title: Self-assembly of Carbon Vacancies in Sub-stoichiometric ZrC(1-x).
abstract: 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.
authors.affiliation: High-performance Ceramics Division, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China.
authors.forename: Yanhui
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China.
authors.forename: Bin
authors.initials: B
authors.lastname: Liu
authors.affiliation: High-performance Ceramics Division, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China.
authors.forename: Jingyang
authors.initials: J
authors.lastname: Wang