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Half-Heusler thermoelectrics: a complex class of materials

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 433201 (http://iopscience.iop.org/0953-8984/26/43/433201) View the table of contents for this issue, or go to the journal homepage for more

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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 433201 (15pp)

doi:10.1088/0953-8984/26/43/433201

Topical Review

Half-Heusler thermoelectrics: a complex class of materials Jan-Willem G Bos and Ruth A Downie Institute of Chemical Sciences and Centre for Advanced Energy Storage and Recovery, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EK14 4AS, UK E-mail: [email protected] Received 9 July 2014, revised 25 August 2014 Accepted for publication 29 August 2014 Published 2 October 2014 Abstract

Half-Heusler thermoelectrics first attracted interest in the late-1990s and are currently undergoing a renaissance. This has been driven by improved synthesis, processing and characterisation methods, leading to increases in the thermoelectric figure of merit and the observation of novel phenomena such as carrier filtering in nanocomposite samples. The difficulty in extracting good thermoelectric performance is at first glance surprising given the relative simplicity of the ideal crystal structure with only site occupancies and lattice parameter as crystallographic variables. However, the observed thermoelectric properties are found to depend sensitively on sample processing. Recent work has shown that prepared ingots can contain a range of inhomogeneities, including interstitials, nano- and micron sized Heusler inclusions and multiple half-Heusler phases. For this reason, the prepared materials are far more complex than initially appreciated and this may offer opportunities to enhance the thermoelectric figure of merit. Keywords: thermoelectric, half-Heusler, nanocomposites, TiNiSn, TiCoSb (Some figures may appear in colour only in the online journal)

1. Introduction

decades a large amount of research has been undertaken to discover materials with improved energy conversion efficiencies. This is the topic of many excellent reviews [4–12]. Among the routes explored are materials with complex unit cells and nanocomposite materials that allow a greater degree of flexibility in terms of optimising the underpinning thermoelectric parameters. The efficiency of a material is typically defined using the thermoelectric figure of merit: ZT = (S2σ/κ)T, where the Seebeck coefficient, S, is the voltage response to a temperature gradient, σ is the electrical conductivity, κ is the sum of the lattice (κlat) and electronic thermal (κel) conductivity, and T is the absolute temperature. The fundamental problem in achieving larger ZT values is that three of the four thermoelectric parameters (S, σ and κel) are linked through the electronic structure and cannot be optimised independently. This manifests itself in the widely reported dependence of S, σ and κel on charge carrier concentration (e.g. in [4]): increases in S

Thermoelectricity is the conversion of heat into electricity or vice versa, which arises due to the coupling of the flow of heat and charge carriers in materials [1]. It is well established that semiconductors show the strongest coupling between these two forms of energy and are therefore the materials of choice for use in thermoelectric waste heat harvesting or refrigeration [1]. In principle, thermoelectric devices can increase the efficiency of any heat generating process through the conversion of waste heat into electricity. However, wide-scale application is limited due to low device efficiencies and a high cost per generated unit electricity [2, 3]. A large variety of materials have been investigated since the 1950s, including the traditional thermoelectric materials: Bi2Te3, PbTe and Si1  −  xGex which have good performance near room temperature, at intermediate and high temperatures, respectively [4]. Over the past two 0953-8984/14/433201+15$33.00

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J. Phys.: Condens. Matter 26 (2014) 433201

