**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 *ZT* value of about 1.1 at 800 K [2]. A systematic study of Mg2Si thermoelectric properties was performed by Tani et.al. They found (*ZT*)max for Mg2Si, doped with 2 at% of bismuth of about 0.86 at 820 K with samples, fabricated by SPS [54]. However, such large (*ZT*)max has been not supported by independent researchers [55]. Sb and P-doped Mg2Si was

investigated from 300 up to 900 K with the Sb content of up to 2% [56] and the P content up to 3% [57]. The samples were prepared from high-purity powder components by SPS. The maximum *ZT* = 0.56 was obtained at 860 K for sample with 2% of Sb due to the lowest thermal conductivity.

tionally 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

Single crystals of Mg2X compounds can be easily produced by any methods of directed

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 [33]. 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 [47]. Annealing is not required

Recently, mechanical alloying in the ball mill followed by spark plasma sintering (SPS) has

As mentioned above, the figure of merit Z is function of free charge carriers' concentration. Optimal concentration yielding maximum *ZT* value is equal to about 1019 to 1020 cm−3. Theoretical and experimental investigations of a doping impurity effect in Mg2Si for a wide range of impurity elements (B, Al, N, P, Sb, Bi, Cu, Ag, Au) were made by Tani and Kido [48, 49]. As, P, Sb, Bi, Al, and N were suggested as n-type dopants whereas Ga is suggested as p-type dopant. For In, Ag, Cu, and Au, the doping effect, i.e. a resulting conduction type, depends on the site in lattice where a doping atom will occupy. Actually, Ag-doped samples show p-type of conductivity. In Mg2Sn-rich solid solutions, impurities Na, Li, Ga, Ag and at low concen-

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 *ZT* value of about 1.1 at 800 K [2]. A systematic study of Mg2Si thermoelectric properties was performed by Tani et.al. They found (*ZT*)max for Mg2Si, doped with 2 at% of bismuth of about 0.86 at 820 K with samples, fabricated by SPS [54]. However, such large (*ZT*)max has been not supported by independent researchers [55]. Sb and P-doped Mg2Si was

synthesis, possibility of *in-situ* or *ex-situ* doping and grain size control.

272 Thermoelectrics for Power Generation - A Look at Trends in the Technology

become the most popular preparation technique for this solid solution.

for the samples produced from nanosize particles.

tration Al and In act as p-type dopants [50–53].

**4.1. Mg2X composites**

**4. Thermoelectric properties of Mg2X and its alloys**

crystallization.

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 *ZT* of 0.65 at 840 K, while Agdoped samples are of p-type (below 650 K) and show a maximum *ZT* of 0.1 at 570 K.

A comprehensive study of a doping mechanism, i.e. location of dopants in Mg2Si was undertaken by Farahi et al. [60]. 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 [61]. 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 *ZT* value of about 0.7 is achieved at 775 K using an optimum doping level with only 0.15% of Bi, which is an order of magnitude lower than that mentioned in Ref. [54].

Temperature dependences of the figure of merit *ZT* of Mg2Si samples doped with different dopants are shown in **Figure 8**.

**Figure 8.** Figure of merit *ZT* temperature dependences of Mg2Si. 1—Mg2Si+0.15% Bi [61]; 2—Mg2Si+0.5% Sb [58]; 3— Mg2Si+2% Sb [54]; 4—Mg2Si+1% Bi [59]; 5—Mg2Si+2% Sb [56]; 6—Mg2Si+3% P [57].

