2018 Volume 59 Issue 9 Pages 1411-1416
This review briefly discusses the relationship between the crystal structures, electronic structures, and thermoelectric properties of materials such as pseudogap quasicrystals and related approximant crystals, narrow-gap binary intermetallic compounds, and lead chalcogenides. The approach used is to identify the materials’ intrinsic physical properties from experimental data and establish a route for tuning their properties based on theoretical models and first-principles calculations. A possible route for improving thermoelectric performance is to use a band engineering approach, such as band convergence and introducing impurity states near the valence and conduction band edges. This approach was successfully applied to TiSi2-type RuGa2 and the lead chalcogenides PbTe and PbSe.
This Paper was Originally Published in Japanese in J. Thermoelectrics Soc. Japan 14 (2018) 120–125.
Extensive studies (both fundamental and applied research) on the fabrication of thermoelectric materials and the development of power generation modules have been performed worldwide. The potential of thermoelectric materials is evaluated via the thermoelectric figure of merit, z, defined as
| \begin{equation} z = \frac{S^{2}\sigma}{\kappa} = \frac{S^{2}\sigma}{\kappa_{\text{el}} + \kappa_{\text{ph}}}, \end{equation} | (1) |
Recently, novel functional materials have been developed using a materials informatics scheme,2) which can enable us to search for new materials with desirable physical properties through machine learning predictions followed by material screening processes. However, most thermoelectric materials simultaneously require carrier engineering3) to enhance S2σ and phonon engineering4) to lower κph. Thus, it is still necessary to establish a way for achieving better thermoelectric performances via understanding the intrinsic physical material properties in combination with both experimental data and theoretical calculations.
In this brief review article, we introduce the most recent basic materials research on (1) quasicrystals and related materials possessing pseudogaps in the electronic density of states (DOS), (2) binary narrow-bandgap intermetallic compounds composed of group-13 elements (Al, Ga, and In) and transition metals (TM; Fe and Ru), and (3) lead chalcogenides (PbTe and PbSe). Our goal is to establish a route for enhancing material’s thermoelectric properties based on experimental data (synthesis, material characterization, and properties measurements) and theoretical calculations.
The discovery of quasicrystals by Shechtman et al.5) caused a redefinition of crystals, i.e., “any solid with an essentially discrete diffraction diagram,” and created a new research field, namely high-dimension and high-symmetry materials. Both basic and applied research into quasicrystals with specific structural features such as a forbidden five-fold rotational symmetry and quasiperiodicity have been extensively studied to date. One of the potential applications is to use materials with such features as thermoelectric materials. The first report on the thermoelectric properties of stable Al–Pd–Mn quasicrystals was published by Pope and Tritt et al. in 1999, who reported a zT value of 0.08 at 300 K;6) however, this is significantly lower than that of the conventional thermoelectric alloy Bi–Te.
Quasicrystals are considered to be stabilized, forming pseudogaps near the Fermi level, EF, owing to Fermi surface–Brillouin zone interactions, the Hume–Rothery mechanism, and covalent bonds including sp–d hybridization. Figure 1 shows the electronic density of states (DOS) for the Quandt–Elser model containing 134 atoms per unit cell.7) A deep pseudogap forms near EF, which can contribute to the material stabilizing as a p-type material; this has been reported to occur for many quasicrystals and related approximant crystals with relatively large S values of over 100 µV K−1 up to 700 K through elemental substitution [Fig. 2(a)]. In particular, the magnitude of S is very sensitive to the sample composition, i.e., a strong e/a (the average valence electron number per atom) dependence of S was observed in Al–Pd–Mn, Al–Pd–Re, and Al–Ga–Pd–Re quasicrystals [Fig. 2(b)].8–10) Those observations are explained via the shifting of EF from lower energy to the bottom of the pseudogap with increasing e/a.
Electronic density of states for an Al–Pd–Mn quasicrystal using the Quandt–Elser model.7)
(a) Distribution of the maximum Seebeck coefficient for various kinds of quasicrystals (QCs) and approximant crystals (ACs). (b) Seebeck coefficient at 523 K as a function of the valence electron number per atom (e/a) for Al–Pd–Mn,8) Al–Pd–Re,9) and Al–Ga–Pd–Re.10) Lines are included for guidance.
Kimura et al. proposed a guiding principle to enhance the thermoelectric properties of complex cluster solids, such as quasicrystals: weakly bonded rigid heavy clusters.11,12) We succeeded in a dramatic enhancement of the zT parameter from less than 0.01 to 0.26 through the optimization of the sample’s composition and via elemental substitution to weaken inter-cluster bonds; a zT value of 0.26 was achieved at 473 K for a Ga-substituted Al–Pd–Mn quasicrystal—this is the highest value reported thus far for stable quasicrystals and related approximant crystals [Fig. 3(a)(b)].13) We attribute the origin of the high zT value to a combination of a weakening of the inter-cluster bonds and the alloying effect through Al–Ga substitution, i.e., the reduction of the following two parameters: the spring constant between clusters (K) and the relaxation time for phonons (τph), which is expressed as
| \begin{equation} \kappa_{\text{ph}} = \frac{1}{3}C\frac{A^{2}K}{M}\tau_{\text{ph}}, \end{equation} | (2) |
(a) Total thermal conductivity (κ) and (b) dimensionless figure of merit (zT) as a function of temperature for an Al71−xGaxPd20Mn9 (x = 0, 2, 3) quasicrystal.13)
One important issue is to develop new thermoelectric materials that can be applied in a temperature range from room temperature to 573 K, just like the well-known Bi–Te alloy. We found that some Al-based quasicrystals that, as complex cluster solids, possess pseudogaps show significant potential for power generation in that temperature range.
