Some parameters of Mg2X compounds.
The silicides have obvious attractive characteristics that make them promising materials as thermoelectric energy converters. The constituting elements are abundant and have low price, many of compounds have good high temperature stability. Therefore, considerable efforts have been made, especially in the past 10 years, in order to develop efficient silicide-based thermoelectric materials. These efforts have culminated in creation of Mg2(Si-Sn) n-type thermoelectric alloys with proven maximum thermoelectric figure of merit ZT of 1.3. This success is based on combination of two approaches to maximize the thermoelectric performance: the band structure engineering and the alloying. In this chapter, we review data on crystal and electronic structure as well as on the thermoelectric properties of Mg2X compounds and their solid solutions.
- magnesium silicide
- figure of merit
Among the large family of silicon-based compounds, semiconducting silicides have received particular interest as thermoelectric materials because they are potentially cheap and mostly stable materials. Comparatively, low charge carriers’ mobility in these semiconductors is compensated by high electron state density, i.e. high effective mass of charge carriers. Therefore, silicides were the main focus of thermoelectric research community since the 1950s . Investigations of these materials were especially active during the past 10 years. The most important results have been achieved for Mg2X (X = Si, Sn, Ge)-based alloys. Based on the Zaitsev et al.  work, n-type Mg2(Si-Sn) solid solutions with thermoelectric figure of merit
Already in the 1960s, it was shown that Mg2X compounds (X = Si, Ge, Sn) and their solid solutions are promising compounds for thermoelectric energy conversion [8, 9]. Very high values of
The maximum conversion efficiency of thermoelectric generator
The unique characteristics of an electronic band structure of Mg2X compounds make possible to explore the combination of two approaches to optimize the thermoelectric performance of such materials: the band structure engineering and the alloying [2, 5]. The combination allows to simultaneously maximize electronic parameters, characterized by power factor
In this chapter, we summarize the present state of the knowledge on the crystal and electronic structure of Mg2X compounds and their alloys, and review experimental data on thermoelectric properties of compounds.
2. Properties of Mg2X compounds
2.1. Physical properties and crystal structure of Mg2X
The basic properties of Mg2X compounds are shown in Table 1. Melting temperature and energy gap,
|Mobility (300 K)||Lattice thermal
|(K)||(Å)||(g cm−3)||(eV)||(cm2 V−1⋅s−1)||(W m−1 K−1)|
|Mg2Si||1375 ||6.338 ||1.88 ||0.77 ||405||65||7.9 |
|Mg2Ge||1388 ||6.3849 ||3.09 ||0.74 ||530||110||6.6 |
|Mg2Sn||1051 ||6.765 ||3.59 ||0.35 ||320||260||5.9 |
Phase diagrams for the systems of magnesium and carbon groups of elements are well known . Each phase diagram contains only one chemical compound of Mg2X-type and two eutectic points. Mg2X compounds crystallize with cubic, CaF2-type, structure (space group Fm3m) [16, 20]. In Mg2X structure, the fluorine atom is replaced by the magnesium atom and the calcium atom is replaced by X atom (Figure 1). Each atom of the X group is surrounded by eight magnesium atoms in a regular cube. The bond in all these compounds is covalent . Lattice parameters of compounds are presented in Table 1.
2.2. Energy spectra of current carriers in Mg2X
Fundamental parameters of the electronic structure of the Mg2X compound can be obtained from optical and electronic transport property measurements on high quality single crystals. Comprehensive review of transport properties and electronic energy structure for Mg2X compounds is given in Ref. .
Based on the analysis of optical and electronic transport data, supplemented by results of band structure calculations, the band structure of Mg2X compounds was proposed [16, 22–27]. Figure 2 shows schematically the most important characteristic of this band structure near to Fermi energy. The valence band of the compounds is similar to the valence band of Si and Ge. It consists of two degenerate bands (
Location of conduction band minimum at the X-point is favorable for thermoelectric performance of a material. In this case, the effective mass of DOS is six times heavier than inertial mass. Because of that n-type Mg2Si has high electrical conductivity and high thermopower. On the other hand, the valence band structure does not have such favorable thermoelectric features. The maximum of the valance band is at Γ-point; thus, the inertial mass and effective mass of DOS are not different. The valence band has three subbands, one of which split due to spin-orbital interaction . This splitting extends with the increasing atom mass.
