Ab-initio calculations, Debye-Wang model and thermodynamic modeling for the short-range order and crystal chemistry characterisation of the τ8-Al₂Fe₃Si₄ solid solution

This paper presents a comprehensive examination of the τ8-Al₂Fe₃Si₄ solid solution, investigating its crystal chemistry and short-range order. To do so, Density functional theory (DFT) calculations were performed, simulating partial substitutions of Al and Si on the four mixed sites of the structure. Our results indicates a negligible contribution from the SRO, allowing the Bragg–Williams approximation to be used to describe its crystal chemistry. Subsequently, systematic substitutions of Al and Si on all mixed sites generated a complete set of ordered structures, called end-members. The formation enthalpies, equation of state and elastic constants for each end-member were calculated, allowing the Gibbs free energy of the solid solution to be derived using the Debye–Wang model. On the basis of this new theoretical insights, a thermodynamic model was developed, predicting the Si occupancy factors in all the mixed sites of the structure at different temperatures, allowing the quantification of its chemical ordering.