Ab initio study of energetics and magnetism of sigma phase in Co–Mo and Fe–Mo systems

Abstract

We analyse, from first-principles, the energetics and magnetic ordering of sigma phases in Co–Mo and Fe–Mo systems. Total energy differences between the sigma phase and Standard Element Reference (SER) structures are calculated in the whole concentration range at equilibrium volumes by means of the linear muffin-tin orbitals method in the atomic-sphere approximation (LMTO-ASA), the full-potential linearised augmented-plane waves (FLAPW) method and the pseudopotential approach. They are compared with the enthalpy of formation of sigma phase obtained from the phase equilibria calculations at higher temperature based on the semiempirical CALPHAD (CALculation of PHAse Diagram) method. It turns out that the binary sigma phases are more stable than the weighted average of the sigma phase of elemental constituents and that this stability for Fe–Mo is higher than for Co–Mo. On the other hand it was found that the binary sigma phases do not exhibit any stability with respect to the weighted average of the SER structures. The magnetic configurations in all systems are investigated and the stabilizing effect of magnetic order in sigma phase at 0 K is presented. It turns out that the atomic magnetic moment strongly depends on the type of occupied sublattice and total composition of the alloy.