#### **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 *ZT*. Temperature dependences of *ZT* are shown for n-type Mg2Si0.4Sn0.6 (left) and Mg2Si0.6Sn0.4 (right) alloys. *CL* and *CH* subbands of the conduction band are close to each other in the Mg2Si0.4Sn0.6 alloy, as the result it has higher *ZT* at lower temperatures. In Mg2Si0.6Sn0.4,subbands *CL* and *CH*are separated by a narrow gap; therefore, at low temperatures *CH* subband gives no contribution to electronic transport. Therefore, *ZT* of Mg2Si0.6Sn0.4 at low temperatures is smaller in comparison with *ZT* of Mg2Si0.6Sn0.4. However, at higher temperatures, the *CH* subband in this alloy gives increasing contribution to electrical conductivity and thermopower, which gives rise to enhanced *ZT* values. Although both solid solutions have high maximum *ZT* values close to 1.2, the average value (*ZT*)*av* of Mg2Si0.4Sn0.6, in the temperature range of 400–850 K, is higher (about 0.83 and 0.78, respectively). This study revealed the best compositions of n-type solid solutions and allowed reproducible synthesis of thermoelectrics with *ZT*max ≈ 1.2 and higher [2, 5]. Comparison of obtained results with the data for the state-of-the-art thermoelectrics revealed that these materials are among the best thermoelectrics of n-type in the temperature range of 600–870 K.

**Figure 9.** Figure of merit *ZT* temperature dependences of alloys Mg2Si0.6Sn0.4 (right) and Mg2Si0.4Sn0.6 (left). *n*, 1020 cm−3: (right) 1—3.17; 2—3.30; 3—3.83; 4—4.54. *n*, 1020 cm−3: (left) 1—2.31; 2—2.52; 3—2.99; 4—3.10.

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.

**4.2. Figure of merit of n-type Mg2X-based solid solutions**

274 Thermoelectrics for Power Generation - A Look at Trends in the Technology

thermoelectrics of n-type in the temperature range of 600–870 K.

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 *ZT*. Temperature dependences of *ZT* are shown for n-type Mg2Si0.4Sn0.6 (left) and Mg2Si0.6Sn0.4 (right) alloys. *CL* and *CH* subbands of the conduction band are close to each other in the Mg2Si0.4Sn0.6 alloy, as the result it has higher *ZT* at lower temperatures. In Mg2Si0.6Sn0.4,subbands *CL* and *CH*are separated by a narrow gap; therefore, at low temperatures *CH* subband gives no contribution to electronic transport. Therefore, *ZT* of Mg2Si0.6Sn0.4 at low temperatures is smaller in comparison with *ZT* of Mg2Si0.6Sn0.4. However, at higher temperatures, the *CH* subband in this alloy gives increasing contribution to electrical conductivity and thermopower, which gives rise to enhanced *ZT* values. Although both solid solutions have high maximum *ZT* values close to 1.2, the average value (*ZT*)*av* of Mg2Si0.4Sn0.6, in the temperature range of 400–850 K, is higher (about 0.83 and 0.78, respectively). This study revealed the best compositions of n-type solid solutions and allowed reproducible synthesis of thermoelectrics with *ZT*max ≈ 1.2 and higher [2, 5]. Comparison of obtained results with the data for the state-of-the-art thermoelectrics revealed that these materials are among the best

**Figure 9.** Figure of merit *ZT* temperature dependences of alloys Mg2Si0.6Sn0.4 (right) and Mg2Si0.4Sn0.6 (left). *n*, 1020 cm−3:

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

(right) 1—3.17; 2—3.30; 3—3.83; 4—4.54. *n*, 1020 cm−3: (left) 1—2.31; 2—2.52; 3—2.99; 4—3.10.

Effects of nanostructuring on Mg2Si were theoretically modeled and systematically analyzed in Ref. [62]. 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 *ZT* of 0.83 at 850 K, which is less than 10% improvement in comparison with the maximum *ZT* of bulk Mg2Si. On the other hand, in the case of nanostructured p-type Mg2Si, a maximum *ZT* of 0.90 at 850 K was predicted, which is nearly 37% improvement over the maximum *ZT* of bulk Mg2Si. The predicted optimum dopant concentration for p-type Mg2Si was equal to 4.3 × 1020 cm3 . In practice, inherent challenge for p-type Mg2Si is a charge carriers' compensation effect that limits the maximum charge carriers' concentration by value 1018 cm−3.

A higher effect of nanostructuring on the efficiency of n-Mg2Si and n-Mg2Si0.8Sn0.2 alloys was predicted in another theoretical work [63]. 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 *ZT* at 850 K in nanostructured materials based on Mg2Si and Mg2Si0.8Sn0.2, respectively. A nanostructured alloy is more favorable for increase in the figure of merit than bulk Mg2Si.