Parameters of band structure for Mg2Sn, Mg2Ge, and Mg2Si are presented in Table 2. The values of indirect band gap
2.3. Thermal conductivity of Mg2X compounds
Figure 3 shows temperature dependencies of reciprocal thermal conductivity of pure Mg2X compounds. One can see that reciprocal thermal conductivity can be described satisfactory by a linear law and residual reciprocal thermal conductivity is zero within experimental uncertainty. The most probable reason for observed difference in data of different authors is dependence of reciprocal thermal conductivity on deviation from stoichiometry.
3. Solid solutions of Mg2X compounds
3.1. Mg2X-based solid solutions
As one can see from Table 1, Mg2X compounds have relatively high thermal conductivity, which should be decreased to make these compounds practically useful thermoelectrics. However, decreasing in thermal conductivity should not lead to a considerable decrease of charge carriers’ mobility. Thermal conductivity can be reduced by selective scattering of phonons and electrons by point defects through forming solid solutions (alloys) between these isostructural compounds.
There is a continuous series of solid solutions in the system Mg2Si-Mg2Ge . Phase diagrams of Mg2Si-Mg2Sn and Mg2Ge-Mg2Sn have wide peritectic region in the middle composition range [15, 33]. Until recently, it was commonly accepted that solid solutions exist only at compositions
Figure 4 shows dependences of lattice parameter (
3.2. Thermal conductivity of Mg2X solid solutions
Figure 5 shows the experimental values of lattice thermal conductivity of Mg2Si1-
3.3. Dependency of energy gap on solid solution composition
Besides lower thermal conductivity, the solid solutions of Mg2X provide opportunity to further enhancement of thermoelectric properties by electronic band structure engineering. Figure 6 shows dependences of energy gap of Mg2X alloys vs. composition [9, 15, 37–40]. From the study of the Mg2Si-Mg2Ge system —one can conclude that energy gap is practically independent of alloy composition.
The situation is very different in other two alloy systems. The Mg2Ge-Mg2Sn system was studied by Busch et al. . Notwithstanding the very narrow band gaps of Mg2Sn and Mg2Ge, it can be concluded that band gap dependence on solid solution composition is nonlinear. Our results of the band gap study of Mg2Ge1-
Calculations show that the most favorable situation realizes when heavy electrons subband lays higher . Another advantage of this situation is the absence of interband scattering .
3.4. Synthesis technology and doping
There are several methods to produce Mg2X compounds. One of them is direct co-melting [8, 10]. This method has some limitation due to the large difference in melting temperature of components and high magnesium vapor pressure. It is necessary to pay a special attention to magnesium losses due to evaporation and segregation of the components (especially for Mg2Sn).
Another way to produce these compounds is through a solid-state reaction. Mg2X compounds have negative heat of formation, i.e. the formation reaction is exothermic [42–45]. However, oxide films on Mg particles prevent the reaction. Therefore, it is necessary to pay attention to the purity of components and avoid oxidization during mixing. Alternative manufacturing route has been developed for magnesium silicide derivatives . Elemental powders were mixed in stoichiometric proportions, cold pressed into cylindrical preforms and heated in an oxygen-free environment to initiate the exothermic reaction. Reaction products were additionally heat treated for homogenization. Dense sinters can be produced by hot uniaxial pressing of the obtained powders under moderate temperature and pressure conditions.
Several advantages were identified in the proposed technology: relatively short time of synthesis, possibility of
Single crystals of Mg2X compounds can be easily produced by any methods of directed crystallization.
