Thermoelectric Properties of p-Type Half-Heusler Compounds FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf)

Abstract

Recently, it has been reported that Hf-substituted Fe(Nb_1−xHf_x)Sb-based p-type half-Heusler compound exhibits exceptionally high thermoelectric (TE) figure of merit zT = 1.5 at 1200 K [C. Fu et al.: Nat. Commun. 6 (2015) 8144.]. However, the effect of substitute elements on the TE properties of FeNbSb is still unclear. Here, we synthesized polycrystalline samples of Fe(Nb_0.9M_0.1)Sb (M = Ti, Zr, Hf) by arc-melting followed by spark plasma sintering, and examined their high-temperature TE properties. The Ti-substituted sample was nearly single phase while the Zr- and Hf-substituted samples contained small amounts of secondary phase. The Ti-substituted sample exhibited the best TE performance. In the present case, Ti is better substituted element than Zr and Hf for enhancement of TE properties of FeNbSb.

1. Introduction

Thermoelectric (TE) devices composed of p- and n-type TE materials can directly convert heat to electricity and vice versa. The efficiency of TE devices is determined by both the temperature gradient across the devices and the properties of TE materials called dimensionless figure of merit, zT. zT is represented as zT = S²σTκ⁻¹, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity (κ = κ_lat + κ_el, the lattice, and electronic contributions, respectively).^1–4) zT ≥ 1 is one of the criteria for commercial use of TE materials. Although conventional TE materials such as Bi₂Te₃ and PbTe exhibit zT ≥ 1,^5,6) these materials contain highly toxic and rare elements which prohibits them for utilization of wide range of commercial applications. Therefore, the TE materials composed of non-toxic and inexpensive elements but showing high zT need to be developed. Half-Heusler (HH) compounds are one of the candidates for such advanced TE materials with outstanding TE properties.^4,7)

HH compounds with 18 valence electrons per unit cell exhibit large S values because of the existence of a narrow gap and sharp slope in the density of states around the Fermi level.^8–11) In several HH compounds, MNiSn and MCoSb (M = Ti, Zr, Hf) have been developed as n- and p-type TE materials, respectively. The maximum zT values of the n-type MNiSn are nearly unity, while those of the p-type MCoSb are still low to be around 0.5.^9,12–14) This big mismatch is one of the obstacles to establish high performance TE devices composed of HH compounds.

Recently, it has been reported that Hf-substituted FeNbSb-based HH compounds exhibit p-type characteristics with a high zT of 1.5 at 1200 K.¹⁵⁾ Furthermore, it has been revealed that FeNbSb is relatively stable at high temperatures and has close thermal expansion coefficient with n-type MNiSn.^16,17) In the n-type MNiSn and p-type MCoSb, the effect of substitute elements on the TE properties is well studied and the chemical composition is optimized.^18–24) However, reports on the effect of substitute elements on the TE properties of p-type FeNbSb is very limited.^25,26)

In this work, we select Ti, Zr, and Hf as the substituent element for FeNbSb, and investigate the effect of the substitution on the TE properties of FeNbSb. The substitution ratio is fixed to be 0.1 for all the system, i.e., the nominal composition of the samples is set as FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf). Polycrystalline bulk samples are synthesized and their high temperature TE properties are examined.

2. Experimental Procedure

Ingots of Ti-, Zr-, and Hf-substituted FeNbSb with the nominal compositions FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf) were synthesized by arc melting in an Ar atmosphere. Chunks of each element with 99.9% purity were used as the starting materials. During arc melting, the ingots were reversed and re-melted at least six times to homogenize them. The obtained ingots were crushed into powders, followed by spark plasma sintering (SPS) at 1157 K for 30 min under 65 MPa in an Ar atmosphere. The crystal structure was identified by powder X-ray diffraction (XRD) analysis. The data were collected on a diffractometer on Rigaku Ultima IV with Cu Kα radiation in air at room temperature. Microstructure of the SPS samples was investigated by scanning electron microscopy (SEM) and chemical composition was analyzed by energy dispersive X-ray (EDX) spectroscopy. The sample density (d) was calculated based on the sample size and weight. Thermal conductivity (κ) was calculated from heat capacity (C_p), thermal diffusivity (α), and d using the relationship κ = αC_pd. α was measured at temperatures ranging from room temperature to 1073 K using a flash diffusivity apparatus (Netzsch LFA-457). C_p was estimated by the model of Dulong and Petit, that is C_p = 3nR, where n is the number of atoms per formula unit and R is the gas constant. S and σ were measured from room temperature to 1073 K using a commercial apparatus (Ulvac ZEM-3) in a He atmosphere.

