Thermoelectric Performance of Ca₂Si Synthesized by High-Temperature Melting

Abstract

Ca₂Si was successfully synthesized via a high-temperature melting furnace and a spark plasma sintering process, allowing its thermoelectric properties to be studied. High-temperature melting furnaces were utilized to inhibit the volatilization of Ca elements during the preparation stage, ensuring the production of high-purity Ca₂Si. The resistivity of Ca₂Si increased gradually with rising temperature and reached 12 mΩ·cm at 873 K, demonstrating semi-metallic characteristics. In the temperature range of 323 K–873 K, Ca₂Si displayed relatively low total thermal conductivity, from 1.1 to 1.7 W·m⁻¹·K⁻¹. Nevertheless, Ca₂Si attained a maximum thermoelectric figure of merit (ZT) of 0.1 due to the atypical behavior and electrical properties of semiconductors. In contrast, Mg₂Si achieved a ZT value of 0.32 at 873 K, owing to its exceptional Seebeck coefficient.

1. Introduction

Thermoelectric materials are a class of materials capable of directly converting thermal energy into electric energy and vice versa. In general, thermoelectric properties are evaluated using the thermoelectric figure of merit (ZT), expressed as ZT = (α²T)/(ρκ), where α is the Seebeck coefficient of the material, ρ denotes the resistivity, κ stands for the thermal conductivity, and T represents the absolute temperature. It is evident from the formula that an ideal thermoelectric material requires a high Seebeck coefficient, low resistivity, and low thermal conductivity [1,2]. However, these factors are not independent of each other. For instance, a low carrier concentration typically results in a high Seebeck coefficient, but the resistivity is often high, which can hinder the achievement of excellent thermoelectric properties. Thermal conductivity is generally considered to be composed of carrier thermal conductivity and lattice thermal conductivity, and the reduction in lattice thermal conductivity can also contribute to the enhancement of thermoelectric properties [3,4].

Over the past two decades, significant progress has been made in the study of thermoelectric materials, leading to the discovery of many compounds with outstanding properties. For instance, Bi₂Te₃ [5,6,7] has shown promise in low-temperature applications and PbTe [8,9] is effective near room temperature, while half-Heusler alloys [10,11,12], chalcogenide compounds [13,14,15], Zintl-phase compounds, etc., have demonstrated excellent performance in high-temperature range [16,17,18]. Thermoelectric devices composed of N-type or P-type doped semiconductors have achieved thermoelectric conversion efficiency values of approximately 12% to 15%.

In recent decades, Si-based thermoelectric materials have garnered significant attention due to their advantageous features, including minimal toxicity, cost-effective manufacturing, and excellent stability [19,20,21]. First-principle atomistic calculations have demonstrated the potential for heavy doping to achieve a sufficiently high charge carrier concentration, and alloying with isoelectronic elements helped to attain suitably low phonon thermal conductivity [22]. In the past decade, significant efforts have been dedicated to the development of an efficient thermoelectric material based on silicide. These endeavors have primarily focused on reducing the lattice thermal conductivity through various techniques, including alloying, nanostructuring, and defect engineering [23]. Among the silicide-based thermoelectrics, Mg₂(Si-Sn) alloys, such as MnSi_1.75 and ReSi_1.75, have emerged as effective materials [24]. Notably, Mg₂Si is widely recognized as one of the best materials for thermoelectric applications. In previous reports, the ZT value of P-type Mg₂Si-doped materials can exceed 0.7, indicating the considerable potential of thermoelectric applications [25,26,27,28,29,30,31,32,33].

Anisotropic, electronic, and phononic transport behaviors in low-dimensional materials have gained more attention in this particular family of materials [34]. Mg₂Ge thin films have shown high electrical conductivity; charge carrier mobility; and concentrations of 141.86 Ω⁻¹·m⁻¹, 2.62 cm²·V⁻¹·s⁻¹, and 8.66 × 10¹⁸ cm⁻³ at room temperature [35]. Furthermore, investigating the thermoelectric properties of CaSi and CaSi₂ films has revealed that their semi-metallic conduction type results in a positive Seebeck coefficient within the temperature range of 330 K–450 K [36].