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 [64]. 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 *ZT* 1.9 at 800 K is predicted for Mg2Si or Mg2Ge nanoparticles in Mg2Si0.4Sn0.6, which is considerably higher than the best experimental value for these alloys.

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 [6]. 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 *ZT* was significantly improved and the maximum value reaches 1.20 at 573 K for the Mg2Si0.4Sn0.6+3% Bi sample, which is higher than that of nondoped samples. In comparison to samples of a similar composition, prepared by a conventional procedure, these samples have very low thermal conductivity, larger thermopower, and lower electrical conductivity.

Another way to increase the *ZT* value is use of quasi-quaternary alloys Mg2Si-Mg2Sn-Mg2Ge. Although theoretical calculation did not predict noticeable influence of Ge on the lattice thermal conductivity of Mg2Si-Mg2Sn [65], it was demonstrated experimentally that *ZT* can be increased up to 1.4 in Bi-doped Mg2Si1−*<sup>x</sup>*−*<sup>y</sup>*Sn*x*Ge*y* (*x* = 0.4 and *y* = 0.05) alloys [3, 66]. Alloys were prepared by solid-state synthesis and sintering via hot pressing. Transmission electron microscopy (TEM) confirmed the coexistence of phases with different stoichiometry and yielded nanofeatures of the Mg2Si1−*<sup>x</sup>*−*<sup>y</sup>*Sn*x*Ge*y* phase. Thermoelectric properties of these materials were affected by different stoichiometry and the Sn-rich phase is believed to play a crucial role. High figure of merit could be attributed to a relatively high power factor that is related to contribution of the Sn-rich phase as well as low thermal conductivity that originates from nanostructuring.

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 [7]. 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 *ZT* of 1.30 at 750 K. However, the Mg2Si0.3Sn0.7 alloy is intrinsically unstable at higher temperatures and tends to decompose into various Si-rich and Sn-rich phases even following the modest annealing at 773 K for 2 h.

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 [67]. Contrary to expectation, no significant reduction of thermal conductivity in nanograined samples was found. *ZT* showed very weak dependence on grain's size with maximum values of about 0.8–0.9 at 900 K.

The best *ZT* results for n-type of Mg2Si-based thermoelectrics are summarized in **Figure 10**.

## **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 *ZT* of p-type Mg2X-based alloys is about 0.5. There are several reasons for this. The high *ZT* of the n-type Mg2(Si-Sn) alloys is connected in part with high valley degeneracy of the conduction band that increases in alloys due to the band inversion effect. The valley degeneracy effect is absent for the valence band, since the top of this band is located at the Γ-point of the Brillouin zone. Furthermore, hole mobility is lower than the electron mobility in all Mg2X compounds; hence, the onset of intrinsic conduction gives a negative impact on thermoelectric performance at lower temperatures in comparison with n-type alloys. The difference between hole and electron mobility is smallest in Mg2Sn, where the electron-tohole mobility ratio is about 1.5. Therefore, one can expect that the most efficient p-type alloy will contain a large fraction of Mg2Sn.

Efficient Thermoelectric Materials Based on Solid Solutions of Mg2X Compounds (X = Si, Ge, Sn) http://dx.doi.org/10.5772/65864 277

Another way to increase the *ZT* value is use of quasi-quaternary alloys Mg2Si-Mg2Sn-Mg2Ge. Although theoretical calculation did not predict noticeable influence of Ge on the lattice thermal conductivity of Mg2Si-Mg2Sn [65], it was demonstrated experimentally that *ZT* can be increased up to 1.4 in Bi-doped Mg2Si1−*<sup>x</sup>*−*<sup>y</sup>*Sn*x*Ge*y* (*x* = 0.4 and *y* = 0.05) alloys [3, 66]. Alloys were prepared by solid-state synthesis and sintering via hot pressing. Transmission electron microscopy (TEM) confirmed the coexistence of phases with different stoichiometry and yielded nanofeatures of the Mg2Si1−*<sup>x</sup>*−*<sup>y</sup>*Sn*x*Ge*y* phase. Thermoelectric properties of these materials were affected by different stoichiometry and the Sn-rich phase is believed to play a crucial role. High figure of merit could be attributed to a relatively high power factor that is related to contribution of the Sn-rich phase as well as low thermal conductivity that originates

