Self-assembly of Carbon Vacancies in Sub-stoichiometric ZrC1-x

Abstract

Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC1-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 ZrC1-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 3rd nearest neighboring vacancies) in all the low energy structures of ZrC1-x. When VC concentration is higher than the critical value of 0.5 (x > 0.5), the 2nd nearest neighboring VC configurations with strongly repulsive interaction inevitably appear, and meanwhile, the system energy (or formation enthalpy) of ZrC1-x increases sharply which suggests the material may lose phase stability. The present results clarify why ZrC1-x bears a huge amount of VCs, tends towards VC ordering, and retains stability up to a stoichiometry of x = 0.5.