Electronic properties governing the phase stability and elastic anisotropy of C14 and C15 Cr–Hf–Nb Laves phases

This study uses Density Functional Theory (DFT) calculations to investigate the structural, energetic, elastic, anisotropic, electronic, and bonding properties of C14 and C15 Laves phases in the Cr–Hf–Nb system. The enthalpies of formation of the C14 Laves phases show that HfNb 2 exhibits a value of − 0.32 kJ/mol, while HfCr 2 and NbCr 2 also show negative enthalpies of formation. The three C14 phases satisfy the mechanical stability criteria. Among the C15 phases, both HfCr 2 and NbCr 2 exhibit negative enthalpies of formation and satisfy the mechanical stability criteria. The elastic anisotropy follows the order HfCr 2 > NbCr 2 > HfNb 2 for the C14 phases and NbCr 2 > HfNb 2 > HfCr 2 for the C15 phases. Finally, electronic structure and ICOHP analyses reveal partial occupation of antibonding M–M states near the Fermi level, which is associated with the lower energetic favorability of the C14 and C15 structures and is more pronounced in C15.