Although Ca₂Si is isomeric with Mg₂Si, thermoelectric properties are still limited by its low conductivity. Therefore, facile synthesis methods and effective conductivity enhancement are crucial for Ca₂Si-based thermoelectric materials. Mg₂Si powder was heat-treated in the Ca gas phase to synthesize polycrystalline Ca₂Si powder (which was further prepared into Ca₂Si-sintered compacts via the SPS method) [31]. Extending the SPS treatment time under higher pressure levels was beneficial in order to obtain Ca₂Si-sintered compacts with a high relative density. In the temperature range of 300–360 K, the Seebeck coefficient and power factor of the Ca₂Si film were 300–320 μV·K⁻¹ and 1.37 × 10⁻⁷ W·m⁻¹·K⁻², respectively [37]. The particle substitution of Ca by Ag in p-type Ca₂Si alloys can significantly improve electrical and thermal properties. The highest ZT value was 0.16 at 837 K, which corresponded to the composition of Ca_(2−x)Ag_xSi [33]. The Seebeck coefficient of the material was 250–300 μV·K⁻¹ in the temperature range of 373–573 K [31,32,38]. Based on the ab initio method and the density functional theory, the ZT optimization value of p-type doping was predicted to be 0.52 at 1000 K [32]. The band gap and Seebeck coefficient of cubic Ca₂Si decreased with increasing pressure, while electronic conductivity increased as the pressure increased [39].

In this paper, the Ca₂Si polycrystalline sample was obtained using the facile vacuum melting method at high reaction temperatures, and the relevant properties were thoroughly characterized. Despite its low thermal conductivity (about 1 W·m⁻¹·K⁻¹), the compound exhibited poor conductivity and a poor Seebeck coefficient, resulting in a ZT value of only about 0.1 at 873 K. However, we believe that thermoelectric performance can be significantly improved if the material’s carrier concentration is increased through future doping.

2. Materials and Methods

2.1. Materials

The raw materials were high-purity metals purchased from Alfa Aesar in Stoughton, MA, USA. Upon receipt, the raw materials were immediately placed in the glove box (O₂ < 0.1 ppm) to avoid oxidation. The purity levels of Ca and Si were 99.5% and 99.999%, respectively.

2.2. Preparation of Ca₂Si

The raw material was sealed in a clean spare Ta tube, based on the stoichiometric ratio (due to the high vapor pressure of Ca, the sealing Ta tube speed required attention, so as to avoid spattering caused by local high temperatures), and then placed in a high-temperature melting furnace. The samples were rapidly heated to 1400 °C and kept at this temperature for 5 min. This synthesis method utilizing melting furnace allows for the rapid attainment of reaction temperatures. This method has two advantages for obtaining high-purity polycrystalline materials: firstly, significantly reduced sample preparation time, thus improving work efficiency; secondly, the ability to heat the raw material to very high temperatures (up to 1600 °C). Next, the Ta tube was then opened in a glove box with O₂ < 0.1 ppm, and the reactants were milled and then packaged in the tube for a second calcination with the same temperature and duration. However, XRD measurements revealed that the products often contained a small amount of CaSi, which should be considered as inclusions of the other silicide phase in Ca₂Si. After many experiments, the pure phase of Ca₂Si was finally obtained at the ratio of Ca:Si = 2.05:1.

The product was moved to a glove box for grinding purposes (for more than 30 min) and placed in a standard graphite mold (with a diameter of 12.7 mm) for discharge plasma sintering (SPS) at 800 °C for 5 min under 50 MPa. By dividing the mass by the volume, the density of the sample was calculated to reach 95% of the theoretical density. After the sintering process, the samples were retrieved and placed inside the glove box, and the pollutants (such as graphite paper on the upper and lower surfaces) were ground off.

2.3. Characterization

The XRD tests were conducted using a D8 ADVANCE multifunctional powder diffractometer, manufactured by Bruker AXS in Karlsruhe, Germany. The test light source was Cu−Kα rays, and the general scanning range was 20° to 60°. The scanning step mode was adopted, with a scanning step width of 0.02° and a scanning speed of 5° per minute. The NETSZCH LAF45 (NETSZCH, Selb, Germany) laser thermal conductivity tester was used for the thermal conductivity test. Pyroceram 9606 (Anter, LA, USA) was used as a reference sample, and the specific heat capacity C_p and thermal diffusion coefficient D were measured. The mass divided by the volume gave the density of the sample (d). The thermal conductivity κ was calculated using the formula: κ = C_pdD. Under the atmosphere of Ar gas, the Seebeck coefficient and conductivity were measured synchronously with a Linseis LSR-3 instrument (Linseis, Selb, Germany). These thermoelectric properties were measured at a temperature in the range of 323 K to 873 K. The Hall coefficient, carrier concentration, and carrier mobility were measured using the van der Pauw method on a MMR K2500 Hall effect measurement system (MMR Technologies, LA, USA). In order to meet the requirements of the test, the sample was first cut into 4 × 4 mm square pieces, thinned down to 0.5 mm, and four symmetrical electrodes were made on the surface.

