Study of phase stability in the $\sigma$-FeCr system

TL;DR

This study investigates the phase stability of the $\sigma$-FeCr alloy system by calculating formation energies and free energies, revealing a minimum in stability within the known phase existence range.

Contribution

The paper introduces a detailed computational analysis of formation energies and configurational entropy effects in the $\sigma$-FeCr phase, providing new insights into its stability range.

Findings

Minimum formation energy occurs within the $\sigma$-phase stability range.

Configurational entropy influences phase stability at 2000 K.

Formation energy varies with Fe occupancy on different lattice sites.

Abstract

Formation energy of the $\sigma$-phase in the Fe-Cr alloy system, $\Delta E$, was computed versus the occupancy changes on each of the five possible lattice sites. Its dependence on a number of Fe-atoms per unit cell, $N_{Fe}$, was either monotonically increasing or decreasing function of $N_{Fe}$, depending on the site on which Fe-occupancy was changed. Based on the calculated $\Delta E$ - values, the average formation energy, $<\Delta E>$, was determined as a weighted over probabilities of different atomic configurations. The latter has a minimum in the concentration range where the $\sigma$-phase exists. The minimum in that range of composition was also found for the free energy calculated for 2000 K and taking only the configurational entropy into account.