We have performed a search for stable compounds in the hafnium-carbon (Hf-C) system at ambient pressure using a variable-composition ab initio evolutionary algorithm implemented in the uspex code. In addition to the well-known HfC, we predicted two additional thermodynamically stable compounds ${\mathrm{Hf}}_3{\mathrm{C}}_2$ and ${\mathrm{Hf}}_6{\mathrm{C}}_5$. The structure of ${\mathrm{Hf}}_6{\mathrm{C}}_5$ with space group $C2/m$ contains 22 atoms in the conventional cell, and this prediction revives the earlier proposal by Gusev and Rempel [Phys. Status Solidi A 135, 15 (1993)]. The stable structure of ${\mathrm{Hf}}_3{\mathrm{C}}_2$ also has space group $C2/m$ and is more energetically favorable than the $Immm,P\overline{3}m1,P2$, and $C{222}_1$ structures put forward by Gusev and Rempel [Phys. Status Solidi A 135, 15 (1993)]. The dynamical and mechanical stabilities of the newly predicted structures have been verified by calculations of their phonons and elastic constants. Structural vacancies are found in the ordered defective rock-salt-type HfC. Chemical bonding, band structure, and Bader charges are presented and are discussed. All three compounds are weak metals with increasing metallicity as the vacancy concentration increases. The mechanical properties of the hafnium carbides nonlinearly decrease with increasing vacancy concentration, indicating the defect tolerance of this refractory compound. It is, therefore, possible to tune the hardness, ductility, and electrical conductivity by varying the stoichiometry of the hafnium carbides.

• Received 19 August 2013

DOI:https://doi.org/10.1103/PhysRevB.88.214107