Thermodynamic properties of Laves phases in the Mg–Al–Ca system at finite temperature from first-principles

First-principles calculations are employed to investigate the structural and thermodynamic properties of binary Laves phases (C14, C15 and C36 structures) in the Mg–Al–Ca system. The enthalpies of formation at 0 K are predicted. The vibrational contributions to Helmholtz free energy for the stable C14-Mg2Ca and C15-Al2Ca phases are determined using both first-principles phonon calculations and Debye–Grüneisen model. The predicted thermodynamic properties of the stable phases, including enthalpy, entropy, bulk modulus, heat capacity, and thermal expansion coefficient, agree well with available experimental data. For the other nonstable phases, the thermodynamic properties are estimated by Debye–Grüneisen models of Moruzzi et al. and of Wang et al. The entropies predicted from these two Debye models have a general agreement with about ±0.5 J/mol K differences for all the three structures.