First-principles study of effective cluster interactions and enthalpies of formation of substoichiometric VC1-x

Self-assembly of Carbon Vacancies in Sub-stoichiometric ZrC(1-x)

Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC(1-x)), maintain structural stability even if they accommodate abundant anion vacancies. This unique character endows them with variable-composition, diverse-configuration and controllable-performance through composition and structure design. Herein, the evolution of carbon vacancy (VC) configuration in sub-stoichiometric ZrC(1-x) is investigated by combining the cluster expansion method and first-principles calculations. We report the interesting self-assembly of VCs and the fingerprint VC configuration (VC triplet constructed by 3(rd) nearest neighboring vacancies) in all the low energy structures of ZrC(1-x). When VC concentration is higher than the critical value of 0.5 (x > 0.5), the 2(nd) nearest neighboring VC configurations with strongly repulsive interaction inevitably appear, and meanwhile, the system energy (or formation enthalpy) of ZrC(1-x) increases sharply which suggests the material may lose phase stability. The present results clarify why ZrC(1-x) bears a huge amount of VCs, tends towards VC ordering, and retains stability up to a stoichiometry of x = 0.5.

Ab initio study of phase equilibria in TiC(x)

The phase diagram for the vacancy-ordered structures in the substoichiometric TiC(x) (x = 0.5-1.0) has been established from Monte Carlo simulations with the long-range pair and multisite effective interactions obtained from ab initio calculations. Three ordered superstructures of vacancies (Ti(2)C, Ti(3)C(2), and Ti(6)C(5)) are found to be ground state configurations. Their stability has been verified by full-potential total energy calculations of the fully relaxed structures.