3. Results and Discussion

3.1. Preparation and Characterization of Ca₂Si

As a first step, the traditional inorganic solid-phase method was used to prepare pure Ca₂Si, but it did not succeed, and many impurity phases occurred in the product. According to phase diagram analysis, the main reason for this was that the reaction temperature of the traditional Muffle furnace was not high enough [40]. In order to obtain a higher reaction temperature, we used a self-made high-temperature melting furnace for reaction purposes, which has the characteristics of a fast warming speed and a high reaction temperature.

The powder XRD diffraction analysis of Ca₂Si is displayed in Figure 1 to confirm the successful synthesis of Ca₂Si. High temperature and high pressure levels in spark plasma sintering had no obvious influence on the crystal lattice. The impurity phase did not precipitate, and the diffraction peaks did not shift significantly. Additionally, the simulated pattern of Ca₂Si came from the standard card (ICSD 191034), which became crystallized in the space group of Pnma. Cell parameters a, b, and c were 7.609 Å, 4.769 Å, and 8.980 Å, respectively. The XRD patterns of synthesized samples were in good agreement with the theoretical patterns. Even after plasma discharge sintering, there was no impurity peak in the XRD pattern.

3.2. Thermoelectric Property

It is known that the Mg₂Si alloy is a promising candidate for thermoelectric energy conversion for the middle–high temperature range. Calcium and magnesium are the same main group elements, and both have the characteristics of low-cost, non-toxic, and abundant reserves. The metal properties of the same main group elements are gradually enhanced from top to bottom, so calcium is more active than magnesium metals. Although Ca₂Si is isomeric with Mg₂Si, their thermoelectric properties differ significantly. In this paper, Mg₂Si served as a reference object, helping us to better grasp their differences and giving us crucial knowledge that is required in order to further enhance the thermoelectric properties of Ca₂Si in future studies.

The Ca₂Si sample was cut into a rectangular bar with a side length of 2 mm using a wire cutter, and the oil and other pollutants on the surface were disposed of in order to prepare for testing. A Seebeck coefficient test and a resistance test were carried out simultaneously, and the test results are shown in Figure 2. The black curve represents the results obtained by our test for Ca₂Si, while the red curve corresponds to the data reported in the literature for Mg₂Si used for comparison purposes. Mg and Si were mixed using a mortar and pestle and heated at 1073 K for 2 h in a graphite crucible with a Mg/Si molar ratio of 2.05:1. Mg excess from stoichiometry composition was used in order to compensate for the high Mg vapor pressure.

As shown in Figure 2a, the resistivity of Mg₂Si gradually decreased with an increase in temperature, from 7.5 mΩ·cm at 323 K to 4.5 mΩ·cm at 873 K. The resistivity of the Ca₂Si sample increased slowly with a rising temperature, indicating semi-metallic behavior. At 323 K, the resistivity of Ca₂Si was about 6.5 mΩ·cm, which is slightly lower than that of Mg₂Si. However, the resistivity of Ca₂Si increased to about 12 mΩ·cm at 873 K, which is basically 2.6 times that of Mg₂Si at the same temperature. Unfortunately, the resistivity of the sample that we synthesized was higher than ~1.2 mΩ·cm at room temperature, as reported by C. Wen et al. [33]. This may be due to different preparation methods and different densities of Ca₂Si bulks. However, high resistivity is unfavorable to the thermoelectric properties of high-temperature regions. As shown in

Table 1. Hall coefficient, carrier concentration, and mobility of Ca₂Si at 323 K.

Hall Coefficient, RH/10−7 m3·C−1	Carrier Concentration, p/1019 cm−1	Mobility, μ/cm2·V−1·s−1
1.06	4.22	15.95

, the carrier concentration and Hall mobility values were 4.22 × 1019 cm⁻¹ and 15.95 cm²·V⁻¹·s⁻¹, respectively.