result in decreases of σ, while any increase in σ is accompanied by an increase in κel. This interdependency limits ZT ≤ 1 for most thermoelectric materials. In order to exceed the ZT = 1 limit different approaches have been tried and probably the most influential guiding principle is that of the phonon-glass electron crystal (PGEC [13]). This states that the ideal thermoelectric material should have the electronic properties of a crystalline solid (i.e. a large S and σ) and the thermal properties of a glass (i.e. a low κlat). Materials with complex structures such as the skutterudites and clathrates have a highly conducting framework and loosely bound rattling ions and behave as PGEC materials [14, 15], which enables ZT  >  1. Another successful approach is that of nanostructuring [5, 6]. At its simplest, this can be a reduction in average grain size into the nanometre regime, which results in the introduction of interfaces in the sample. These are often effective at disrupting lattice vibrations while having less impact on the electron transport. This approach was for example successfully used to increase the ZT of Bi2Te3 alloys from 1 to 1.5, a 50% improvement [16]. Another approach based in solid state chemistry or metallurgy is exploiting metastability to induce phase segregation and the formation of nanoinclusions. This has been used to great effect in PbTe based thermoelectric materials with a highest ZT = 2.2 [17]. The main impact of the inclusions is a reduction of the lattice thermal conductivity, which approaches the amorphous limit for some of the PbTe based materials [17–19]. In this context it is also worth mentioning the recent report of ZT = 2.5 in SnSe single crystals [20]. This again is based on an ultra low thermal conductivity (κ ≈ 0.3 W m−1 K−1) which is linked to the unique crystal structure and the presence of Sn 5s2 lone-pair electrons. To summarise, most of the current high-performing bulk thermoelectric materials have low thermal conductivities ( >  2. The question that needs to be answered is what the most effective dopants, nano-inclusions and sample processing conditions for the half-Heuslers are. Some of the recent concepts in optimising the thermoelectric performance of half-Heuslers are illustrated in figure  1. These include samples that consist of multiple half-Heusler phases with a range of compositions, leading to compositional variations within the ingot. This has been linked to the observation of the low thermal conductivities (κ = 2–3 W m−1 K−1) that usually underpin the observation of ZT  >  1 (see section 4). The other two images illustrate the other focus of the review which is nanocomposite samples with Heusler (e.g. TiNi2Sn in TiNiSn with overall composition TiNi1 + ySn) or zincblende (e.g. InSb in TiCoSb) inclusions. In these cases there exists a clear structural link between inclusion and host (see section 2) which favours a coherent embedding and facile electron transport across the interfaces, leading to the observation of interesting electronic effects while also reducing the lattice thermal conductivity. Both types of nanocomposite are prepared through phase segregation by selecting an appropriate starting composition and heating protocol. Selected maximum ZT values for p-type XCoSb and n-type XNiSn based half-Heusler materials are given in table 1. These are divided into parent materials, samples that have been optimised by alloying (e.g. mixing Ti, Zr and Hf) and carrier doping, and a selection of nanostructured compositions. There are a number of recent reviews dealing with halfHeuslers and nanostructured half-Heuslers [21–23], and a number of papers that deal with the application of these materials in devices [23, 51]. Here we focus on the link between sample processing, experimental compositions and properties for (nano)composite half-Heusler samples. The review is organised as follows: section 2 provides background information on XNiSn and XCoSb half-Heusler thermoelectrics. Section  3 focuses on embedded nano-inclusions that form through phase segregation. Section  4 deals with the observation of low thermal conductivities in samples that contain mixtures of half-Heusler phases. The overall conclusion is that an understanding of the structure at all length scales is required for further progress in this field. 2.  Structure and properties of XNiSn and XCoSb (X = Ti, Zr, Hf) The X(YZ) half-Heuslers are one family of only a few materials that are semiconducting despite containing exclusively metallic elements. Here X is an electropositive element (commonly Ti, Zr or Hf), Y is a transition metal (e.g. Co or Ni) and Z is a main group element (either Sn or Sb). The halfHeusler structure can be described in several ways [21]. One insightful way is to consider a face centred cubic main group lattice with the electropositive X metals in all octahedral holes, while the transition metal occupies half of the tetrahedral sites. This leads to rocksalt (XZ) and zincblende (YZ) 2

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Figure 1.  Overview of the some of the recent approaches and lengthscales investigated in half-Heusler thermoelectrics research. The top left figure illustrates the presence of a range of Ti1 − xZrxNiSn half-Heusler compositions in a nominal Ti0.5Zr0.5NiSn sample. Reproduced from [28]. Published by The Royal Society of Chemistry. The resulting interfaces have been linked to reduced thermal conductivities (see section 4). Rietveld Analysis of x-ray or neutron powder diffraction enables an average experimental composition to be determined, while peak broadening can give an indication of (nanoscale) phase segregation. The top right figure illustrates the phase segregation into TiNiSn and TiNi2Sn observed for a nominal TiNi1.15Sn sample (section 3). This was determined using a combination of scanning electron microscopy (SEM) and Energy Dispersive x-ray (EDX) elemental mapping. Reproduced with permission from [29]. The bottom figure is a high-resolution transmission electron microscopy (TEM) image showing the interface between a half-Heusler (labelled hH) and Heusler (labelled fH) phase in a nanocomposite XCo1 + ySb sample (see section 3). Reproduced from [30] with permission of The Royal Society of Chemistry.

favourable for a large Seebeck coefficient and good electrical conduction [21]. Experimentally the n-type XNiSn materials have larger carrier mobilities than the p-type XCoSb materials leading to large power factors (≤6 mW m−1 K−2 [58]), while the p-type half-Heuslers require larger carrier concentrations to obtain sufficient electrical conduction. This reduces the Seebeck coefficient and lower power factors (≤3 mW m−1 K−2) are generally observed for the p-type materials [59]. Many chemical substitutions are possible to tune the charge carrier concentration but most often used are Sb for n-type doping in XNiSn and Sn as a p-type dopant in XCoSb [35, 57, 60–63]. The structural stability was investigated by several authors and this revealed substantial energy penalties for disordering the X, Y and Z metals, in keeping with the partially covalent nature of the bonding in the half-Heuslers [21, 64, 65]. The lowest energy defect for Ni based half-Heuslers was found to be Ni atoms occupying the vacant 4d tetrahedral site. Both the experimental and calculated phase diagram for Ti–Ni–Sn suggest that there is very limited, if any, solubility of Ni in TiNi1 + ySn [29, 66, 67]. A combined experimental-calculated ternary phase diagram for Ti–Ni–Sn is given in figure  3 and this illustrates some of the challenges in the preparation of TiNiSn. The main problem is the vicinity of a number of high-melting point binary Ti–Sn phases and the Heusler phase TiNi2Sn. These phases crystallise first upon cooling from the melt

