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

This study utilizes Density Functional Theory (DFT) to investigate the thermodynamic stability, elastic anisotropy, and electronic properties of C14 and C15 Laves phases within the Cr--Hf--Nb system. Both formation enthalpies and comprehensive elastic property analyses confirm the energetic and mechanical stability of the C14 (HfNb$_2$, HfCr$_2$, NbCr$_2$) and C15 (HfCr$_2$, NbCr$_2$) phases. Furthermore, the evaluation of elastic anisotropy reveals a descending order of HfCr$_2$ > NbCr$_2$ > HfNb$_2$ for the C14 phase, contrasting with NbCr$_2$ > HfNb$_2$ > HfCr$_2$ for the C15 phase. Finally, electronic structure and COHP analyses indicate that strong anti-bonding behavior near the Fermi level within the XM$_2$ M--M bonds acts as a primary destabilization mechanism for both of these Laves phases.