The Seebeck coefficient of Mg₂Si was 220 μV·K⁻¹ at 323 K, and then increased slowly with an increase in temperature, reaching the highest value of 310 μV·K⁻¹ at about 623 K. Although the Seebeck coefficient of Mg₂Si slowly declined with an increasing temperature after 623 K, it still stayed around 250 μV·K⁻¹ at 873 K, which is comparable to many excellent thermoelectric materials.

In contrast, the Seebeck coefficient of Ca₂Si showed a contrast difference. At room temperature, the Seebeck coefficient was only about 60 μV·K⁻¹. Although the Seebeck coefficient had an obvious upward trend with an increase in temperature, due to the slow slope, it only reached 140 μV·K⁻¹ at 873 K, which is still much lower than the value of Mg₂Si (250 μV·K⁻¹).

Based on Weidmann–Franz law (κ_e = L₀Tσ, where L₀ is the Lorentz constant and the value is 2.45 × 10⁻⁸ W·Ω·K⁻²), the carrier thermal conductivity of Ca₂Si material was calculated, as shown in Figure 3a. The lattice thermal conductivity was obtained by deducting the contribution of the carrier part from the measured total thermal conductivity, as shown in Figure 3b.

It was found that both materials have very low carrier thermal conductivity (about 0.1 W·m⁻¹·K⁻¹) at low temperatures. With an increase in temperature, an increase in the carrier thermal conductivity of Mg₂Si material was obvious. While not the case for Ca₂Si, this is favorable for a decrease in thermal conductivity. When the temperature reached 873 K, the carrier thermal conductivity of Mg₂Si material increased to about 0.5 W·m⁻¹·K⁻¹, while Ca₂Si remained below 0.2 W·m⁻¹·K⁻¹.

Compared with the change in carrier thermal conductivity, the difference in lattice thermal conductivity was more obvious, as shown in Figure 3b. At room temperature, the lattice thermal conductivity of Mg₂Si material was about 5.3 W·m⁻¹·K⁻¹, and the lattice thermal conductivity of Ca₂Si material was only about 1.4 W·m⁻¹·K⁻¹, which is less than one third of that of Mg₂Si. The lattice thermal conductivity of Mg₂Si decreased to about 4 W·m⁻¹·K⁻¹ when the temperature reached 873 K. Meanwhile, that of Ca₂Si was only about 1 W·m⁻¹·K⁻¹ at 873 K, which is very favorable for thermoelectric materials.

The total thermal conductivity is shown in Figure 4a. The total thermal conductivity of Ca₂Si material was only about 1.4 W·m⁻¹·K⁻¹ at 323 K. The thermal conductivity of Ca₂Si reached its minimal value (1.0 W·m⁻¹·K⁻¹) at 673 K. As the temperature increased, its thermal conductivity also increased, but this trend is not obvious. Even at 873 K, the thermal conductivity of Ca₂Si was only 1.2 W·m⁻¹·K⁻¹, which is comparable to some thermoelectric materials with low thermal conductivity. In contrast, the thermal conductivity of Mg₂Si (5.4 and 4.5 W·m⁻¹·K⁻¹ at 323 and 673 K, respectively) was 2.6 times that of Ca₂Si.

After the comprehensive consideration of electrical and thermal factors, the final results are shown in Figure 4b. Although Ca₂Si material has low thermal conductivity, the ZT of Ca₂Si reached about 0.1 at 873 K due to its poor electrical properties. Due to its excellent Seebeck coefficient, the ZT of Mg₂Si reached 0.32 at 873 K.

4. Conclusions

Given the abundance of Si in the Earth’s crust and the limited research on the thermoelectric properties of Si-based compounds, this study focused on investigating the thermoelectric properties of Ca₂Si. Pure-phase polycrystalline samples of Ca₂Si were prepared using a self-made high-temperature melting furnace. The results showed that despite the thermal conductivity of Ca₂Si being low (about 1 W·m⁻¹·K⁻¹), Ca₂Si’s ZT value was only 0.1 at 873 K, primarily due to its poor electrical properties. In comparison to Mg₂Si, Ca₂Si exhibited a lower Seebeck coefficient and increased resistivity with rising temperature. Consequently, future efforts can be directed towards improving the electrical properties of Ca₂Si through doping, with the aim of enhancing its thermoelectric performance.