Prediction of stable hafnium carbides: Stoichiometries, mechanical properties, and electronic structure

Hafnium carbides are studied by a systematic search for possible stable stoichiometric compounds in the Hf-C system at ambient pressure using variable-composition ab initio evolutionary algorithm implemented in the USPEX code. In addition to well-known HfC, we predicted two additional compounds Hf3C2 and Hf6C5. The structure of Hf6C5 with space group C2/m contains 11 atoms in the primitive cell and this prediction revives the earlier proposal by A. I. Gusev. The stable structure of Hf3C2 also has space group C2/m, and is more energetically favorable than the Immm, P-3m1, P2 and C2221 structures put forward by A. I. Gusev. Dynamical and mechanical stability of the newly predicted structures have been verified by calculations of their phonons and elastic constants. The bulk and shear moduli of Hf3C2 are 195.8 GPa and 143.1 GPa, respectively, while for Hf6C5 they are 227.9 GPa and 187.2 GPa, respectively. Their mechanical properties are inferior to those of HfC due to the presence of structural vacancies. Chemical bonding, band structure, and Bader charge are presented and discussed.