On the origin of the non-stoichiometry of theτ₁-Al₂Fe₃Si₃solid solution

This study aims to understand the origin of the significant non-stoichiometry observed for theτ₁-Al₂Fe₃Si₃solid solution. First, the short-range order (SRO) was investigated by systematically examining the coordination polyhedra of the five mixed sites of the structure. This straightforward analysis revealed that the SRO is weak in this structure and can be neglected, thus validating the use of the Bragg-Williams approximation to describe the configurational entropy of the solution. Subsequently, a complete set of end-members was generated by systematically substituting Al and Si on the five mixed sites of the structure. The formation enthalpies and equations of state were determined for each end-member using density functional theory calculations, and the Gibbs free energy was derived using the Debye-Wang model. These thermodynamic data enabled quantitative prediction of the mixed site fractions as a function of temperature. The elucidation of the chemical ordering mechanisms underlying the non-stoichiometry of this phase was used to derive an optimal Calphad model for this solution.