It is hard to produce homogeneous solid solutions via a liquid phase through co-melting of the components. One of the problems is related to large difference in masses of magnesium, silicon, germanium, and tin atoms. Without stirring, segregation by specific weight occurs. The other problem relates to phase diagrams of solid solutions, which have large difference in liquidus and solidus curves in a wide range of compositions . Therefore, compositional segregation occurs during crystallization as well. In order to homogenize alloys, a long-term annealing is necessary. The necessary homogenization annealing time is determined by diffusion processes, which depend on temperature and crystallite size. Temperature cannot be high due to magnesium evaporation. In order to shorten the annealing time, hot pressing can be utilized. Ingots of alloys are crushed into powder and then powder is pressed in a vacuum. The finer grain size the less time for homogenization is needed . Annealing is not required for the samples produced from nanosize particles.
Recently, mechanical alloying in the ball mill followed by spark plasma sintering (SPS) has become the most popular preparation technique for this solid solution.
As mentioned above, the figure of merit Z is function of free charge carriers’ concentration. Optimal concentration yielding maximum
4. Thermoelectric properties of Mg2X and its alloys
4.1. Mg2X composites
As it was already mentioned that the new wave of research activity on Mg2X-based thermoelectrics was initiated by work of Zaitsev et al., who demonstrated stable Mg2(Si-Sn) alloys with a maximum
Samples of Mg2Si, undoped and doped with Bi and Ag, were grown by a vertical Bridgman method [58, 59]. The n-type Bi-doped samples have a maximum
A comprehensive study of a doping mechanism, i.e. location of dopants in Mg2Si was undertaken by Farahi et al. . Samples of Sb- and Bi-doped Mg2Si were prepared via two-stage annealing of powder mixtures of individual components at 823 K for 3.5 days and at 873 K for 5 days, followed by hot pressing. It was shown that part of dopants replaces Si, while the rest forms, Mg3Sb2 and Mg3Bi2, found between the grains of doped Mg2Si particles. As doping of Sb and Bi only partly led to Si substitution, experimentally determined charge carriers’ concentration was lower than originally expected.
Using a technique of incremental milling, phase pure Mg2Si was produced within a few hours with negligible oxygen contamination . In this technique, to prevent agglomeration of ductile Mg during ball milling, Mg is added to Si + doped mixture by small portions followed a comparatively short milling period until the stoichiometric amount of Mg is attained. More effective Bi doping is achieved with higher mobility values at lower concentrations of dopant compared to previous work. A peak
Temperature dependences of the figure of merit
4.2. Figure of merit of n-type Mg2X-based solid solutions
Analysis of transport properties and band structure features has shown that the Mg2Si-Mg2Sn system is the most promising for development of efficient n-type thermoelectrics. Figure 9 shows the effect of high band degeneracy on
Several approaches have been used in order to maximize the figure of merit, including optimization of alloy composition and doping level, various types of nanostructuring. The nanostructuring is currently considered as the most promising and universal approach to enhance the thermoelectric performance. There are a number of technological approaches for producing different kinds of nanostructured materials. Most important among them are nanocrystalline materials, materials with nanoprecipitates of second phase and materials with nanoinclusions of foreign substance. All these approaches were applied with different degree of success to Mg2X compounds and related alloys.
