Thermodynamic modelling of the ternary Bi-Ga-Te system for potential application in thermoelectric materials

Thermoelectric materials have drawn widespread attention because they can enable the direct conversion between electric and thermal energy. Over the years, different materials such as skutterudites, clathrates, intermetallic alloys, eutectic alloys, chalcogenides have been explored for Thermoelectric (TE) applications. Amongst the eutectic alloys, the Bi-Ga-Te system exhibits promising potential as a TE material. Accordingly, in this study, we performed the thermodynamic optimization and critical evaluation of binary Bi–Ga, Bi–Te, Ga–Te, and ternary Bi-Ga-Te systems using the CALPHAD method. It is observed that the Ga–Te system shows asymmetric liquid solution properties with strong negative enthalpy of mixing, whereas the Bi–Te liquid exhibits the symmetric regular solution behavior. Moreover, the Bi–Ga liquid solution has a positive enthalpy of mixing. Therefore, Modified Quasichemical Model (MQM) using pair approximation was utilized to describe the diversified thermodynamic properties of liquid solution in sub-binaries by taking into account the Short-Range Ordering (SRO). By merging the binary optimization results with a proper interpolation method, the liquid solution properties and phase diagram information in the Bi-Ga-Te ternary system were also reproduced successfully without any adjustable ternary parameter. Several ternary eutectic compositions were suggested for designing TE alloy with enhanced properties using the developed database.     

Phase formations in low density high entropy alloys

Phase formations in high entropy alloys (HEAs) with at least two light elements in literature are predicted by CALPHAD (CALculation of PHAse Diagrams) thermodynamic calculations and the results are compared with experimental observations. The comparison suggests that the applicability of traditional CALPHAD calculations depends on the manufacturing processes of HEAs. Factors such as solute trapping, energies of defects need to be considered while predicting phases in HEAs prepared by non-equilibrium processes. The effects of light elements (Al, Ti, Si, alkali and alkaline earth metals) on the phase formations in HEAs are discussed. Especially, intermetallics predicted for Si-containing HEAs by traditional CALPHAD calculation can be suppressed in rapid solidification process, due to the solute trapping effect. Mg or other alkali and alkaline earth metals can lead to the formations of various intermetallics in HEAs prepared by conventional casting, but could be dissolved into solid solutions by non-equilibrium processes such as mechanical alloying. It is proposed that non-equilibrium processes may be an effective way to introduce light elements Si, alkali and alkaline earth metals into HEAs.     

Thermodynamic and diffusion kinetic studies of the Fe-Co system

The phase equilibria, thermodynamic properties and diffusion mobilities of the Fe-Co system were carefully assessed through the CALPHAD methods. As an indispensable tool, the first-principles calculations were carried out to study the magnetic moments and the enthalpies of mixing of the bcc_A2, bcc_B2, fcc_A1 and hcp_A3 phases as well as the point defect types of the bcc_B2 phase. In order to verify the heat capacities reported in the literature, new measurements were conducted in a high-temperature calorimetric apparatus using the three-dimensional calorimetric method. Because of the revision of the thermodynamic parameters in the present work, the diffusion mobilities for the fcc_A1 phase were reassessed. The diffusion mobilities for the bcc_A2 phase were established for the first time based on the experimental diffusion coefficients. For the low-temperature bcc_B2 phase, the diffusion couple experiments conducted in the present work show that the diffusion process is sluggish and the interdiffusion coefficients are difficult to determine. Therefore the tracer diffusivities of Co and Fe in the Fe-Co alloys were used to assess the diffusion mobilities for the bcc_B2 phase, while the composition-distance profile of one diffusion couple was served as a validation of its diffusion mobilities.     

Thermodynamic assessment of the La-Mg system

A thermodynamic modeling and optimization of the La-Mg system is carried out by means of the CALPHAD method taking into account the latest experimental results. The liquid, bcc-La, fcc-La, dhcp-La and hcp-Mg solutions are modeled as substitutional solutions (La, Mg) using the Redlich-Kister formalism. The LaMg, LaMg₂, La₅Mg₄₁, La₂Mg₁₇ and LaMg₁₂ phases are treated as stoichiometric compounds, and the non-stoichiometry of LaMg₃ is described as (La,Mg)_0.25Mg_0.75. The results are in good agreement with the set of experimental data which were carefully discussed and selected.     

Thermodynamic assessment of the Pt–Si binary system

The Pt–Si binary system was thermodynamically assessed using the CALPHAD method based on the available experimental data from the literature. The solution phases, including Liquid, Fcc_A1 (Pt) and Diamond_A4 (Si), were treated as substitutional solution phases, of which the excess Gibbs energies were expressed with Redlich–Kister polynomial functions. Meanwhile, the intermetallic compounds, PtSi, Pt₆Si₅, Pt₂Si, Pt₁₇Si₈, Pt₅Si₂, Pt₃Si and Pt₂₅Si₇, were modeled as stoichiometric compounds. Subsequently, a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases were obtained and the calculated values of phase diagram and thermodynamics were found to be in reasonable agreement with experimental data.