Synthesis and thermoelectric properties of high-entropy half-Heusler MFe1−xCoxSb (M = equimolar Ti, Zr, Hf, V, Nb, Ta)
Graphical Abstract
Introduction
Thermoelectric materials can realize direct conversion between heat and electricity, which is of great interest for both power generation and electrical cooling. The thermoelectric performance of a material can be quantified by its dimensionless figure-of-merit, which is defined as, where α is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity and T is the absolute temperature [1], [2]. κ comprises two parts, κ = κe + κL, where κe is the electronic thermal conductivity and κL is the lattice thermal conductivity. A good thermoelectric material should simultaneously possess a high power factor () and low κ, but it is difficult to optimize the properties individually due to their strong interconnections [3].
Half-Heusler (HH) compounds have great potential for power generation in the mid temperature regime (700 – 1000 K), as they generally have high power factors, robust mechanical properties, good thermal stability, low-toxicity and relatively inexpensive constituent elements. Maximum zT values of ~1.6 were reported for half-Heusler compounds and, a high efficiency of ~11.4% was obtained at 973 K with a temperature gradient of 656 K [4], [5], [6], [7], [8]. HH compounds are intermetallics with a simple cubic structure. They have a general composition formula of XYZ, where X and Z occupy a NaCl lattice and Y occupies half of the tetragonal sites. For better interpretation of their semiconducting properties, HH compounds can be also described as partially ionic Xn+(YZ)n− based on the Zintl–Klemm concept. In this case, the most electropositive element X acts as a cation and donates all of its valence electrons, while (YZ) form a covalent tetrahedrally bonded sublattice and act as an anion, resulting in a similar electronic structure to that of ZnS [9]. Based on the Zintl concept, a 18 valence electron count (VEC) per unit cell can be used to guide the identification of stable HH compounds as potential thermoelectric materials. MNiSn (n-type) and MCoSb (p-type) (M = Ti, Zr, Hf) are the most common HH compounds with a 18 VEC. They have been studied intensively and high zT values over 1 have been reported for both n- and p-type HH compounds [10], [11], [12], [13]. Some other 18 VEC HH compounds have also been reported, such as NbFeSb [14], [15], NbCoSn [16], VFeSb [17], ZrCoBi [18], [19] and TaFeSb [8]. Besides, there are many predicted 18 VEC HH compounds that have not been reported experimentally [20].
The vast variety of HH compounds with simple crystal structure motivates the idea of applying the high-entropy concept to the HH system. The high-entropy concept was first demonstrated in metal alloys that are composed of five or more elements in equimolar ratio, such as CuCoNiCrAlFe, FeCrMnNiCo and TiZrHfNbTa [21], [22], [23], which show interesting mechanical properties. The high-entropy concept has now been applied to other high-entropy compounds (HECs), including oxides [24], [25], nitrides [26], carbides [27], [28], borides [29], and chalcogenides [30], [31]. In these compounds, the equimolar elements are on the cation sublattice, and their large configurational entropy contributes to their formation as a single-phase [32]. Compared to the conventional solid-solutions with low amounts of additions, the high-entropy effect with equimolar components can overcome limited solubilities and structural mismatches. It was first demonstrated by synthesizing an equimolar mixture of MgO, CoO, NiO, CuO and ZnO, in which the limited solubilities of MgO–ZnO and CuO–NiO and the structural mismatches of tenorite CuO and wurtzite ZnO were overcome by the entropy effect, and a single-phase (MgCoNiCuZn)O with a rock-salt structure was formed [25]. The study of HECs has generated interesting results in different fields, such as dielectrics [33], Li-ion battery [34], [35], ultra-high temperature ceramics [27], and thermoelectrics [31]. In terms of HH thermoelectrics, the high-entropy concept could be an effective way to reduce their lattice thermal conductivity. HHs have relatively high thermal conductivities (10–20 Wm−1K−1 at 300 K for typical unalloyed compositions) which limits their zT values. An overview of the κL of some of the end-member HH alloys used here is given in Fig. 5(c). The multi-elements in the X sublattice will introduce point defects, mass contrast, structural complexity and possibly local phase separation, which could all contribute to the suppression of κL. Recently, there are two reports related to high-entropy HH compounds. Yan et.al. reported Nb1−xMxFeSb (M = Ti, V, Hf, Mo and Zr with an equimolar ratio) HH compounds [36]. The reported samples contained an impurity of NbSb2 and the multiple elements were not homogeneously distributed. However, there is an obvious reduction in the lattice thermal conductivity (κL is reduced by ~56% in x = 0.4 sample) and also an increase in hardness. Karati et.al. reported a Ti2NiCoSbSn HH compound that was claimed to be a high-entropy alloy, but it only contains at most 2 elements per atomic site [37]. The samples contained impurities of TiC and Sn and showed poor thermoelectric performance, but they found that the use of multi-elements improved the synthesisability and extended the solid solubility limits. Due to the limited research, it is still not clear what is the effect of the high-entropy approach on the synthesisability and properties of HH compounds.
