Thermodynamic behavior of the τ₁₁-Al₄ Fe₁.₇Si solid solutions from 0 K to 1270 K

This study discusses the atomic interactions between Al and Si in the mixed sites of the τ₁₁-Al₄ Fe₁.₇Si solid solution structure, with respect to chemical composition and temperature. We first investigated the crystal structure of the τ₁₁-Al₄ Fe₁.₇Si solid solution using Density Functional Theory (DFT), confirming recent findings suggesting significant changes to the solution structure. Subsequently, we quantified the 0 K short-range ordering (SRO) in the structure by analysing the coordination polyhedra of the mixed sites and calculating the energies of structures with mixed Al/Si occupations. Our results indicate that the SRO contribution can be neglected. In addition, we generated all the end-members corresponding to the substitution of Al by Si on the mixed sites of the structure and considering site 2 as occupied by Fe or vacant. We calculated the formation enthalpies of these end-members by DFT and determined their isobaric heat capacities by using a Debye–Wang model together with the DFT calculations of their equation of state. Using these calculations, we determined Si site fractions over a temperature range from 0 K to the decomposition temperature of the solid solution, applying a model derived from the Bragg–Williams approximation. Our findings enable us to propose reliable sublattice model for the solid solution, which differ significantly from existing models in the literature.