Effects of nanostructuring on Mg2Si were theoretically modeled and systematically analyzed in Ref. . It was shown that nanostructuring limits the energy-dependent phonon mean free path in Mg2Si, which results in significant reduction (50%) in lattice thermal conductivity. However, it was also concluded that nanostructuring in both p-type and n-type Mg2Si increases significantly charge carrier scattering and leads to unfavorable reduction in electrical conductivity. A decrease in charge carriers’ mobility of nanostructured Mg2Si strongly affects the power factor, resulting in only minor enhancement in the overall figure of merit. In the case of nanostructured n-type Mg2Si, an optimal doping concentration of 8.1 × 1019 cm−3 was estimated for achieving
A higher effect of nanostructuring on the efficiency of n-Mg2Si and n-Mg2Si0.8Sn0.2 alloys was predicted in another theoretical work . It was shown that relatively higher depression of lattice thermal conductivity compared to decrease in electrical conductivity due to grain boundary scattering can lead to 10 and 15% increase of
The presence of nanoinclusions is considered as an alternative approach to achieve nanoscale effects. Theoretical estimate of additional scattering on nanoinclusions of Mg2Si and Mg2Ge in the n-Mg2Si0.4Sn0.6 matrix predicted a considerable increase in the figure of merit . A small concentration of nanoparticles (about 3.4%) can lead to 60% reduction of thermal conductivity at 300 K and to 40% at 800 K with the optimal particle size of a few nanometers. The best value of
Various material synthesis technologies and alloy compositions were used in experiments in order to increase the figure of merit. Combination of induction melting, melt spinning (MS), and spark plasma sintering (SPS) methods were used to produce n-type Mg2Si0.4Sn0.6 alloys doped with Bi . Multiple localized nanostructures within the matrix containing nanoscale precipitates and mesoscale grains were formed, resulting in a remarkable decrease of lattice thermal conductivity, particularly for the samples with nanoscale precipitates having a size of 10–20 nm. Meanwhile, electrical resistivity was reduced and the Seebeck coefficient was increased by Bi-doping, causing improved electrical performance. Figure of merit
Another way to increase the
Homogeneous alloys Mg2Si0.3Sn0.7 were successfully prepared by nonequilibrium synthesis (melt spinning) followed by hot pressing and a plasma-assisted sintering (MS-PAS) technique . Microstructure homogenization promotes charge carrier transport and effectively enhances the power factor. As a result, the MS-PAS sample achieved the highest figure of merit
The influence of grain size on thermoelectric properties of Mg2Si0.8Sn0.2 doped with Sb was investigated using samples prepared by hot-pressing synthesized powders with grain sizes in the range from 100 to below 70 nm . Contrary to expectation, no significant reduction of thermal conductivity in nanograined samples was found.
4.3. Figure of merit of p-type Mg2X solid solutions
To realize high performance of n-type Mg2X-based alloys in practical applications, one needs to have a matching p-type material, preferably of the same base material. Therefore, considerable efforts have been made to the development of p-type Mg2X-based alloys. However, progress with this development has been not so impressive as with n-type materials. At present, the maximum
There are several potential p-type dopants for Mg2X compounds. The most effective impurities for Mg2Sn-rich alloys are Ga and Li. Both of these dopants provide hole concentrations higher than 1020 cm−3. Our study shows that these impurities yield one hole per dopant atom up to 2.5% Ga and 1.5% Li. Alloy Mg2Si0.3Sn0.7 doped with these impurities has a maximum
Experimental and theoretical studies of effects related to Ga doping of the Mg2Si compound and the Mg2Si0.6Ge0.4 alloy by measurements of electrical resistivity, thermopower, Hall coefficient, and thermal conductivity, supplemented by electronic band structure calculations, have shown that p-type materials with the maximum
Another p-type dopant is silver. The maximum figure of merit
Investigation on the effect of Li doping on electrical and thermal transport properties of Mg2Si0.3Sn0.7 alloys indicated that Li is an efficient dopant occupying Mg sites. Theoretical calculations as well as experiments indicate that Li doping preserves high hole mobility. While overall thermal conductivity increases with an increase in the Li content (due to enhanced electrical conductivity) at low to mid-range temperatures, the beneficial effect of Li doping is shifting the onset of bipolar conductivity to higher temperatures and thus extending the regime, where thermal conductivity benefits from Umklapp phonon scattering. As a consequence, thermoelectric performance is significantly improved with the figure of merit
Known attempts to use nanostructuring have not yielded positive results for p-doped Mg2X-based alloys. Another practically important problem with p-type alloys containing a large fraction of Mg2Sb is their intrinsic instability.
The last decade comprehensive study of Mg2X and Mg2X-based alloys has yielded rather impressive results. Mg2X-based n-type alloys are sufficiently stable at a temperature up to about 800 K and have maximum figure of merit close to 1.5. The combination of high-thermoelectric performance with low cost of raw elemental materials places these materials among the best thermoelectrics for temperature range from 300 to 800 K. However, there are still many problems to be solved in order to bring these alloys to the application stage. The most important problem is the failure to develop a matching p-type thermoelectric material. The best
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