Vacancy ordered phases of nonstoichiometric hafnium carbide from evolutionary crystal structure predictions

Abstract

Carbides of IV and V group transitional metals with B1 structure have large homogeneity regions due to high amounts of vacancies in the carbon sublattice. Ordering of the vacancies leads to formation of new phases with different compositions and crystal structures. In this work, we performed a theoretical search for the ordered phases in hafnium carbide using evolutionary algorithm USPEX for crystal structure prediction. Four thermodynamically stable compounds with stoichiometries Hf3C2, Hf4C3, Hf7C6 and Hf9C8 as well as near-to-equilibrium variants Hf9C7, Hf5C4, and Hf6C5 have been found in the composition range HfC0.67-HfC1.0. All the stable and meta-stable phases are formed by vacancy ordering in the carbon sublattice of B1 structure. We also described possible ordered structures for hypothetical compositions Hf10C7, Hf7C5, Hf8C7 and Hf10C9. This allowed us to investigate the effect of vacancy concentration on the structural and mechanical properties. The calculations have demonstrated the ordered vacancies with a concentration of less than approximately 11% do not deteriorate the mechanical properties of hafnium carbide. The hardness of ordered phases with vacancy concentrations less than 16.7% is higher as compared to the defect-free HfC.