Study of phase stability in the $\sigma$-FeCr system
  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. 
J. Cieslak, J. Tobola and S.M. Dubiel
cond-mat.mtrl-sci