3. Results and Discussions

The powder XRD patterns of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf) are shown in Fig. 1. The sample of FeNb_0.9Ti_0.1Sb is HH single phase with no remarkable secondary phases. On the other hand, the samples of FeNb_0.9Zr_0.1Sb and FeNb_0.9Hf_0.1Sb contain small amounts of secondary phases of Fe₂Nb, SbFe, and Fe_0.7Hf_0.3.

Fig. 1

Powder X-ray diffraction patterns of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf).

Actual composition determined by EDX, lattice parameter of the HH phase, and density of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf) are summarized in Tables 1, 2, and 3, respectively. In all samples, the actual compositions especially the Fe and Nb contents are different from the nominal ones. There are 2 possible reasons of this composition difference; (1) evaporation of Sb during the synthesis process and (2) unreacting of Fe and/or Nb with Sb to form the HH phase due to the large difference in the melting points. In case of the Hf-doped system, the phenomenon (1) would be predominant, which results in the higher Nb content than the nominal one. On the other hand, in cases of the Zr- and Ti-doped systems, the phenomenon (2) would be predominant, which results in the lower Fe and Nb contents than the nominal ones. In order to understand the phase state more certainly, the Fe–Nb–Sb ternary phase diagram needs to be developed. The lattice parameters of the Zr- and Hf-substituted samples are similar but higher than that of the Ti-substituted sample, which can be explained by the difference of atomic radii of each element. All samples have high relative density, above 95% of the theoretical density.

Table 1 Comparison between our data and literature data on the zT_max and samples’ characteristics for Hf-doped FeNbSb.

Table 2 Comparison between our data and literature data on the zT_max and samples’ characteristics for Zr-doped FeNbSb.

Table 3 Comparison between our data and literature data on the zT_max and samples’ characteristics for Ti-doped FeNbSb.

The SEM images of the polished surface of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf) are shown in Fig. 2. It can be confirmed that all samples are dense with no remarkable cracks. The EDX point analysis revealed that the white inclusions observed in the SEM images of the Zr-substituted sample are an Sb–Fe alloy and an Fe–Nb alloy. On the other hand, the dark area observed in the Hf-substituted sample is determined as an Fe–Hf alloy. These results are well consistent with the results of the XRD analysis. Furthermore, it is also confirmed that the bright and dark area in Fig. 2(a) correspond to the HH phase with the similar chemical composition with the matrix phase while some of the black spots are a Ti-rich phase and most of those are pores.

Fig. 2

SEM images of the SPS bulk samples of (a) FeNb_0.9Ti_0.1Sb, (b) FeNb_0.9Zr_0.1Sb, and (c) FeNb_0.9Hf_0.1Sb.

Figures 3(a) and 3(b) show the temperature dependences of κ and κ_lat of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf), where the literature data for FeNb_0.88Hf_0.12Sb which exhibits zT = 1.5 at 1200 K are shown for comparison. κ_lat was obtained by subtracting the electronic component (κ_el) from the κ, where κ_el was estimated via Wiedemann-Franz relationship, i.e., κ_el = LσT (L is the Lorenz number 2.44 × 10⁻⁸ WΩK⁻²). As can be seen in Fig. 3(b), the Hf substitution is very effective to reduce the κ_lat of FeNbSb compared with the Ti- and Zr-substitutions. This is because that the substitution by heavy element makes large mass fluctuation leading to effective scattering of heat carrying phonons. On the other hand, all samples exhibit similar κ_lat values above 800 K, which is because the phonon-phonon scattering is predominant at high temperatures, while the phonon-impurity scattering is predominant at low temperatures. The κ_lat values of our sample FeNb_0.9Hf_0.1Sb are clearly higher than the literature data for FeNb_0.88Hf_0.12Sb in spite of their similar chemical compositions. It is considered that the differences in the microstructure and actual composition would cause this κ_lat difference.

