Influence of boron vacancies on phase stability, bonding and structure of MB₂ (M  =  Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) with AlB₂ type structure

Transition metal diborides in hexagonal AlB₂ type structure typically form stable MB ₂ phases for group IV elements (M  =  Ti, Zr, Hf). For group V (M  =  V, Nb, Ta) and group VI (M  =  Cr, Mo, W) the stability is reduced and an alternative hexagonal rhombohedral MB ₂ structure becomes more stable. In this work we investigate the effect of vacancies on the B-site in hexagonal MB ₂ and its influence on the phase stability and the structure for TiB₂, ZrB₂, HfB₂, VB₂, NbB₂, TaB₂, CrB₂, MoB₂, and WB₂ using first-principles calculations. Selected phases are also analyzed with respect to electronic and bonding properties. We identify trends showing that MB ₂ with M from group V and IV are stabilized when introducing B-vacancies, consistent with a decrease in the number of states at the Fermi level and by strengthening of the B–M interaction. The stabilization upon vacancy formation also increases when going from M in period 4 to period 6. For TiB₂, ZrB₂, and HfB₂, introduction of B-vacancies have a destabilizing effect due to occupation of B–B antibonding orbitals close to the Fermi level and an increase in states at the Fermi level. (paper)