sublattices. A schematic representation of the structure is given in figure 2. The balls and sticks emphasise the Y-Z and Y-X bonds in the half-Heusler structure. The transition metal (Y) is tetrahedrally coordinated by both main group (Z) and electropositive (X) element leading to a cubic coordination environment. Figure 2 also illustrates the vacant tetrahedral site that is occupied in the Heusler structure (XY2Z). Throughout this review we refer to the Y sites (4c and 4d) as tetrahedral sites, while the vacant site (4d) is also referred to as the interstitial site. A starting point for the description of the electronic structure can be obtained from molecular orbital theory [21]. This analysis suggests considerable bonding between Y and Z sand p-states on the zincblende sublattice, and predicts that the valence and conduction bands are made up of hybridized X and Y d-states. This is confirmed by electronic band structure calculations [52, 53], and is also in keeping with a simple Zintl model where the valence electrons from the electropositive Xn+ are transferred to a covalent YZn− framework so that all elements have a closed valence shell (for 18 e−) and semiconducting behaviour results. Density functional theory calculations indicate an indirect bandgap of 0.5 eV for XNiSn [54, 55], while TiCoSb has a larger gap of 0.95 eV and ZrCoSb and HfCoSb are reported to be semimetals [56, 57]. The states near the Fermi level nearly all result from d–d bonding and this leads to a large and structured density of states, which is 3

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Table 1.  Overview of reported maximum thermoelectric figure of merit values for selected half-Heusler compositions. These include

parent materials, compositions optimised through alloying and carrier doping, mechanical reduction of the grain size, and XNi1 + ySn, XCo1 + ySb and InSb-XCoSb nanocomposite samples. Unless indicated the samples are n-type conductors. Composition: XNiSn / XCoSb:  TiNiSn  TiCoSb  TiFe0.15Co0.85Sb (p-type)  ZrNiSn  HfNiSn XNiSn with alloying and carrier doping:  Hf0.75Zr0.25NiSn0.975Sb0.025  Ti0.95Hf0.05NiSn0.99Sb0.01  Zr0.5Hf0.5Ni0.8Pd0.2Sn0.99Sb0.01  Zr0.3Hf0.65Ta0.05NiSn  Ti0.3Zr0.35Hf0.35NiSn  Ti0.37Zr0.37Hf0.26NiSn  Ti0.5Zr0.25Hf0.25NiSn0.998Sb0.002  Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002 Mechanical reduction of the grain size:  Hf0.75Zr0.25NiSn0.99Sb0.01  Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2 XNi1 + ySn, XCo1 + ySb and InSb-XCoSb nanocomposites:   X = Ti; y ~ 0.1   X = Ti; y = 0.03–0.06   X = Ti; y = 0.05   X = Ti; y = 1.15   X = Zr0.25Hf0.75 y = 0.02  Ti0.5Hf0.5Co1.05Sb0.9Sb0.1 (p-type)  Ti0.5Zr0.25Hf0.25Ni0.95Co0.05Sb with 1% InSb  TiCo0.85Fe0.15Sb with 1% InSb (p-type)

ZTmax

@

Reference

0.4 0.0075 0.45 0.5 0.55 0.48

775 K 400 K 850 K 875 K 800 K 1000 K

[31] [32] [33] [31] [34] [34]

0.8 0.78 0.7 0.85 0.82 1 1.2 1.5

950 K 770 K 800 K 870 K 700 K 750 K 800 K 700 K

[35] [36] [37] [38] [39] [40] [41] [42]

1 1

873 K 1073 K

[43] [44]

0.67 0.6–0.7 0.56 0.44 0.7 0.3 0.5 0.33

700 K 700 K 775 K 800 K 775 K 760 K 820 K 900 K

[45] [46] [47] [48] [49] [30] [50] [26]

composition and homogeneity [28]. Other routes employed are melt-levitation [29, 48], reaction between a pre-reacted TiNi alloy and a Sn melt [45], and microwave assisted reactions [70]. The latter promise great reductions in sintering times which may be useful for the large scale preparation of these materials. An illustration of the impact of sample processing on the thermoelectric parameters is given in figure 4. This shows the temperature dependence of the thermal conductivity of three well annealed XNiSn (X = Ti, Zr and Hf) parent materials. At low temperatures the thermal conductivity is limited by point defect and boundary scattering, while phonon–phonon scattering dominates at higher temperatures [71]. The magnitude of the peak at 50 K reflects the degree of structural order in the sample, and is known to depend strongly on annealing for the Zr and Hf materials, with better ordered samples having larger peak thermal conductivities [72]. The data in figure 4 therefore suggests that the TiNiSn sample is considerably more disordered. The type of disorder is not clear from the available data but could include point defects but also a different nanoor microstructure (see section 3.1). The traditional approach to reducing the thermal conductivity is to introduce point defects by alloying with Ti, Zr and Hf on the X site [74], while Pd on the Ni site has also been shown to be effective at reducing κ [37] (see also table 1). A recent analysis of the thermal transport in Hf0.65Zr0.35Ni1  −  zPtzSn (z  ≤  0.15) does indeed show that the dominant reduction in thermal conductivity comes from alloying but that other mechanisms including boundary and electron–phonon scattering also play a role [27]. Great gains in performance have

