The imperative demand for alternative and sustainable energies and energy conversion technologies to reduce our global reliance on fossil fuels leads to important regimes of research, including that of thermoelectricity. Thermoelectricity is the simplest technology applicable to achieve the direct conversion between heat and electricity. The dimensionless figure of merit (ZT) is determined by ZT = α²σT/κ = α²T/ρ(κ_L + κ_e), where α is the Seebeck coefficient (i.e., thermopower), σ the electrical conductivity, ρ, the electrical resistivity, κ, the thermal conductivity (including the lattice thermal conductivity, κ_L, and the carrier thermal conductivity, κ_e), and T the absolute temperature. A high efficiency thermoelectric (TE) device consists of legs (pellets) each made of high dimensionless figure of merit n-type or p-type material. These n-type or p-type legs are connected electrically in series and thermally in parallel to form a TE module or device. According to the definition of ZT, then a high ZT material is essentially a “phonon-glass electron-crystal” (PGEC) system with a large Seebeck coefficient [1,2]. Apparently, it is difficult to satisfy these criteria in a material with a simple crystal structure since the three physical properties (α, σ, and κ) that govern the ZT are interdependent: a modification to any of these properties often adversely affects the other properties. Thus, the ZT values of most state-of-the-art TE materials, such as Bi₂Te₃ [3,4,5], SiGe [6,7,8], and PbTe [9,10,11,12], are below or around to the value of unity, i.e., ZT_max ≈ 1. The conversion efficiency of TE device is determined by both the Carnot efficiency and the ZT values of the TE materials. For example, the maximum conversion efficiency of TE power generation, η, is given by: (1) where T_H is the hot side temperature, T_C the cold side temperature, and T_m the mean temperature. Of course, the first term in parenthesis is the Carnot efficiency. For a given working temperature, e.g., T_C = 300 K and T_H = 800 K, the maximum conversion efficiency dependence of ZT values can be obtained by Equation 1 and illustrated in Figure 1. As shown in Figure 1, for T_C = 300 K and T_H = 800 K, if the ZT = 1, the maximum η is around 10%, which is much lower than the Carnot efficiency (62.5%). Although the low efficiency of current TE materials is the main drawback of TE technology, nevertheless TE technology still plays an important role in the recovery of industrial or automotive waste heat [13,14,15,16,17,18,19,20,21], utilization of solar thermal energy (infrared) [22,23,24,25,26,27,28,29], and the application of solid-state refrigeration [30,31,32,33]. It is important to note and remember that waste heat is a 0% efficiency process and thus any cost effective technology that can recover some part of this waste heat is very important. Furthermore, unused thermal energy is very abundant, such as industrial or automotive waste heat.

The key goals of TE research are to discover brand new classes of materials with high TE performance and/or improve the performance of the existing well-known materials, such as Bi₂Te₃, SiGe, and PbTe alloys. These materials ideally, should also be stable at high temperature, possess low contact resistance and exhibit low parasitic losses. Among the wide variety of TE materials, half-Heusler (HH) compounds are intermetallic compounds formulated as MNiSn [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] and MCoSb [49,50,51,52,53,54,55,56,57,58,59,60,61,62] (M = Ti, Zr, or Hf) and it was pointed out as one kind of new promising TE materials in the temperature range around 700 K and above. Band structure calculations [63,64,65,66] show that many HH systems with 18-valence electrons are narrow band gap semiconductors, which will result in a high effective mass and a large Seebeck coefficient. For instance, the Seebeck coefficient of HH compounds TiNiSn, ZrNiSn and HfNiSn are in the range of −200 to −400 µV/K (n-type) at room temperature [36,62], which is higher than that of the state-of-the-art Bi₂Te₃ compounds. For this reason, HH compounds have attracted considerable attention as a promising candidate material for moderate and high temperature TE power generation applications. However, the biggest disadvantage for the HH compounds is their relatively high thermal conductivity. Two of the authors (Poon and Tritt) have been collaboratively working on these materials for over more than a decade. For the most widely investigated MNiSn and MCoSb (M = Ti, Zr, or Hf) systems, the thermal conductivity is on the order of 10 Wm⁻¹K⁻¹ at room temperature [34,36,67,68], which is almost 5 times higher than that of commercial Bi₂Te₃ compounds [3,4,5]. Therefore, over last two decades, the main research efforts have focused extensively on methods and techniques in order to significantly decrease the thermal conductivity of these HH compounds, while simultaneously maintaining their high power factors, PF (PF = α²σ = α²/ρ). The power factor reflects primarily the electronic transport component of the figure of merit, ZT.

