than those obtained for the NbCoSn–NbCoSb solid-solutions, in which the disorder and Nb vacancies have a strong impact on the phonon conduction.33
Owing to the simultaneously decreased κL and improved power factor, Pt substitution is effective in improving the figure of merit zT of NbCoSn (Fig. 5d). A 100% increase in the peak zT is observed for NbCo0.95Pt0.05Sn, compared to that for NbCoSn, leading to a maximum value of ∼0.6 at 773 K. This value is similar to that of Sb-doped NbCoSn system but occurs at a lower temperature. Furthermore, the almost linear temperature dependence of zT in all the studied NbCo1−xPtxSn samples suggests that a higher peak zT can be achieved at higher temperatures. Post-annealing to eliminate the negative effect of grain boundary on carrier transport should also be helpful for improving the zT of the other n-type NbCoSn system.
Footnote |
† Electronic supplementary information (ESI) available: Calculated heat capacity, coefficient of linear thermal expan-sion, electronic contribution to thermal conductivity, structural parameters of Rietveld refinement of SXRD patterns. See DOI: 10.1039/d0ta04644b |
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