1ST-PRINCIPLES STUDY OF EFFECTIVE CLUSTER INTERACTIONS AND ENTHALPIES OF FORMATION OF SUBSTOICHIOMETRIC VC(1-X)

We have performed extensive first-principles electronic structure calculations on a series of ordered VC1-x compounds using the full-potential linear-muffin-tin-orbitals method. The results are fitted to equations of state and volume-dependent effective cluster interactions (ECI's) are determined. A set of eight composition-independent ECI's including pair interactions up to the third-nearest neighbors as well as some multiplet clusters are found to reproduce the total electronic energies of all ordered VC1-x compounds within 1 mRy/atom. These ECI's are used to derive the enthalpy of formation at 0 K, DELTAH-0(dis)(x), for VC1-x with a completely disordered vacancy configuration. DELTAH-0(dis)n(x) is higher than DELTAH-0[VC] for all vacancy concentrations x not-equal 0. The energy gain due to ordering is approximately 10 mRy/V atom. This energy is enough to yield enthalpies of formation of some ordered structures (e.g., V8C7 and V6C5) that are below the enthalpy of formation for VC. We conclude that the ground state of VC1-x at zero temperature occurs for x not-equal 0. Lattice relaxations around vacant sites are not accounted for by our ECI's. These will further decrease the total energy of VC1-x and thus stabilize the vacancies. We present a simple band-filling model which qualitatively explains the limited stability range of vacancy formation.