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 [7]. 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 *ZT* of 1.30 at 750 K. However, the Mg2Si0.3Sn0.7 alloy is intrinsically unstable at higher temperatures and tends to decompose into various Si-rich and Sn-rich phases even following the modest

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 [67]. Contrary to expectation, no significant reduction of thermal conductivity in nanograined samples was found. *ZT* showed very weak dependence

The best *ZT* results for n-type of Mg2Si-based thermoelectrics are summarized in **Figure 10**.

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 *ZT* of p-type Mg2X-based alloys is about 0.5. There are several reasons for this. The high *ZT* of the n-type Mg2(Si-Sn) alloys is connected in part with high valley degeneracy of the conduction band that increases in alloys due to the band inversion effect. The valley degeneracy effect is absent for the valence band, since the top of this band is located at the Γ-point of the Brillouin zone. Furthermore, hole mobility is lower than the electron mobility in all Mg2X compounds; hence, the onset of intrinsic conduction gives a negative impact on thermoelectric performance at lower temperatures in comparison with n-type alloys. The difference between hole and electron mobility is smallest in Mg2Sn, where the electron-tohole mobility ratio is about 1.5. Therefore, one can expect that the most efficient p-type alloy

on grain's size with maximum values of about 0.8–0.9 at 900 K.

**4.3. Figure of merit of p-type Mg2X solid solutions**

276 Thermoelectrics for Power Generation - A Look at Trends in the Technology

will contain a large fraction of Mg2Sn.

from nanostructuring.

annealing at 773 K for 2 h.

**Figure 10.** The best figure of merit of the Mg2Si-Mg2Sn alloy. 1—Mg2Si0.4Sn0.6+Sb [2]; 2—Mg2Si0.3Sn0.7+0.6% Sb [5]; 3— Mg2Si0.4Sn0.6+1% Bi [6]; 4—Mg2Si0.53Sn0.4Ge0.05Bi0.02 [3]; 5—Mg2(Si0.3Sn0.7)0.98Sb0.02 [7].

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 *ZT* of up to 0.45 at 650 K [4, 68].

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 *ZT* value of 0.36 at 625 K can be obtained for Mg2Si0.6Ge0.4:Ga (0.8%) [69].

Another p-type dopant is silver. The maximum figure of merit *ZT* of 0.38 was achieved at 675 K for Mg1.98Ag0.02Si0.4Sn0.6 [70]. It was found that the solubility of Ag in Mg2Si0.4Sn0.6 is about 2%. Oversaturated Ag doping in Mg2Si0.4Sn0.6 is unfavorable for the improvement of thermoelectric properties.

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 *ZT* reaching a value of 0.50 at around 750 K at the Li doping level of 0.07 [71]. **Figure 11** summarizes *ZT* temperature dependences for the best p-type Mg2X-based alloys.

**Figure 11.** The figure of merit for the state-of-the-art p-type Mg2Si-Mg2Sn alloys. 1—Mg2(Si0.3Sn0.7)0.985Ga0.015 [4]; 2— Mg2Si0.6Ge0.4+0.8% Ga [69]; 3—Mg1.98Ge0.4Sn0.6Ag0.02 [70]; 4—Mg1.86Si0.3Sn0.7Li0.14 [71]; 5—Mg1.99Si0.3Sn0.7Li0.01 [68].

Known attempts to use nanostructuring have not yielded positive results for p-doped Mg2Xbased alloys. Another practically important problem with p-type alloys containing a large fraction of Mg2Sb is their intrinsic instability.

#### **5. Conclusion**

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 *ZT* value for p-type Mg2X-based alloys does not exceed 0.5. Moreover, the p-type alloys are not sufficiently stable. Another problem is the absence of technology for making stable, high quality electrical contacts with the alloys. However, this problem certainly can be solved with adequate efforts and resources.