Fig. 3

Temperature dependences of (a) total thermal conductivity (κ), and (b) lattice thermal conductivity (κ_lat) of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf).

Temperature dependences of σ, S, S²σ, and zT of the SPS bulk samples of FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf) samples are shown in Figs. 4(a), 4(b), 4(c), and 4(d), respectively. In these figures, the literature data^8,15) are shown for comparison. The σ values decrease while the S values increase with increasing temperature for all samples, showing metal-like behavior. The origin of the peaks observed in the temperature dependence of S is now unclear. The S values of the Ti- and Zr-substituted samples are very similar and clearly higher than those of the Hf-substituted sample, even though the nominal doping rate is the same for all samples. This can be explained from the actual composition of the HH phase summarized in Tables 1, 2, and 3, i.e., the actual Nb/Ti and Nb/Zr ratio is almost the same but clearly different from that of Nb/Hf. On the other hand, the σ values of the Ti- and Hf-substituted samples are very similar and clearly higher than those of the Zr-substituted sample, which would be caused by both the actual composition of the HH phase and the amount of the secondary phases. As can be confirmed in Fig. 1, the Ti-substituted sample has no remarkable secondary phases, which leads to high mobility compared with those of other samples containing some secondary phases and thereby high σ values as well as large S values are achieved in the Ti-substituted sample. As the results of σ and S, the Ti-substituted sample exhibits the best TE performance, the maximum S²σ and zT values are around 6 mW m⁻¹ K⁻² at 350 K and 0.7 at 1073 K, respectively.

Fig. 4

Temperature dependences of (a) electrical conductivity σ, (b) Seebeck coefficient S, (c) power factor (S²σ), and (d) zT of our samples having the nominal compositions FeNb_0.9M_0.1Sb (M = Ti, Zr, Hf), together with the literature data.^8,15)

In the Hf- and Zr-doped systems, as can be confirmed in Fig. 1 and Tables 1 and 2, our samples contain secondary phases Fe_0.7Hf_0.3, SbFe, and Fe₂Nb, which results in the difference between the nominal and the actual compositions. The samples reported in the literatures¹⁵⁾ have no such secondary phases and their actual compositions are similar with the nominal ones. The HH phases of our samples have larger M/Nb (M = Zr, Hf) ratio than the nominal ones, which leads to high doping ratio and thus small values of the Seebeck coefficient, as can be confirmed in Fig. 4(b). On the other hand, the secondary phases in our samples would scatter charge carriers, which leads to low carrier mobility. This low carrier mobility results in the similar values of the electrical conductivity between our data and the literature data (Fig. 4(a)), even though our samples might have larger carrier concentration than those in the literatures. This composition difference and existing of the secondary phases would effect on the low zT of our samples (Fig. 4(c)). On the other hand, in the Ti-doped system, as can be confirmed in Fig. 1 and Table 3, our samples contain no remarkable secondary phases and the Ti/Nb ratio is similar with the literature one.⁸⁾ As the results, our sample shows similar TE properties with the literature data.⁸⁾ Therefore, it can be concluded that synthesizing pure HH phase with optimized composition is important to obtain high zT.

4. Conclusion

The TE properties of FeNbSb substituted 10% Nb site with Ti, Zr, or Hf were investigated from room temperature to 1073 K. The Ti-substituted sample was nearly single phase while the Zr- and Hf-substituted samples contained secondary phases in addition to the HH phase. These secondary phases had large influences on the TE properties. In the present case, the Hf-substituted sample exhibited the lowest κ_lat, while the Ti-substituted sample exhibited the highest power factor. As the results, the Ti-substituted sample exhibited the best zT values, zT_max = 0.7 at 1073 K.

Acknowledgments

This work was supported in part by JST, PRESTO Grant Number JPMJPR15R1.

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