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 MB2 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 MB2 structure becomes more stable. In this work we investigate the effect of vacancies on the B-site in hexagonal MB2 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 MB2 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.