Over the past several years, one successful strategy that has been used to decrease the thermal conductivity in several TE materials is that of nanostructuring or introducing nano-scale secondary phases into the host matrix to form nanocomposites. Indeed, the nanostructuring approach significantly enhances the ZT values of HH nanocomposites by significantly reducing the lattice thermal conductivity [69,70,71,72,73,74,75,76,77,78]. However, more recently, it is reported that, in addition to the reduction in the lattice thermal conductivity, nanostructuring can also increase the power factor, PF, in some HH nanocomposites [79,80]. In other words, it is possible that in some material systems the three interrelated physical properties (α, σ, and κ) can be decoupled by introducing nanostructures.

Herein, we review the recent progress in improving the TE performance of several HH compounds by utilizing the strategy of forming HH nanocomposites. Before the detailed review of HH nanocomposites, we would like to provide some important background by introducing the structure of HH compounds, and highlight some of the more typical strategies that have been previously used in order to enhance the TE properties of HH compounds. After that, we will review the recent progress in HH nanocomposites, which can be classified according to the various types of microstructures. Finally, we finish with a discussion of challenges and promising strategies for further research directions in these materials.

The half-Huesler phase is one kind of the best known intermetallic compounds, and it is represented by the general formula ABC, where A and B are transition metals, and C is an sp metalloid or metal [62,81]. The crystal structure of a typical HH compound ABC is MgAgAs type with space group of , and is shown in Figure 2. In the structure shown in Figure 2, it consists of three filled interpenetrating face-centered cubic (fcc) sublattices and one vacant fcc sublattice. One should note that the full Huesler material would contain all four interpenetrating sublattices and would be of the form, AB₂C. In the HH compounds, the elements A and C form a rock salt structure and B is located at one of the two body diagonal positions (1/4, 1/4, 1/4) in the cell with leaving the other one (3/4, 3/4, 3/4) unoccupied. The more detail introduction of HH structure can be found in review by Graf et al. [82].

One of the first strategies for enhancing ZT values (not only for HH materials, but for all TE materials) is by tuning the carrier concentration via doping. Because the electrical conductivity σincreases with an increase in carrier concentration, and while the Seebeck coefficient α decreases, the power factors (PF = α²σ) typically exhibit their highest values at carrier concentrations between 10¹⁹ and 10²¹ carriers per cm³ [83]. This indicates that heavily doped semiconductors, either narrow band gap or degenerate semiconductors, usually result in the best TE materials. For HH compounds, due to their specific structural features, it is possible to dope each of the three occupied fcc sublattices individually for tuning and optimizing the carrier concentration. Moreover, significant doping (or atomic substitutions) in the HH compounds can also introduce point defects, mass fluctuation scattering and strain field effects that can be utilized in order to effectively scatter short- and mid-wavelength heat-carrying phonons, which will significantly reduce the lattice thermal conductivity. In the most widely investigated MNiSn and MCoSb (M = Ti, Zr, or Hf) systems, it is typical to alter the number of charge carriers by doping on Sn and Sb site, and simultaneously introduce disorder by isoelectronic alloying on M site with Ti, Zr and Hf. For example, in the TiNiSn system, using x = 1%–5% Sb for Sn, in TiNiSn_1−xSb_x) yield the best changes in the band structure in order to effectively reduce the resistivity. Furthermore, using isoelectronic doping on the A and B sites, e.g., Ti_1−yMyNi_−zR_zSn_1−xSb_x (M = Zr, or Hf) for the A site and (R = Pd or Pt) for the B site work best for manipulating or significantly lowering the lattice thermal conductivity. One can see that the compositions can get extremely complex. Thus, the ZT values of MNiSn and MCoSb (M = Ti, Zr, or Hf) systems can be significantly improved. Figure 3 presents an overview on the most promising doped n and p-type HH compounds with relatively high ZT values. For the doped n-type TiNiSn and TiCoSb systems, the reproducible highest ZT values are achieved to values of ZT ≈ 1 [84,85] and ZT ≈ 0.7 [49], respectively, which are much higher than that of the undoped compounds. One must also make note that one of the very important attributes of these materials is that they exhibit excellent thermal stability to temperatures as high as 900 °C in the Ti_1−yMyNi_−zR_zSn_1−xSb_x system. Also by doping the p-type HH compounds they obtain their highest ZT values of ZT ≈ 0.5 at 1000 K [86].

