  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.