Figure 2.  Ball and stick representation of the X(YZ) half-Heusler crystal structure. The tetrahedral interstitial sites that are occupied in the XY2Z Heusler structure are at the centres of the open cubes. The space group is F-43m; X (light blue) 4a (0, 0, 0); Y (dark blue) 4c (¼, ¼, ¼); Z (gold) 4b (½, ½, ½); vacant site 4d (¾, ¾, ¾).

and then slowly react to form TiNiSn [68, 69]. The formation of competing phases and slow reaction kinetics means that there are inherent problems with sample homogeneity which will affect the thermoelectric performance parameters. Annealing and post synthesis processing are therefore important experimental parameters that can induce differences in performance between nominally identical samples. Direct reaction between elemental powders in principle avoids the formation of the Heusler and Ti–Sn binary phases, and is expected to give a better control over final 4

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Figure 3.  Interpolated contour map of the melting temperatures of Ti–Ni–Sn ternary phase diagram. The ‘valley’-like location of TiNiSn makes phase-pure synthesis difficult from the melt. Reproduced with permission from [29].

3. Nanocomposites In this section  we review XNiSn and XCoSb half-Heusler nanocomposites with Heusler (XNi2Sn) or InSb inclusions. As discussed in section  2, the half-Heusler structure differs from the Heusler structure by filling of the vacant tetrahedral site, while it also contains a zincblende (YZ) substructure. It follows that there is a direct structural link between the Heusler and zincblende inclusions and the half-Heusler host. This structural relationship favours the coherent embedding of the inclusions, which is essential for facile transfer of charge carriers. Unconventional enhancements in performance due to carrier filtering by potential barriers have been predicted for coherently embedded metallic nanoparticles [80]. A related carrier filtering effect based on a semiconductor–semiconductor junction, which is proposed to be present for small Heusler inclusions, has been suggested to lead to enhanced power factors [49]. A schematic of the proposed semiconductor-semiconductor heterojunction is shown in the left hand side of figure 5. The basic hypothesis is that the potential barriers filter low energy charge carriers, thereby reducing the carrier concentration. This leads to an increase in Seebeck coefficient but also to an improved carrier mobility due to reduced electron–electron scattering, which offsets the reduced carrier concentration. The composite therefore maintains a good electrical conductivity (despite the reduction in carrier concentration) and has a substantially enhanced power factor. This is discussed in more detail in section 3.2. The important parameter for the observation of carrier filtering is the conduction band offset (ΔE) which determines the height of the potential barrier (figure 5, left). The magnitude of ΔE is determined by the offset between the conduction band minima of the host and the guest. Experimentally this can be influenced by the size of the inclusion, with smaller particles having a larger bandgap and ΔE. This is in keeping with the

Figure 4.  Temperature dependence of the thermal conductivity for XNiSn samples (X = Ti, Zr and Hf). Data reproduced from [60, 72, 73].

been achieved by using ball-milling and spark-plasma sintering (SPS). This involves reducing the grain sizes of arcmelted stoichiometric n-type (Zr,Hf)NiSn and p-type (Zr,Hf) Co(Sb,Sn) with κ = 4–5 W m−1 K−1 to the 200–300 nm regime, and consolidating those powders using spark plasma sintering (SPS [43, 44, 75–78]). This leads to a reliable reduction in lattice thermal conductivity (Δκ =  −1–2 W m−1 K−1) due to increased interface scattering, and ZT  ≈  1 in both n- and p-type based systems (table 1). It is therefore clear that reductions in average grain size are efficient at reducing the lattice thermal conductivity while not disturbing the electronic transport significantly. A similar observation was made earlier by Bhattacharya et al who reported a systematic drop in κlat as the average grain size diameter was reduced in TiNiSn1 − xSbx samples [73, 79]. We do not discuss mechanical nanostructuring any further and instead focus on off-stoichiometric nanocomposites (e.g. XNi1 + ySn) where inclusions have formed via phase segregation. 5

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Figure 5.  Left: nanometre scale hetero-junction between bulk half-Heusler matrix and nanometre scale Heusler inclusion highlighting the proposed low energy carrier filtering mechanism. Reproduced with permission from [49]. Right: schematic of the band energies of a TiNiSnTiNi2Sn semiconductor-metal heterojunction. Energy values correspond to the valence band maximum and conduction band minimum for the semiconductor TiNiSn, and the Fermi level of TiNi2Sn. Reproduced with permission from [48].

observation of these electronic effects for low y-values and small inclusions in XNi1 + ySn composites. The right hand side of figure 5 illustrates the situation for a metallic Heusler inclusion. At low temperature the Heusler inclusion is expected to withdraw charge carriers from the host, while at high temperatures carriers may be excited into the conduction band of the matrix [48]. No carrier filtering is predicted for large inclusions and the main impact is on the carrier concentration [29, 48]. Both semiconducting and metallic inclusions create additional interfaces and are expected to disrupt the flow of phonons, and reduce the lattice thermal conductivity. The InSb inclusions that have been exploited in the TiCoSb based half-Heuslers also impact on the thermoelectric properties in a manner that cannot be explained by conventional charge carrier doping alone (section 3.3). We will start by discussing the segregation of the excess Ni in TiNi1 + ySn composites (section 3.1). In principle, a whole spectrum of statistically distributed interstitials, via nanoinclusions to fully segregated Heusler phases is expected. This is followed by a summary of the literature on composites with Heusler (section 3.2) and InSb-inclusions (section 3.3) where ‘unconventional’ electronic effects have been observed.

