Crystal structure and crystal chemistry of the τ-Mg₃₂(Al,Zn)₄₉ solid solution using first-principles calculations and thermodynamic modelling

This paper presents a study of the crystal structure and crystal chemistry of the τ-Mg32(Al,Zn)49 phase. We first performed DFT calculations to resolve conflicting data concerning the occupancy of site 2a of the solid solution crystal structure. Subsequently, 16 ordered configurations derived from the mixing of Al/Zn on sites 24g1, 24g2 and 48h of the solid solution structure, as well as the mixing of Mg/Zn on site 12e1 were generated. We then used DFT calculations to derive the formation enthalpies of all the end-members of the solid solution, their elastic constants by imposing 51 finite deformations for each end-member, and their energies as a function of volume. These calculations were used in a Debye-Wang model (in Slater form) to calculate the heat capacities of the 16 end-members and to obtain in fine their Gibbs energies. At last, these calculations were used to support a thermodynamic model based on the Bragg-Williams approximation, enabling all mixed sites occupancies to be calculated at any temperature and chemical composition. For instance, the predictions we carried out at 633 K and 800 K are in very good agreement with the available measurements. On the basis of these new results, we have determined the chemical ordering of the solid solution over a very wide range of chemical composition and temperature, which has enabled us to propose a new sublattice model for the τ-Mg32(Al,Zn)49 solid solution. This sublattice model is both simpler and more accurate than all the other models used in the literature since it agrees with the crystal structure and the crystal chemistry of the τ-Mg32(Al,Zn)49 phase in a large range of temperature and chemical composition.