Investigating the Al/Si mixed site occupancy in the ß-AlFeSi phase.

This work investigates the mixed site occupancy of aluminium and silicon atoms in the ß-AlFeSi phase. For this purpose, the six mixed Al/Si sites of the ß-AlFeSi structure were considered independent and alternatively substituted by Al or Si, thus generating 64 ordered structures or end-members. The enthalpy of formation of each end-member was calculated by DFT. These calculations allowed us to derive the enthalpy of mixing of the solid solution at 0 K, over a wide range of chemical compositions, from the Al-Fe binary system to the Si-Fe binary system. In addition, the heat capacities of the solid solution were determined using a Debye model based on the calculation of the elastic constants and the equation of state of each end-member. These heat capacity values were used along with the enthalpy of formation we calculated to determine the Gibbs free energies of all the end-members of the ß-AlFeSi structure. Finally, the configurational entropy of mixing from the Compound Energy Formalism (CEF) for the configurational entropy of mixing was subsequently used to calculate the occupation fractions of the Si sites on the Al sites of the ß-AlFeSi structure, at 300 K and 938 K, the latter being the thermal decomposition temperature of this compound. These original site occupancy data were used to quantify the chemical ordering of the solid solution and to compare different sublattice (SL) models. We thus highlight that the SL model of the ß-AlFeSi solution most commonly accepted in the literature generates considerable errors in its thermodynamic description, contrary to the model proposed in this paper, which is both simple and particularly accurate, consisting in merging the sites Al(1)-Al(6), the sites Al(2)-Al(3) as well as the sites Al(4)-Al(5).

On the elaboration of the next generation of thermodynamic models of solid solutions.

Thermodynamic models of solid solutions used in computational thermochemistry have not been modernized in recent years. With the advent of fast and cheap computers, it is nowadays possible to add, at a minimal computational cost, physical ingredients such as coordination numbers, inter-atomic distances and classical interatomic potentials to the function describing the energetics of ordered and disordered solid solutions. As we show here, the integration of these elements into a robust statistical thermodynamic model of solution establishes natural connections with other deterministic and stochastic atomistic methods such as Monte Carlo and molecular dynamics simulations. Ultimately, all these numerical approaches need to be self-consistent and generate complementary sets of numerical thermo-physical properties. The present work proposes a new formalism to define the Gibbs free energy of ordered and disordered solid solutions. It allows for a complete prediction of the thermal, volumetric and compositional dependence of the Gibbs free energy by solving a constrained minimization problem. As a proof of concept, we explore the energetic behavior of pure face-centered cubic gold as well as the AuCu L10 ordered solution as a function of both temperature and pressure. We finally compare these results with the average properties obtained from classical molecular dynamics simulations and explain the origin of the existing differences between the two approaches based on how the temperature is accounted for in each method.