Figure 6.  Close up of the (422) reflection for TiNiSn prepared by solid state reaction (SSR) and arc-melting (AM), followed by 2 weeks days annealing at 900 °C. (Powder x-ray diffraction collected on a Bruker D8 Advance diffractometer with monochromatic CuKa1 radiation). Details on the synthesis can be found in [28, 46].

of experimental x-ray photo electron spectroscopy data and the calculated electronic density of states suggested that the excess Ni is present as statistically distributed atoms occupying the vacant 4d tetrahedral site. Neutron powder diffraction analysis of arc-melted samples also suggested the presence of up to 6% statistically distributed interstitial Ni on the 4d site [46]. However, no information about the spatial distribution can be obtained from diffraction in this case, i.e. the data can be fitted equally well using TiNi1 + ySn or a mixture of (1 − y)TiNiSn and (y)TiNi2Sn with the same lattice parameter. A comparison of the x-ray diffraction patterns of arc-melted TiNiSn, arc-melted TiNiSn0.95 and a TiNiSn sample prepared by solid state reactions is presented in figure 6. This demonstrates significant increases in lattice parameter and peak broadening for the arc-melted samples that contain 4–6% excess Ni from the Rietveld analysis of neutron powder diffraction data (i.e. TiNiSn → TiNi1.04Sn and TiNiSn0.95  →  TiNi1.06Sn [46]). The larger lattice parameters are consistent with the partial occupation of the interstitial

3.1.  Segregation of excess Ni in TiNi1 ± ySn composites

The TiNi1 + ySn system has attracted considerable interest as it eliminates the need for the relatively expensive Zr and Hf, both of which are commonly used to reduce the lattice thermal conductivity (see also section 4). Improved ZT values (table 1) due to the presence of excess Ni were reported using arcmelting (κ = 4 W m−1 K−1; ZT = 0.6–0.7 [46]), liquid quenching [81, 82], induction levitation melting [29, 48], microwave synthesis [47] and solid state reaction between gas-atomised Ti–Ni alloys (20–30 µm particle size) and elemental Sn [45, 83, 84]. One of the first studies of non-stoichiometric TiNiSn was undertaken by Hazema et al who reported on samples with x = Ni/(Ti + Sn) between 0.47 (y = −0.06; Ni deficient) and 0.57 (y = 0.14 [81, 82]). These samples were prepared using induction heating and rapid quenching followed by spark plasma sintering. They reported a linear change in lattice parameter up to x = 0.54 and a lowest thermal conductivity of 2.9 W m−1 K−1 for x = 0.54 at room temperature. A comparison 6

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Figure 7.  Evolution of the Heusler inclusions as a function of their size. Part (a) shows the tetragonal distortion of the inclusions. This reflects the gradually increasing strain upon increasing inclusion size and reaches a maximum beyond which the inclusions are incoherently embedded. Part (b) shows TEM images that illustrate the changes in size and morphology of nanoparticles with increasing particle thickness: I (coherent nanoparticles), II (coherent nanodiscs), III (coherent platelets), IV (semicoherent platelets) and V (semicoherent spheres). Reproduced with permission from [84].

4d site, while the peak broadening could signal microstrain due to the presence of inclusions. In contrast, the SSR sample has sharp x-ray reflections and a smaller lattice parameter but was still found to contain a small amount (1–2%) of interstitial Ni in a neutron powder diffraction experiment (i.e. TiNiSn → TiNi1.02Sn [85]). The sharp x-ray reflections suggest that the excess Ni in this sample is in an earlier state of coarsening i.e. either statistically distributed or perhaps short range clustered. These results therefore suggest that it may be possible to incorporate a few percent statistically distributed Ni on the 4d site in TiNiSn before segregation into Heusler inclusions occurs. This is supported by a gradual increase in half-Heusler lattice parameter up to y = 0.1 in TiNi1 + ySn samples [29]. The arc-melted samples also contain substantial fractions (up to 10%) of fully segregated Heusler impurities, while these are absent in the sample prepared using solid state reaction. The absence of Heusler impurities is consistent with a reaction path that does not proceed via the melt (section 2).

A detailed electron microscopy study of TiNi1 + ySn samples prepared through reactive sintering between micron sized TiNi alloy particles and molten Sn has been reported [84]. This demonstrates a wide range of inclusions from particles to discs, to platelets and nano-spheres, which can be coherently or incoherently embedded. These results are summarised in figure 7. The inclusions were only found to be slightly Ni rich with Ti:Ni:Sn ratios of 1:1.1:1 for the smallest inclusions, and 1:1.2:1 for larger micron sized particles. These values are comparable to those reported by the same authors in an earlier report [83] and may reflect the difficulty of extracting accurate compositions in a TiNiSn background. The observation of such a wide range of sizes, varying from clusters at the few unit cells, to large incoherently embedded nano-inclusions, suggests a gradual coarsening of statistically distributed Ni atoms into segregated inclusions. The extent of coarsening is expected to depend on the processing used, which provides a possible explanation for differences observed between 7

