Ab initioanalysis of energetics of σ-phase formation in Cr-based systems

Abstract

A theoretical approach to the explanation of experimentally determined positive enthalpy of formation in Cr-based phases is presented. It turns out that the energy of formation of phases in Cr-Co and Cr-Fe systems is found to be negative taking the pure components in the -phase structure as the standard states. Our treatment represents a first step to a model of an explanation of the stability of the phase.

Ab initio study of formation energy and magnetism of sigma phase in Cr–Fe and Cr–Co systems

“…However, the LMTO-ASA method does not provide reliable structural energy differences for structures of different symmetry, although the total energy differences calculated by this method for the same crystallographic structure are considered to be quite reliable [12,32,33]. Thus, we employed the FLAPW and pseudopotential method to establish the bridge between the LMTO energies of formation of sigma phase related to the weighted average of energies of sigma phases of pure constituents on one hand and the RS structures on the other hand.…”

“…Let us note that vast majority of all measured values of enthalpy of formation reported by various authors [8][9][10][11] in Cr-Fe and Cr-Co systems as well as the calculated values [12,13] is positive. Therefore, from this point of view we could expect that the sigma phase is unstable with respect to the RS.…”

“…In our previous paper [12], the calculations of energies of formation of sigma phase were performed at experimental lattice volumes of sigma phases, which is the first approximation only. The aim of this paper is to carry out these calculations on the physically more appropriate equilibrium volume basis.…”

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

“…Particularly the latter might not be negligible for alloy compositions different from the equiatomic composition, especially for those sublattices with small deviations from integer occupation, e.g., the A and D sublattices for x V = 0.60 or the B sublattice for x V = 0.40. These effects could be taken into account similiar as for the equiatomic composition (see Equation (6)), but such calculations are not presented in this work. Table 5.…”

“…Recently the site occupation in the σ-phase has been widely studied by such methods [5][6][7][8][9][10][11][12][13]. However, most of these methods were based on a formalism, which is quite computationally demanding.…”