  By using evolutionary algorithm USPEX, we have predicted a number of stable
zirconium carbides. In addition to the well-known rocksalt-type stoichiometric
ZrC (Fm-3m), present prediction also identifies five stable substoichiometric
zirconium carbides adopting rocksalt-type structures with ordered carbon
vacancies, Zr8C7 (P-1), Zr6C5 (C2/m), Zr5C4 (P-1), Zr3C2 (C2/m), and Zr2C
(Fd-3m). The effects of carbon vacancies on structural and mechanical
properties are investigated. We highlight that the distribution of carbon
vacancies has significant influence on volume, Pugh's ratio, and hardness. We
further propose that hardness can be enhanced by replacing carbon vacancies
with suitable elements, in particular nitrogen and oxygen.