Further significant improvements in the TE properties of HH compounds are thus dependent upon new materials design approaches other than just simple doping or substitutions. The most probable of these is the recent successful strategy of utilizing a nanostructuring approach in these materials. Nanostructuring has become a new paradigm approach of TE materials research that has been widely used to improve the ZT of several bulk TE materials over the past several years [92,93,94,95,96,97,98,99,100]. In the nanostructured bulk materials, or nanocomposites, the presence of multiple length-scales down to a few nanometers (), provides new avenues for phonon scattering in addition to the mass fluctuation alloying (), grain boundary or surface scattering (), phonon-phonon interactions (), and strain fields (), which all can occur in parallel and thus each adds to the process according to the Matthiessen’s rule, given below in Equation 2, with the shortest scattering process dominating. (2)

Therefore, all these various scattering processes cover a wide range of phonon wavelengths in order to more effectively reduce the lattice thermal conductivity. Meanwhile, it is also expected that, in a system with a semiconductor host matrix with metallic nanoinclusions, the Seebeck coefficient can be increased without significantly sacrificing electrical conductivity by interface charge carrier energy filtering effect [101,102,103,104,105]. Many different HH nanocomposites were investigated in the past with regards to improving their TE properties, and the details will be reviewed in section 3. Implementation of the nanostructuring process in HH compounds has indeed led to enhancement of ZT, which is due to the significant reduction of the lattice thermal conductivity in most cases [69,70,71,72,73,74,75,76,77,78], and also a substantial improvement of the power factor [79,80].

In this section, we categorize the HH nanocomposites in terms of the type of microstructure: (1) micro-scale HH matrix with nano-scale inclusions (shown in Figure 4a), and (2) nano-scale HH phase with nanoinclusions (shown in Figure 4b). For the two kinds of nanocomposites, there are also several different preparation methods for each of them. For example, nanoinclusions in a micro-scale HH matrix can be prepared by in-situ formation [79,80,106] as well as ex-situ mixing [71,77,78,107,108,109,110], and the nano-scale HH phase can be obtained by either ball milling [53,67,72,73,111] or melt spinning [74,112,113]. It is not our intent (which would be quite daunting) to cover all the possible preparation methods for HH nanocomposites in this article. Instead, the purpose of this review lies in depicting the most representative HH nanocomposites with particular emphasis on the relation between their nanostructure and the resulting TE properties from results obtained over the last several years.

Figure 21 shows the overall trend in the development of the ZT (TE performance) of HH compounds over last two decades. First, doping/substitution can optimize the carrier concentration to achieve the highest power factor as well as ZT values. Furthermore, the ZT values of doped HH compounds can be further enhanced by the nanostructuring approach due to boundary scattering effect and energy filtering effect. Now one should ask the question: what is the next step to enhance ZT?

One such question; is there still some ability to further reduce the lattice thermal conductivity by nanostructuring? In order to investigate just how much more further reduction of the lattice thermal conductivity are possible, then we need to estimate the minimum lattice thermal conductivity, κ_min, for the specific materials. For example, κ_min is estimated for the ZrNiSn compound by applying a model developed by Cahill et al. [137]: (3) where the summation is over the three polarization modes and k_B the Boltzmann constant. The cut-off frequency (in unit of Kelvin) is , where n_a is the number density of atoms, the reduced Planck constant, v_i the sound velocity for each polarization modes. The κ_min of ZrNiSn, calculated by Zhu et al. [138], is shown in Figure 22, and thermal conductivity of ZrNiSn based nanocomposites are included for comparison. From this plot (Figure 22) it is apparent that there is still some opportunity of further significant reduction of κ_L between the κ_min of ZrNiSn and the lowest κ_L of ZrNiSn based nanocomposites in the higher temperature range. Immediately, one might propose that nanostructures with even smaller sizes could further reduce the lattice thermal conductivity for a ZrNiSn based nanocomposite. However, the estimated phonon mean free path of HH-x nanocomposite is on the order of ~1 nm at high temperature [unpublished], which is comparable to the lattice parameter of the HH compound, so this approach is not likely to be effective. And, we should keep in mind that if the size of the HH matrix decreases to ~1 nm the effect of the small grains will also significantly decrease the carrier mobility through enhanced electron scattering [136]. Therefore, just blindly pursuing even smaller nanostructure is not likely to lead to the desired effect of enhancing the ZT but would most likely lead to a decrease in the ZT.