Some quasicrystals and related approximant crystals, which are classified as complex cluster solids, are potential candidates for use as thermoelectric materials because they have a relatively large zT value from room temperature up to 573 K. However, the number of quasicrystals and related approximant crystals with a large S of over 100 µV K−1 is limited because their electronic structures do not form real gap states, instead forming pseudogaps. Therefore, we focused on binary narrow-gap compounds, such as TiSi2-type RuAl214) and RuGa2,15) which are considered to be similar to Al-based quasicrystals.
Figure 4 shows a comparison of the crystal structures, electronic structures, and chemical bonding nature as analyzed by a maximum entropy method/Rietveld analysis and calculated by first-principles band structure calculations for TiSi2-type RuAl2 and RuGa2 as well as for CoGa3-type FeGa3 and RuIn3. These two series of compounds form narrow bandgaps near EF despite being composed of only metallic elements. Based on both the experimental and calculated electron density distribution, strong interactions are observed between the group-13 element (Ga) and the TM (Ru). The origin of the narrow bandgap can be attributed to a strong hybridization effect between the sp orbitals of the group-13 elements and the d orbitals of the TMs.
Crystal structures, electronic structures, and bonding nature for TiSi2-type RuAl2 and RuGa2 as well as for CoGa3-type RuGa3 and RuIn3.
Our calculation using the Boltzmann transport theory indicated that a large S value over 200 µV K−1 could be obtained for these compounds.16) The experimental results have shown a high thermoelectric performance, in particular, for TiSi2-type RuAl2 and RuGa2. The obtained (zT)max values were 0.20 and 0.50 for RuAl2 and RuGa2, respectively, which are significantly higher values than those of other intermetallic compounds.17,18) Takahashi et al. reported the effect of chemical doping on the thermoelectric properties of RuAl2.19) They found that substituting Fe and Mn for Ru lowered κph, and they found that the conduction type can be controlled by such chemical substitutions.19) However, so far no enhancement of the (zT)max value has been reported.
Table 1 lists the reported dopants and (zT)max values for TiSi2-type RuAl2 and RuGa2 as well as for CoGa3-type RuGa3, FeGa3, and RuIn3.16–24) The thermoelectric properties of undoped TMGa3 (where the TM was either Fe, Ru, or Os) were reported by Amagai et al. in 2004.25) The conduction type of these compounds can be controlled by selecting a suitable dopant, and subsequent tuning of the carrier concentration can lead to enhancements of S2σ. The reported (zT)max for Zn-doped RuIn3 as a p-type material was 0.80.24) Meanwhile, a relatively large (zT)max of 0.31 was observed in Ir-doped RuGa2 as an n-type material.16) There are a limited number of binary intermetallic compounds that form narrow bandgaps near EF; examples of such materials are the above-mentioned TiSi2-type RuAl2 and RuGa2 as well as CoGa3-type RuGa3, FeGa3, and RuIn3. Although they do not crystallize in complex crystal structures, the origin of their relatively large (zT)max is attributed to a large S2σ of a few mW m−1K−2 because of the formation of real bandgaps.
To search for new thermoelectric materials, we have recently focused its attention on Al-based ternary alloy systems, such as the MoSi2-type Al6Re5Si4 compound26) whose crystal structure is recognized as being similar to the crystal structure of TiSi2-type compounds. We succeeded in the synthesis of both p- and n-type materials by tuning the contents of Al and Si and found a relatively large S2σ of over one mW m−1K−2 at room temperature for the p-type material.26) The recently characterized Al2Fe3Si3 ternary alloy composed of only common and low-cost elements is attractive for low-temperature applications below 500 K.27,28) The conduction type and power factor of this material can be simultaneously tuned by controlling the Al and Si content. At this stage, although the obtained S2σ values of these Al-based ternary materials are lower than those of conventional thermoelectric materials, their non-toxic properties and the low-cost of the materials, in particular for the Al2Fe3Si3 compound, are attractive for the fabrication of thermoelectric modules.
The results mentioned above indicate that screening materials based on their electronic structure is an effective way to search for new thermoelectric materials in multi-element systems and will constitute the next platform for materials discovery.
In general, it is necessary to tune the carrier concentration to optimize the thermoelectric performance of many thermoelectric semiconductors including some intermetallic compounds to form narrow bandgaps near EF. A widely used approach is to optimize the sample composition and to chemically dope the semiconductors. As already described in Section 3 (see Table 1), the resulting thermoelectric properties depend on the dopants. Dopants can produce carriers, but they also form impurity bands, which may lower the carrier mobility. Thus, the establishment of a method for selecting an appropriate dopant will accelerate the development of materials with better thermoelectric efficiencies.
