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The site occupation of binary Fe-Cr, Co-Cr, Re-W and Fe-V sigma phases is studied in the present work with a first-principles-based single-site mean field theory. We show that the alloy components in these systems exhibit similar site preferences except for the Re-W system, where the occupation of two sites is reversed in agreement with previously published works. In case of the FeV sigma phase, for which the size mismatch between the alloy components is large, we also include into our consideration the effect of local lattice relaxations. The obtained results are found in good agreement with the experimental data and previous theoretical studies.