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Figure 8.  TEM images of spark plasma sintered pellets of Zr0.5Hf0.75Ni1 + ySn nanocomposites containing 2 mol % (a) and 5 mol % (b)

Heusler inclusions (FH = Heusler). The spherical shape of the precipitates suggests their nucleation and isotropic growth as well as their endotaxial insertion within the half-Heusler matrix. In addition to spherical precipitates, 2–8 nm thick and up to 30 nm long lamellar structures are also observed in panel B. Reproduced with permission from [49].

the studies cited in this section report a reduction of the lattice conductivity down to κ = 3–4 W m−1 K−1 with largest ZT values of around 0.7 being reported (table 1).

composites with nominally similar compositions. The authors also provide an explanation for the evolution of coherent to incoherently embedded inclusions with increasing size, and link this to a destabilising interfacial strain due to the smaller lattice parameter of the half-Heusler matrix. Douglas et al report on samples prepared using levitation melting [48]. These contain micron sized segregated Heusler inclusions leading to a decrease of the thermal conductivity and an increase to ZT = 0.44 (κ = 5.5 W m−1 K−1 at RT) at 800 K for a TiNi1.15Sn sample. A follow up paper [29] reports that the inclusions span several length scales (~20 µm and 500 K). The nanostructure thus leads to significantly different carrier energies and transport properties. Interestingly, this is only observed for the y = 0.02 sample but not for the y = 0.05 sample that shows an increase in carrier concentration, a reduced S and increased σ and has a similar power factor S2σ as the y = 0 reference sample (figure 9). The absence of the carrier filtering for the y = 0.05 sample is consistent with the larger average size of the inclusions in this sample. This initial report was followed by a study of Ti0.1Zr0.9Ni 1 + ySn (y ≤ 0.1) which revealed increases of up to 200% for the Seebeck coefficient and up to 43% for the carrier mobility [88]. The authors observe a constant lattice parameter for the half-Heusler phase in keeping with the segregation of the excess Ni into Heusler domains. The y = 0.04 sample yields 10–60 nm diameter precipitates. There is no

obvious strain at the interfaces, in agreement with the close structural relationship between host and guest. It is thought that these inclusions grow via a co-nucleation and growth mechanism, leading to particles as small as 2–3 nm (3–5 unit cells). Improvements in performance are observed for y = 0.04 and 0.1. Both samples have similar temperature dependences of the carrier concentration but y = 0.1 has a much larger S linked to a larger effective carrier mass, which confirms that the inclusions (carrier filtering) not only lead to a lower carrier concentration but also impact on the mobilities. The carrier effective mass does not show a systematic trend with y. The estimated values are 0.6me for y = 0 and 0.02, 0.5me for y = 0.04; and 0.8me for y = 0.1. This indicates that the carrier relaxation times are affected by the presence of the inclusions. The highest observed ZT = 0.3 at 800 K, compared to ZT = 0.1 for the y = 0 reference sample. Another study by the same group focuses on the Sb doped analogues of Ti0.1Zr0.9Ni1 + ySn [89]. Again a constant lattice parameter is observed in keeping with the phase segregation of Heusler phases. These samples have a much larger σ due to the increased carrier concentration resulting from the Sb doping. The mobilities are comparable to the non-Sb doped samples reported in their earlier report, while the Seebeck coefficient is reduced [88]. The samples have similar power factors and the inclusions do not appear to have a carrier-filtering effect. This could be because of the increased carrier concentration which may render the 9

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Figure 10.  Temperature dependence of the measured (top) and calculated (bottom) electrical resistivity (σ) and Seebeck coefficient (α) for

XCoSb − x% InSb nanocomposites. Reproduced with permission from [50].

indicates that the improvements in mobility are linked to better relaxation times.

potential barriers ineffective. This suggests that deeper wells or a different strategy altogether are needed to manipulate the properties of optimised bulk compositions. The carrier effective masses fall between 2.6me and 3.5me, which are larger than for the non-Sb doped samples [88]. Enhancements of the power factor were also observed in p-type samples with composition Ti0.5Hf0.5Co1 + ySb0.9Sn0.1 [30]. The y = 0.05 samples showed spherical nanoparticles with sizes ranging from 5–60 nm randomly dispersed in the half-Heusler matrix. TEM revealed a coherent to semi-coherent relation between the lattice planes in the inclusion and host. The small size and spherical nature of the inclusions along with the coherent boundaries suggest that the inclusions either form through the nucleation of seeds within a formed h­ alf-Heusler matrix, followed by isotropic growth relying on Co diffusion or by a competing co-nucleation of both half-Heusler and Heusler seeds during the solid state synthesis from elemental powders. The Heusler inclusions remain small in keeping with the dilute nature of the Heusler seed points within the reaction mixture. The impact of the inclusions is similar to that observed in the n-type materials: reductions in carrier concentration and increases in hole mobility. The carrier mobilities in these nanocomposite samples are much smaller ~1 cm2 V−1 s−1 than for comparable n-type samples 20–50 cm2 V−1 s−1. Effective carrier masses of 4.3me (y = 0), 4.9me (y = 0.05) and 6.3me (y = 0.04) are observed. The small increase in effective mass