In addition, besides reducing the lattice thermal conductivity, one should also be more attentive of ways to further improve the power factor by nanostructuring, especially enhancing the Seebeck coefficient. The above discussion mentioned that the special potential energy barrier generated by nanoinclusions can selectively scatter low energy carriers and thus result in a significant improvement in the Seebeck coefficient. At the same time, if the nanoinclusions can donate high mobility carriers into the matrix to compensate for the carrier loss in the energy filtering process, the enhancement in Seebeck coefficient should not significantly reduce the electrical conductivity. Such specific nanoinclusions can induce the energy filtering effect, the carrier injection effect and the boundary scattering effect to simultaneously improve the Seebeck coefficient, increase electrical conductivity, and decrease lattice thermal conductivity. Such cases are observed in micro-scale HH matrix with nanoinclusions [79,80], but not in nanoscale HH matrix with nanoinclusions. However, the first significant challenge is how to choose the correct secondary phase as the best nanoinclusions. According to previous experimental results, it seems that a metallic phase (e.g., full Heusler phase Hf_0.75Zr_0.25Ni₂Sn) or a semiconductor with highly carrier mobility (e.g., InSb) might be able to fulfill such requirements. Nevertheless, the theoretical calculations and the theoretical ability to predict the behavior of such materials is still quite lagging the experimental work in this field. Therefore, more theoretical calculations and modeling in order to produce predictive directions are highly desirable in order to better direct the most promising routes or directions to obtain the most favorable TE nanoinclusions.

Moreover, the above reviewed nanocomposites have two common characteristics: (1) nanoinclusions are randomly distributed, and (2) their sizes are to a large extent uncontrollable. If the nanoinclusions could uniformly distribute in the matrix, and also the size can be more precisely controlled, it would be much more straightforward to investigate how the size and the distribution of nanoinclusions affect the TE transport properties. Then the most favorable distribution of size, position and distribution for nanoinclusions for the best TE performance can be found. Although Chen points out that the surface per volume (S/V) ratio is more important than the periodicity distribution of the nanostructure for the reduction in the lattice thermal conductivity, it would be even more desirable if the uniform distribution of the nanostructures can even enhance the electrical conductivity. It is not expected that nanostructures result in strong carrier scattering, and also defects induced by nanostructures can dramatically change the carrier concentration. Recently Liu et al. [139] points out that ordered nanocomposites with various well-organized (distributed) nanostructures may reconstruct a carrier transport channel, as to depress lattice thermal conductivity without significantly affecting the electrical conductivity. The second open challenge for theorists and experimentalists is how the size and distribution of nanoinclusions can be more precisely controlled within a certain TE matrix and this has been explicitly been shown here for the case on half Huesler alloys.

One of the newest directions in TE materials research over the past two decades is the concept of nanostructure-engineering. Certainly nanostructuring or nanocomposites is the new paradigm of TE materials research. In the HH nanocomposite materials, the TE performance can be significantly enhanced by decreasing the lattice thermal conductivity as well as enhancing the power factor. Nanoinclusions that can induce both a boundary scattering effect and energy filtering effect can effectively decouple the interrelated thermal and electrical transport properties. After numerous efforts in 20 years (or so), the highest ZT values of HH compound is pushing to 1–1.2 in HH nanocomposites from 0.1–0.2 in undoped HH ingot. At this date, it is unknown how far nanostructuring can further achieve progress in these materials. Continuing to follow the concept of nanostructuring is a positive direction, but exploring several other scientific and engineering directions for further enhancing ZT of HH materials should be pursued as well as achieving device applications of these HH nanocomposites.

(1) Two new physical ideas related to band structure engineering were introduced in TE research field, such as distortion of the electronic density of states (resonant energy level) in Tl doped PbTe [140], and convergence of electronic bands in Na-doped PbTe_1−xSe_x [141]. The idea of introducing a resonant level in HH compound was achieved in V doped Hf_0.75Zr_0.25NiSn HH compound [142]. Even though, the maximum PF of V doped Hf_0.75Zr_0.25NiSn does not result in the best working temperature range (above 700 K), the band structure engineering strategy, such as distortion of the electronic density of states, is highly recommended in the future work.

(2) One very positive aspect of the HH alloys in their bulk form in their very favorable thermal stability. But, several points should be taken into account with regards to potential HH applications. First, the mechanical properties of HH nanocomposites should be more fully understood before designing HH modules; second the thermal stability of nanostructures in HH nanocomposites should be more thoroughly investigated (even though the matrix has been shown to be very stable); and third, the possibility of scale-up production for high TE performance HH nanocomposites should be further investigated and evaluated.

Although to date, the current TE materials cannot be in used in very broad applications due to their low conversion efficiency. However, if the combination of combined mechanisms to enhance ZT in HH alloys, such as nanostructuring and band structure engineering, are able to achieve values of the ZT to 2 or even higher, improve the mechanical properties and maintain their good thermal stability with the nanostructuring processes, then the broad range of potential applications for waste heat recovery using TE devices based on this next generation of HH alloys will be very promising.