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.
Highlights
Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC1−x), maintain structural stability even if they accommodate abundant anion vacancies
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
All the results show that self-assembling of 3NN VC triplets is the key factor to maintain phase stability of defective ZrC1−x with high concentration of VCs, and to realize short-range and long-range ordering of VCs
Summary
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. Most covalent and ionic crystalline solids (daltonide) hold exact stoichiometry in order to keep translational symmetry and atomic coordination Another group of compounds (berthollide, such as binary transition metal carbides and nitrides) maintain structural stability in a wide sub-stoichiometric range[1,2,3]. Zirconium carbide (ZrC) is a representative non-stoichiometric interstitial compound It shows high hardness, high melting point, excellent high temperature thermal/mechanical properties, good wear and corrosion resistance, resistance to fission product attack and low neutron cross-section[10,11,12]. The underlying mechanism pushing forward the evolution of VC configurations is not fully understood
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