Electronic structure, cohesive properties, and phase stability of ${\mathrm{Ni}}_3$V, ${\mathrm{Co}}_3$V, and ${\mathrm{Fe}}_3$V

The electronic structure and cohesive properties (including equilibrium lattice constants, bulk modulus, and formation energy) of the intermetallic compounds ${\mathrm{Ni}}_3$V, ${\mathrm{Co}}_3$V, and ${\mathrm{Fe}}_3$V in their L$1_2$, D$0_{22}$, and D$0_{19}$ structures have been determined by means of the self-consistent total-energy linear-muffin-tin-orbital method based on the local-density approximation. The correct phase preference and stability of these compounds are obtained; the rigid-band approximation is found to hold well for describing the electronic structure of these compounds having the same crystal structure. The correlation between the ordered structure and the semiempirical rule of Liu on the number of valence electrons per atom is shown to be associated with the filling up of the bonding states in a specific structure.