Contribution of first-principles energetics to the Ca–Mg thermodynamic modeling

Abstract

The first-principles energetics of the constituent elements Ca and Mg and the Mg 2Ca C14 laves phase (C14) in the Ca–Mg binary system were used in the computational thermodynamic modeling, with models for the Gibbs energy of individual phases. C14 was modeled as (Ca,Mg) 2(Ca,Mg) 1 with four end-members. The first-principles calculations were performed using two computer codes: (i) WIEN2K based on the full-potential linearized augmented plane-wave (FLAPW) method and (ii) VASP based on the pseudo-potentials and a plane wave basis set. The total energies of the pure Ca and Mg in the fcc, bcc, and hcp structures, three laves phase structures of Mg 2Ca, and the four end-members of C14 were calculated at 0 K. The enthalpies of formation of the four end-members were obtained accordingly and used as input data in evaluating the Gibbs energy functions of C14. The entropy contribution in the Gibbs energy function for C14 was obtained through its liquidus data. Special quasirandom structures are used to mimic random mixing in the C14 laves phase for two compositions, i.e. (Mg) 2(Ca 0.5,Mg 0.5) and (Ca 0.5,Mg 0.5) 2(Ca). The complete thermodynamic description of the Ca–Mg binary system with C14 modeled as a solution phase was obtained by this combined computational thermodynamics/first-principles approach showing a good agreement with experimental data and previous modeling in the literature.