## **Author details**

reaching a value of 0.50 at around 750 K at the Li doping level of 0.07 [71]. **Figure 11** summarizes

**Figure 11.** The figure of merit for the state-of-the-art p-type Mg2Si-Mg2Sn alloys. 1—Mg2(Si0.3Sn0.7)0.985Ga0.015 [4]; 2—

Known attempts to use nanostructuring have not yielded positive results for p-doped Mg2Xbased alloys. Another practically important problem with p-type alloys containing a large

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 *ZT* value for p-type Mg2X-based alloys does not exceed 0.5. Moreover, the p-type alloys are not sufficiently stable. Another problem is the absence of technology for making stable, high quality electrical contacts with the alloys. However, this problem certainly can be solved with

Mg2Si0.6Ge0.4+0.8% Ga [69]; 3—Mg1.98Ge0.4Sn0.6Ag0.02 [70]; 4—Mg1.86Si0.3Sn0.7Li0.14 [71]; 5—Mg1.99Si0.3Sn0.7Li0.01 [68].

fraction of Mg2Sb is their intrinsic instability.

**5. Conclusion**

adequate efforts and resources.

*ZT* temperature dependences for the best p-type Mg2X-based alloys.

278 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Vladimir K. Zaitsev1 , Grigoriy N. Isachenko1,2\* and Alexander T. Burkov1,2

\*Address all correspondence to: isachenko@inbox.ru

1 Ioffe Institute, Politeknicheskaya ul., Saint Petersburg, Russia

2 ITMO University, Kronverkskiy pr., Saint Petersburg, Russia

## **References**


[25] Au-Yang MY, Cohen ML.: Electronic structure and optical properties of Mg2Si, Mg2Ge and Mg2Sn. Physical Review. 1969;178(3):1358–1364.

[10] Nicolau MC. Material for direct thermoelectric energy conversion with a high figure of merit. In: Proceedings of International Conference on Thermoelectric Energy Conver-

[11] Noda Y, Kon H, Furukawa Y, Nishida IA, Masumoto K.: Temperature dependence of thermoelectric properties of Mg2Si0.6Ge0.4. Materials Transactions, JIM. 1992;33(9):851–

[12] Ioffe AF. Semiconductor Thermoelements and Thermoelectric Cooling. London:

[13] Chasmar RP, Stratton R.: The thermoelectric figure of merit and its relation to thermoelectric generators. Journal of Electronics and Control. 1959;7(1):52–72. DOI:

[14] Baker H, editor. ASM Handbook, Volume 03 – Alloy Phase Diagrams. USA: ASM

[15] Busch G, Winkler U.: Electrical conductivity of intermetallic solid solutions. Helvetica

[16] Grosch GH, Range KJ.: Studies on AB2-type intermetallic compounds. I. Mg2Ge and Mg2Sn: single-crystal structure refinement and ab inito calculations. Journal of Alloys

[17] Zintl E, Kaiser H.: On the ability of elements to bind negative ions. Zeitschrift für

[18] Winkler U.: Electrical properties of intermetallic compounds Mg2Si, Mg2Ge, Mg2Sn

[19] Martin JJ.: Thermal conductivity of Mg2Si, Mg2Ge and Mg2Sn. Journal of Physics and

[20] Sacklowski A.: X-ray investigations of some alloys. Annalen der Physik. 1925;382(11):

[21] Zaitsev VK, Fedorov MI, Eremin IS, Gurieva EA.: Thermoelectrics on the base of solid solutions of Mg2BIV compounds (BIV=Si, Ge, Sn). In: D.M. Rowe, editor. CRC Handbook

of Thermoelectrics: Macro to Nano. New York: CRC Press; 2006. p. 29-1-29-11.

[22] Koenig P, Lynch DW, Danielson GC.: Infrared absorption in magnesium silicide and magnesium germanide. Journal of Physics and Chemistry of Solids. 1961;20(1/21961):

[23] Lipson HG, Kahan A.: Infrared absorption of Mg2Sn. Physical Review. 1964;133A:

[24] Lott LA, Lynch DW.: Infrared absorption in Mg2Ge. Physical Review. 1966;141(2):681–

anorganische und allgemeine Chemie. 1933;211(1/2):113–131.

and Mg2P. Helvetica Physica Acta. 1955;28(7):633–666.

sion; Arlington, Texas. 1976. p. 59.

