Thermodynamic modeling of the Ca–In and Ca–Sb systems supported with first-principles calculations

Based on the critical evaluation of the phase diagram and thermodynamic data available in literature, thermodynamic optimization for the Ca–In and Ca–Sb systems was conducted via the CALPHAD (CALculation of PHAse Diagram) approach. The solution phases including liquid, (Sb), (In), (βCa), and (αCa) were modeled using substitutional regular solution model. The six intermetallic compounds, i.e. Ca8In3, CaIn2, Ca2Sb, Ca5Sb3, Ca11Sb10 and CaSb2, were described as stoichiometric phases. The order–disorder transition of bcc_B2 (CaIn) and bcc_A2 (βCa) was considered and one single Gibbs free energy function was employed to describe both the ordered and disordered parts. By means of first-principles calculations, the enthalpies of formation for the intermetallic compounds at 0 K were computed and were used in the thermodynamic modeling. A set of self-consistent thermodynamic parameters for both Ca–In and Ca–Sb systems was finally obtained, respectively. Comprehensive comparisons showed that the calculated phase diagrams and thermodynamic properties agreed well with the experimental ones.