The experimental Fe-Ni-Cr ternary diagrams are extended into the quaternary X-field for X = Mo, Ti, Mn, Si, Nb, Ta using pair potential models for the fcc, bcc and sigma phases and free energy relations deduced for the Fe-Ni-Cr system by Kaufman and Nesor. The constrained diagrams for constant pct X are in agreement with observations made by others. Also, a correlation is found between the calculated effect of a given addition of X on the difference in energies between the sigma and fcc phases and its Cr equivalent deduced empirically from impact energy measurements by Hull. It is suggested that the procedures developed in this investigation should have wide applicability in alloy design. In particular, it may be helpful in discovering sigma free compositions for stainless steels. © 1979 American Society for Metals and the Metallurgical Society of AIME.