Linking first-principles energetics to CALPHAD: An application to thermodynamic modeling of the Al-Ca binary system

First-principles (FP) energetics of both the constituent elements and the compounds in the Al-Ca binary system are used in the CALPHAD (CALculation of PHase Diagrams) approach of thermodynamic modeling. First-principles calculations are performed using both an all-electron full-potential linearized augmented plane-wave method, as well as an ultrasoft pseudopotential/plane wave method. We perform calculations of T = 0 ground state total energies of the pure Al and Ca in fcc, bcc, and hcp structures, and the binary compounds in their observed crystal structures. Al₄Ca, Al₁₄Ca₁₃, and Al₃Ca₈ are modeled in CALPHAD as simple stoichiometric compounds; however, the Laves C15 compound, Al₂Ca, is modeled using two sublattices (Al,Ca ₂(Al,Ca)₁, necessitating first-principles energies of both the stable Al₂Ca compound as well as the three nonstable Al₂Al, AlCa₂, and Ca₂Ca compounds. From these total energies, we obtain the formation enthalpies of all the binary compounds that are then used to assist in evaluating the Gibbs energy functions for the individual phases. The entropy contribution in the Gibbs energy function for each individual compound is obtained via the observed equilibria with the liquid phase. We provide a complete thermodynamic description of the Al-Ca binary system, evaluated by this combined CALPHAD-FP approach.