Atomic and Effective Pair Interactions in FeC Alloy with Point Defects: A Cluster Expansion Study

Abstract

The Cluster Expansion Method (CEM) is used to investigate the pair interactions in body centered cubic (BCC) FeC alloy in the presence of vacancies. Within the CEM framework, the relation of cluster (point and pair) probabilities and set of independent correlation functions are derived. These are then applied to calculate the effective cluster interaction and atomic pair interaction energies for Fe, C and vacancy in FeC system. We found that, in this alloy, the interaction mostly comes from the first nearest neighbor pairs, and, to some degree, from the third nearest neighbor pairs. Detailed analysis shows that, within the first nearest neighbor pair interactions approximation, the C-C and Fe-C pair interactions are repulsive where the former one is more dominant. This is attributed to the local stress field formed in the vicinity of C atoms which pushes the first nearest neighbor atoms away to maintain the equilibrium distances. Moreover, there is an attractive interaction between C and vacancy which implies the possibility of C atoms to be trapped at vacancy site.From Eqs. (5) and (7), the point probabilities of the 4-constituent system above become: ..... (35) Here, J R α is not the same as the original J α in Eq. (29) but it is the linear combination of J α , obtained by replacing the linearly-dependent correlation functions ξ α with the linearly-independent ones. From the internal energies per lattice site in (34) and the correlation functions in matrix B, the effective cluster interaction energies (in eV) are calculated and listed below: