Configurational thermodynamics of the Fe-Crσphase

Ab Initio Study of Lattice Site Occupancies in Binary Sigma Phases Using a Single-Site Mean Field Model

“…We assume here that the alloy components are distributed randomly on each site and there is no mutual correlation between them on different sublattices. As has been demonstrated in [16], this is a valid approximation at high temperatures at least in the case of the Fe-Cr σ-phase. Thus, the total energy (per unit cell), E tot ({c α }), can be written in a simplified form as…”

“…Furthermore, as has already been discussed in our previous works [14,16], longitudinal spin fluctuations should exist at high temperature. These are thermal Stoner-like many-body excitations which lead to fluctuations of the magnitude of the local magnetic moments.…”

“…However, as we have shown in [16], the on-site interaction parameters are dominant in the total energy expansion. The summation in Equation (3) runs only over four sublattices, since the occupation at the fifth sublattice is determined by the alloy composition c and the concentrations at the other four sublattices c α .…”

“…In order to find the atomic occupancies of the σ-phase sublattices, we minimize the Helmholtz free energy F , which can be written in the following form for a given composition and temperature [14][15][16]:…”

“…However, most of these methods were based on a formalism, which is quite computationally demanding. Alternatively, we have recently proposed a simpler approach to calculate the site preference in the binary σ-phases [14][15][16]. It is based on a simple single-site mean-field model, which recently has demonstrated to be able to produce quite accurate results for the site occupancy of Fe and Cr in the Fe-Cr σ-phase.…”