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.
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