First-Principles Study of the Mechanical Properties of (Ti,V)C Solid Solutions

Ternary transition metal carbides like Ti1-xVxC offer potential for enhanced mechanical properties, but exploring the vast compositional space is challenging. This study employs first-principles calculations combined with the Cluster Expansion (CE) method to systematically investigate the phase stability, elastic properties, hardness, and electronic structure of the Ti1-xVxC system. Density Functional Theory (DFT) calculations using VASP informed the CE model constructed via the ATAT toolkit, which predicted several stable intermediate configurations at 0 K relative to TiC and VC. Elastic constants calculated for these stable phases revealed non-monotonic trends, with Shear (G) and Young's (E) moduli peaking near x = 0.5. Vickers hardness (Hv), estimated by averaging five empirical models based on calculated Bulk (B) and G moduli, was found to reach a maximum of approximately 32.6 GPa at the Ti0.67V0.33C composition, surpassing the calculated values for the binary endpoints. Analysis of Pugh's ratio (B/G) indicated intrinsic brittleness across all compositions, with maximum brittleness correlating with the region of maximum stiffness. Electronic structure calculations (DOS, ELF, Deformation Density) using the BAND code confirmed strong covalent p-d hybridization as the origin of the high stiffness and revealed composition-dependent changes related to Fermi level shifts. This work identifies Ti0.67V0.33C as the most promising composition for maximizing hardness in this system and provides theoretical guidance for designing advanced carbide-based materials.