3.3.  Electronic effects in composites with InSb inclusions

The second route that has been explored to prepare coherently embedded inclusions is through the phase segregation of InSb inside a XCoSb matrix. The literature contains two notable papers on this type of composite [26, 50]. The first paper describes n-type Ti0.5Zr0.25Hf0.25Co0.95Ni0.05Sb alloys with 0, 1, 3 and 7 at% InSb inclusions [50]. These samples were prepared from the elements by induction melting, followed by mechanical homogenisation and SPS. InSb nanoparticles with diameter 10–30 nm were found evenly distributed at the grain boundaries. The authors compared their measured transport data with an effective medium model after Bergman and Fell [90] and were able to show that although the electrical conductivities are comparable to the expected average of TiCoSb and InSb, the Seebeck coefficient is much enhanced (figure 10). This leads to an enhanced power factor beyond that expected for a simple mixture of the two materials. The thermal conductivity is also somewhat reduced and this leads to a maximum ZT = 0.5 at 800 K compared to ZT = 0.2 for a sample without InSb inclusions. The second paper describes p-type TiCo0.85Fe0.15Sb samples with 0, 0.7, 1, 1.5 and 3 at% InSb inclusions [26]. These 10

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Figure 11.  SEM image and elemental mapping of a nominal Ti0.37Zr0.37Hf0.26NiSn sample. Heat capacity and thermoelectric figure of merit (ZT) for the same sample. Reproduced with permission from [40].

observation of ZT > 1 is unusual as most good n-type samples, even those processed using ball-milling and SPS have ZT = 1 (table 1). However, in some instances a favourable combination of a large power factor (5–6 mW m−1 K−2) and low thermal conductivity (2–3 W m−1 K−1) has been achieved. This has only been reported for mixtures of Ti, Zr and Hf and never for samples that contain only two out of these three elements. The first example was published in 2005 and discussed the evolution of the thermoelectric parameters upon substitution of Ti into Zr0.5Hf0.5NiSn [42, 91]. The samples were prepared using arc-melting, followed by pulverisation, and densification using a hot-press at a pressure of 100 MPa and 1200 °C for 1 h. The changes in thermoelectric parameters upon introduction of Ti are dramatic, and improvements in S, ρ and κ are reported. The room temperature resistivity decreases from 10–5 mΩ cm, while the Seebeck increases from −175 µV K−1 to a peak value of  −350 µV K−1. These changes were tentatively attributed to changes in the electronic structure but are highly unusual due to the inverse relationship on carrier concentration that normally links the thermoelectric parameters. The thermal conductivity decreases from 4 W m−1 K−1 to 3 W m−1 K−1. Antimony substitution gives a response consistent with electron doping but also reduces the overall thermal conductivity (despite an increased electronic contribution). This result has remained controversial [35] but recently some progress has been made towards the understanding of ZT > 1 in these compositions.

samples were prepared using a similar methodology. The average grain size of the half-Heusler matrix decreases from 30–50 µm to 5–10 µm as the amount of InSb is increased. In addition, a large number of InSb precipitates with typical size of 20–60 nm were found on the boundary of the half-Heusler matrix. The electrical conductivity is found to increase which is primarily due to an increase in carrier mobility and not concentration. This is in keeping with the exceptionally high carrier mobility of InSb (104 cm2 V−1 s−1) compared to the matrix (~0.5 cm2 V−1 s−1). The Seebeck coefficient is again enhanced and does not follow the usual inverse relationship with carrier concentration, suggesting that the variation of S with InSb content is linked to the scattering parameter. The largest power factor is 360% increased compared to the matrix. Modest reductions of the high-temperature thermal conductivity are also observed. The lowest thermal conductivity is around 4 W m−1 K−1 at 900 K. The ZT is enhanced to 0.33 at 900 K, which is a 450% improvement over the matrix. 4.  High ZT in multiphase half-Heusler thermoelectrics The other area of great interest is the observation of ZT > 1 in some XNiSn samples containing mixtures of Ti, Zr and Hf. These elements induce strong alloy scattering of phonons, and are effective in reducing the lattice thermal conductivity. The 11

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Figure 12.  Element-specific EDX mappings of the five constituents of the phase separated Ti0.5Zr0.25Hf0.25NiSn compound with brightness proportional to the concentration. Temperature dependence of the Figure of Merit and the thermal conductivity of the Ti0.5Zr0.25Hf0.25NiSn1 − xMx compounds. Reproduced from [41] with permission from the PCCP Owner Societies.

Populoh et al used arc-melting followed by annealing to synthesise a sample of composition Ti0.37Zr0.37Hf0.26NiSn from elemental precursors [40]. Elemental mapping and x-ray diffraction showed the presence of Ti rich and poor halfHeusler regions with compositions Ti0.72Zr0.22Hf0.06NiSn and Ti0.2Zr0.47Hf0.33NiSn, rather than a uniform distribution of Ti, Zr and Hf. The elemental maps are shown in figure  11, and the segregation occurs over rather long length scales ~5–10 µm. The thermoelectric properties were investigated in the 2–900 K interval and the main result is the observation of a low lattice thermal conductivity of 2.3 W m−1 K−1 between 575 and 700 K. Low resistivities on the order of 2 mΩ cm at 900 K and large Seebeck coefficients −325 µV K−1 lead to ZT ~ 1 between 650 and 800 K. A significant observation is that the heat capacity of some samples is suppressed near 625 K (figure 11), and this can lead to an unrealistic high ZT = 1.5 at that temperature. The suppression is linked to samples with a dendritic microstructure and the authors suggest that these samples may undergo a spinodal decomposition which leads to an apparent reduction of the heat capacity and thermal conductivity.