280 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Infosearch; 1957. 184 p.

10.1080/00207215908937186

International; 1992. 512 p.

Physica Acta. 1953;26(5):578–583.

and Compounds. 1996;235(2):250255.

Chemistry of Solids. 1972;33(5):1139–1148.

855.

241–272.

122–126.

800–810.

686.


[51] Isoda Y, Tada S, Nagai T, Fujiu H, Shinohara Y.: Thermoelectric properties of p-type Mg2.00Si0.25Sn0.75 with Li and Ag double doping. Journal of Electronic Materials. 2010;39(9):1531–1535. DOI: 10.1007/s11664-010-1280-7

[39] Fedorov MI, Zaitsev VK, Eremin IS, Gurieva EA, Burkov AT, Konstantinov PP, Vedernikov MV, Samunin AYu, Isachenko GN.: Kinetic properties of p-type Mg2Si0.4Sn0.6 solid solutions. In: Proceedings of Twenty-Second International Conference on Thermoelec-

[40] Fedorov MI, Pshenay-Severin DA, Zaitsev VK, Sano S, Vedernikov MV.: Features of conduction mechanism in n-type Mg2Si1-xSnx solid solutions. In: Proceedings of Twenty-Second International Conference on Thermoelectrics, ICT'03; IEEE; 2003, p. 142.

[41] Pshenay-Severin DA and Fedorov MI.: Effect of the band structure on the thermoelectric properties of a semiconductor. Physics of the Solid State. 2007;49(9):1633–1637. DOI:

[42] Clark CR, Wright C, Suryanarayana C, Baburaj EG, Froes FH.: Synthesis of Mg2X (X = Si, Ge, or Sn) intermetallics by mechanical alloying. Materials Letters. 1997;33(1-2):71–

[43] Xiaoping Niu, Li Lu.: Formation of magnesium silicide by mechanical alloying.

[44] Riffel M, Schilz J.: Influence of production parameters on the thermoelectric properties of Mg2Si. In: Proceedings of 16th International Conference on Thermoelectrics,

[45] Schilz J, Muller E, Kaysser WA, Langer G, Lugscheider E, Schiller G, Henue R.: Graded thermoelectric materials by plasma spray forming. In: Shiota I, Miyamoto Y, editors. Functionally Graded Materials 1996. Netherlands: Elsevier Science B.V.; 1997. p. 563–

[46] Godlewska E, Mars K, Zawadzka K.: Alternative route for the preparation of CoSb3 and Mg2Si derivatives. Journal of Solid State Chemistry. 2012;193:109–113. DOI: 10.1016/

[47] Samunin AYu, Zaitsev VK, Konstantinov PP, Fedorov MI, Isachenko GN, Burkov AT, Novikov SV, Gurieva EA.: Thermoelectric properties of hot-pressed materials based on Mg2SinSn1−n. Journal of Electronic Materials. 2013;42(7):1676–1679. DOI: 10.1007/

[48] Tani J-I, Kido H.: First-principles and experimental studies of impurity doping into Mg2Si. Intermetallics. 2008;16(3):418–423. DOI: 10.1016/j.intermet.2007.12.001

[49] Tani J-I, Kido H.: Thermoelectric properties of Al-doped Mg2Si1−xSnx (x ≦ 0.1). Journal of Alloys and Compounds. 2008;466(1–2):335–340. DOI: 10.1016/j.jallcom.2007.11.029

[50] Tani J-I, Kido H.: Impurity doping into Mg2Sn: A first-principles study. Physica B.

2012;407(17):3493–3498. DOI: 10.1016/j.physb.2012.05.008

Advanced Performance Materials. 1997;4(3):275–283.

trics, ICT'03; IEEE; 2003. p. 134.

282 Thermoelectrics for Power Generation - A Look at Trends in the Technology

10.1134/S1063783407090053

ICT'97; 1997. p. 283.

j.jssc.2012.03.070

s11664-012-2372-3

75.

568.

