Ab initio study of formation energy and magnetism of sigma phase in Cr–Fe and Cr–Co systems

First-principles electronic structure calculations of total energy differences between the sigma phase and Reference States (RS) of pure constituents in Cr–Fe and Cr–Co systems performed by various methods are presented and compared with enthalpies of formation measured by calorimetry. Both measurements and calculations provide positive values of enthalpy of formation with respect to the RS. Negative values can be obtained when the pure constituents in the sigma phase structure are taken as the RS. Total energy differences of all sigma phase configurations involved are calculated at equilibrium volumes, reproducing well the experimental energy of formation of the sigma phase. The magnetic configurations in Cr–Fe and Cr–Co are also investigated and the stabilizing effect of magnetic ordering in sigma phase at 0 K is demonstrated. It turns out that the magnetic moment depends on the type of the occupied sublattice and total composition of alloy.