The second paper reported a large ZT in lightly doped Ti0.5Zr0.25Hf0.25NiSn samples which were prepared using repeated arc-melting, followed by ball-milling, cold pressing and sintering at 1000 °C [41]. Synchrotron x-ray diffraction again revealed the presence of multiple half-Heusler phases and EDX elemental mapping suggested a homogenous distribution of Zr, Ni and Sn, while the Ti and Hf distributions complement each other (figure 12). A maximum ZT = 1.2 was observed for a sample with 0.2% Sb. This is again based on a low thermal conductivity with a minimum of 2.5 W m−1 K−1 between 600–800 K. Interestingly, the reported thermal conductivities show a strong scatter despite the minimal differences in composition (figure 12). We investigated the structures and thermoelectric properties of Ti1 − xZrxNiSn (x = 0, 0.25, 0.50, 0.75 and 1), Ti0.5Hf0.5NiSn and Zr0.5Hf0.5NiSn [28] samples prepared via solid state reactions. Careful analysis of powder x-ray diffraction data revealed that all samples containing mixtures of X elements show multiphase behaviour (see also figure  1). This is even the case for Zr0.5Hf0.5NiSn where there is only a small size difference between the two X metals. The presence of wide 12

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distributions of phases, instead of two limiting compositions suggests that this is a kinetic effect and is not driven by phase separation. The Seebeck coefficient and resistivity do not appear to be adversely affected by the multiphase behaviour. The impact on the thermal conductivity was measured for a Ti0.5Zr0.5NiSn sample annealed for different lengths of time, and was found to be almost constant at 4 W m−1 K−1 despite significant changes in phase distribution. This suggests that the main reduction in lattice thermal conductivity comes from the alloying of Ti and Zr and not from the multiphase behaviour in this particular system. A detailed study on the formation of a Ti0.33Zr0.33Hf0.33NiSn sample was reported [92]. These samples were prepared using repeated arc-melting and annealing without post synthesis densification. Powder x-ray diffraction and SEM/ EDX revealed that a Ti-rich phase surrounds Zr and Hf rich grains with some evidence for TiNi2Sn segregation within the Ti-rich domains. This is in keeping with the Zr and Hf-rich phases with higher melting points crystallising first. An oxidation study also demonstrated that the Ti-rich domains decompose into TiNi2Sn, Ti6Sn5 and Sn at a much lower temperature than previously thought (473 K). In another study, Ti0.3Zr0.35Hf0.35NiSn was prepared by arc-melting, ball-milling and densification by SPS [39]. SEM and EDX revealed metallic Hf-rich domains after SPS, which were reduced upon annealing at 890 °C (for 20 and 25 d). Multiphase behaviour was observed in powder x-ray diffraction for all prepared samples. The high temperature thermal conductivity decreases upon annealing. A relatively high thermal conductivity of 3.5 W m−1 K−1 and a low ZT = 0.7 were observed for the sample annealed for 25 d. These recent results demonstrate that mixing Ti, Zr, and Hf on the X-site does not result in simple alloys with statistically distributed X metals but that instead a complex distribution of half-Heusler phases with different ratios of X-metals occurs. The length scales over which changes in composition occur appear to be on the order of 5–10 µm (figures 11 and 12 [28, 40, 41]). This is far larger than a typical electron mean free path and only a small fraction of the phonon spectrum should be affected [24]. The presence of multiple half-Heusler phases has been linked to the reduced thermal conductivities in that occur in some XNiSn samples. If this is correct, structural changes on shorter length scales should also be present. It is also clear that the heat capacities of these samples should be measured independently to prevent artefacts from suggesting a reduced thermal conductivity.

potential benefits are enormous: if thermal conductivities on the order of 1 W m−1 K−1 could be achieved without degrading the electronic properties ZT >>  2 should be achievable. The enhancements in electronic properties attributed to carrier filtering are of enormous interest but have so far not led to ZT > 1. This appears to be related to the larger electron concentrations in optimised samples, which render the potential barriers less effective. A similar problem was reported for the resonant doping observed in V ( 2. To achieve this, it will be necessary to manipulate the structure at all length scales with the aim of reducing the thermal conductivity towards the calculated minimum value.

5. Conclusions

Acknowledgements

We have reviewed the recent literature on nanocomposite and multiphase XNiSn and XCoSb half-Heuslers with promising thermoelectric properties. It is evident that sample processing plays a key role in the observed properties and that a better understanding of the composition, processing and structure at all levels, including unit cell, nano and microstructure is needed in order to extract the maximum performance from these materials. Uniting large power factors with low thermal conductivities remains a significant challenge. However, the

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Half-Heusler thermoelectrics: a complex class of materials.

Half-Heusler thermoelectrics first attracted interest in the late-1990s and are currently undergoing a renaissance. This has been driven by improved s...
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