In this work we investigated the synthesisability and thermoelectric properties of high-entropy HH compounds with six equimolar elements on the cation sublattice, of which the designed composition is MFe0.5Co0.5Sb (M = equimolar Ti, Zr, Hf, V, Nb, Ta) with a 18 VEC. As Sb-based HH compounds show very promising thermoelectric performance, the composition is based on six simple HH compounds of TiCoSb, ZrCoSb, HfCoSb, VFeSb, NbFeSb and TaFeSb. All of these compounds have the same crystal structure and a 18 VEC. A schematic crystal structure of MFe0.5Co0.5Sb is shown in Fig. 1, showing the mix of elements on the individual sites. The ideal configurational entropy of a compound with different cation sites and anion sites can be calculated using the following equation:where R is the gas constant, M, N and L are the number of constituent elements on X, Y and Z sites, and xh, xi and xj are the mole fraction of elements on X, Y and Z sites [38]. For MCo0.5Fe0.5Sb, the ideal configurational entropy is 2.485 R, which can be classified as high-entropy. The atomic radius of the smallest atom (V) and the largest atom (Zr) differ by more than 15%, which is not favorable to form a solid solution as suggested by the Hume-Rothery rule [39], but a single phase MFe0.5Co0.5Sb was formed by using the simple processing method of ball-milling (BM) the constituent elements, and there was no phase separation or impurity in the sample after sintering by using spark plasma sintering (SPS). MFe0.5Co0.5Sb has n-type semiconducting behavior and a very low lattice thermal conductivity of ~ 2.2 Wm−1K−1 at 300 K and ~1.8 Wm−1K−1 at 923 K. The thermoelectric performance of MFe0.5Co0.5Sb was improved by tuning the Fe/Co ratio. Moreover, the MFe1-xCoxSb system showed great tunability as a pure HH phase was maintained with VEC from 17.9 to 18.5, and the system can behave as both n- and p-type depending on the VEC.
Section snippets
Experimental details
Polycrystalline MFexCo1−xSb (M = equimolar Ti, Zr, Hf, V, Nb, Ta) samples were prepared by BM + SPS. Starting powders of Ti (- 325 mesh, 99.99%, Alfa Aesar), Zr (- 325 mesh, 98.8%, Alfa Aesar), Hf (- 325 mesh, 99.6%, Alfa Aesar), V (- 325 mesh, 99.5%, Alfa Aesar), Nb (-325 mesh, 99.8%, Alfa Aesar), Ta (-325 mesh, 99.97%, Alfa Aesar), Fe (<10 µm, 99.9+ %, Alfa Aesar), Co (-100 + 325 mesh, 99.8%, Alfa Aesar) powder and Sb (- 100 mesh, 99.5%, Alfa Aesar) were weighed according to the required
Results and discussion
Fig. 2(a) shows the XRD patterns of the high-entropy HH MFe0.5Co0.5Sb (M = equimolar Ti, Zr, Hf, V, Nb, Ta) samples after BM and after SPS. The MFe0.5Co0.5Sb compound exhibited a cubic structure with space group of . The samples after BM and after SPS were both single phase and no impurity was observed within the detection limit of XRD. Reference data for VFeSb (ICSD:152794) and ZrCoSb (ICSD:108317) are included for comparison. In all six related ternary HH compounds, VFeSb has the
Conclusions
High-entropy HH compounds of MFe1-xCoxSb (M= equimolar Ti, Zr, HF, V, Nb, Ta) were successfully prepared by a fast and scalable method of ball-milling and rapid SPS consolidation. XRD and EDX results indicates high purity and homogeneity, despite the fact that the atomic radius of the smallest atom (V) and the largest atom (Zr) differ by more than 15%. The six equimolar elements in the X cation sublattice, which have large configurational entropy, could contribute to the formation of a
CRediT authorship contribution statement
Kan Chen: Conceptualization, Methodology, Investigation, Writing – original draft. Ruizhi Zhang: Formal analysis, Writing – review & editing. Jan-Willem G. Bos: Writing – review & editing. Michael J. Reece: Conceptualization, Resources, Writing – review & editing, Supervision, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
We gratefully acknowledge the support from European Thermodynamics Ltd. J-W. G. B acknowledges Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/N01717X/1).
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2023, Journal of Alloys and CompoundsCitation Excerpt :High-entropy ceramics (HECs) with five or more cations have recently attracted significant attention due to their superior properties such as superionic conductivity [14], better oxidation resistance [15], good mechanical properties [16], low thermal conductivity [17,18] for various structural and functional applications [19]. High-entropy engineering provides a possible powerful strategy to explore thermoelectric performance by extending the composition design and was confirmed to increase the Seebeck coefficient and decrease lattice thermal conductivity in Sn0.25Pb0.25Mn0.25Ge0.25Te [20], chalcogenides [21], and half-Heusler [22]. Yunpeng ZHENG et al.’s work designed high-entropy (Ca0.2Sr0.2Ba0.2La0.2Pb0.2)TiO3 ceramics and obtained the minimum thermal conductivity of 1.17 W/(m·K) at 923 K and ZT of 0.2 at 873 K [18].