Evaluating effective pair and multisite interactions for Ni-Mo system

Abstract

Cluster expansion (CE) method was used to calculate the energies of various Ni-Mo phases. The clusters comprising of few nearest neighbours can describe any phase of Ni-Mo system by suitable choice of effective pair and multisite interaction parameters (ECI). The ECIs were evaluated in present study by fitting the ground state energies obtained by first principle calculations. The ECIs evaluated for Ni-Mo system were mostly pair clusters followed by triplets and quadruplet clusters with cluster diameters in the range 2.54 - 10.20 Å. The ECI values diminished for multi-body (triplets and quadruplets) clusters as compared to 2-point or pair clusters indicating a good convergence of CE model. With these ECIs the predicted energies of all the Ni-Mo structures across the Mo concentration range 0-100 at% were obtained. The quantitative error in the energies calculated by CE approach and first principle is very small (< 0.026 meV/atom). The appreciable values of 2-point ECIs upto 4th nearest neighbour reveal that two body interactions are dominant in the case of Ni-Mo system. These ECIs are compared with the reported values of compositional dependent effective pair interactions evaluated by first principle as well as by Monte Carlo method.