Study of phase stability in the σ-FeCr system

Formation energy of the σ-phase in the Fe-Cr alloy system, ΔE, 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, NFe, was either monotonically increasing or decreasing function of NFe, depending on the site on which Fe-occupancy was changed. Based on the calculated ΔE values, the average formation energy, 〈 Δ E 〉 , was determined as a weighted over probabilities of different atomic configurations. The latter has a minimum in the concentration range where the σ-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.