Here we present a case study for impurity band engineering for TiSi2-type RuGa2. To determine the formation of the impurity bands formed by various types of dopants, we calculated the electronic structures using the Korringa–Kohn–Rostoker Green function formalism under the coherent potential approximation (KKR-CPA)29) for randomly disordered Ru1−xTMxGa2. Here, we selected the following TMs: Mn, Mo, and Re as p-type dopants and Co, Ni, Rh, Pd, and Ir as n-type dopants. Among these dopants, Re (p-type) and Ir (n-type) were the most promising dopant candidates because they form minor impurity bands, and such impurity bands should lower the carrier mobility less, as shown in Fig. 5.
Compared with the prediction and subsequent experimental results, Re substitution significantly enhanced S2σ at 373 K.20) The S2σ at 373 K was enhanced by approximately 70% from 1.5 to 2.5 mW m−1 K−2, which is close to that predicted by the calculations. This is attributed to the fine tuning of the carrier concentration without changing the effective mass obtained from a single parabolic band model and the lowering of the carrier mobility through suitable dopant selection, as predicted by the KKR-CPA calculations [Fig. 6].
In contrast, n-type characteristics were successfully sustained up to 1000 K with Ir substitution while other dopants could not produce a sufficient carrier concentration. However, the obtained S values were notably low in comparison with the calculated values, and the resulting (zT)max was thus still 0.31.16) The main reason why the obtained (zT)max was low is attributed to a decrease in the effective mass of the conduction bands, as shown in Fig. 6. With increasing Ir content, the effective mass was significantly reduced from 6.3 me to 3.2 me, which should lower the magnitude of S more than we had expected from the calculations assuming a simple rigid band approximation.16) Other n-type dopants (Co, Ni, Rh, and Pd) could not produce sufficient carrier numbers, mainly because of the formation of significant impurity bands.21) These results indicate that determining impurity band formation using theoretical calculations would be a beneficial way to select a suitable dopant for tuning a material’s thermoelectric properties.
The second case study is for the lead chalcogenides, PbTe and PbSe. We calculated the DOS for various kinds of dopants (Na, K, Tl, I, and La) in PbTe, as shown in Fig. 7(a) and (b).30,31) Here we introduce two examples of improving a material’s thermoelectric properties, namely doped PbTe and PbSe. For PbTe, the specific example is I-doped PbTe [(zT)max = 1.4].32) It is a known fact that substitution on the Pb site leads to lower carrier mobility, while substitution on the Te site has a minor effect. We investigated the effects of La- and I-doping in PbTe on the local DOS around the conduction bands, i.e., PbTe1−xIx and LaxPb1−xTe, respectively. We reported that the effective mass of La-doping is found to be higher than that of I-doping,31) which supports the reported experimental results.32) The example for PbSe is specifically for Sr-doped PbSe [(zT)max = 1.5].33) Pei et al. demonstrated that the thermoelectric properties of rocksalt-type lead chalcogenides are significantly enhanced when the energy of the primary valence band (the L band) converges with that of the second valence band (the Γ band).34) Similarly to PbTe, the band convergence scheme can be applied to isostructural PbSe. The calculated DOS of Pb1−xSrxSe confirmed both the increase in bandgap and the decrease in energy separation between the L and Γ bands, which quantitatively agrees with the experimental results.33) Such significant band convergence between the L and Γ bands and the alloying effect through the Sr-doping enhanced S and lowered κph could greatly enhance the zT values.
A widely used approach to develop new thermoelectric materials uses first-principles band structure calculations, which are now possible owing to both improvements in computing systems and the proliferation of calculation code such as WIEN2k and VASP. In this brief review article, we introduced the most recent basic materials research on pseudogap and narrow-bandgap compounds that are used as thermoelectric materials. The insight obtained from first-principles band structure calculations and model calculations can enhance our understanding of the experimental data. In particular, such integrated materials research that includes machine learning techniques can help the development of new materials and establish a way toward achieving better performing materials.
The author acknowledges Prof. Dr. Kaoru Kimura (The University of Tokyo), Prof. Dr. Jeffrey Snyder (Northwestern University), as well as Dr. Yoshikazu Shinohara, Dr. Yukihiro Isoda, and Dr. Masahiro Goto (National Institute for Materials Science) for their kind support and fruitful discussions. This work is partially supported by KAKENHI grants Nos. 21860021, 23760623, 26709051, and 17H03421 from the Japan Society for the Promotion of Science, the Thermal & Electric Energy Technology Foundation, the Sumitomo Foundation, and the Murata Science Foundation. A synchrotron radiation X-ray diffraction measurement was performed at the BL02B2 beamline of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (proposal Nos. 2011A1230 and 2013A1495). This work was partially supported by “Materials research by Information Integration” Initiative (MI2I) project of the Support Program for Starting Up Innovation Hub from Japan Science and Technology Agency (JST).
