First-principles calculations and thermodynamic modelling of long periodic stacking ordered (LPSO) phases in Mg-Al-Gd

In the present work, thermodynamic modelling of four long periodic stacking ordered (LPSO) phases, i.e., 10H, 18R, 14H, and 24R, in the Mg-Al-Gd system was performed using the CALPHAD (calculation of phase diagram) approach with input from the present first-principles calculations and experimental data in the literature. Sublattice models were developed to describe these LPSO phases. Especially, an L1₂-type clusters in the FCC stacking layers of LPSO phases and the atomic occupancy in the center of L1₂ cluster were considered based on experimental observations and energetics from first-principles calculations. The calculated phase equilibrium results are in good agreement with experiments about the phase stability of 14H and 18R and the mole fraction of Gd and Al in these LPSO phases. The present modeling provides a new approach to describe the thermodynamic properties of LPSO phases and can be applied to other alloy systems.