Phases of vanadium under pressure investigated from first principles.

The existence and stability under pressure of three phases of vanadium are calculated from first principles. The phases are one body-centered cubic (bcc) and two rhombohedral phases (rh(u) and rh(l)), which have greater and lower α values than the primitive bcc rhombohedral cell. The bcc phase is shown in two ways to become unstable at 0.65 Mbar, in agreement with an observed phase transition, but in disagreement with previous higher estimates. The rh phases exist when the bcc phase is unstable, but the bcc phase stabilizes again at 3 Mbar, and the rh phases disappear. At 1.15 Mbar the rh(u) phase becomes and remains unstable and the rh(l) phase becomes the ground state up to 3 Mbar, where the rh(l) phase disappears and the bcc phase takes over. The theory gives four phase transitions among the phases over the pressure range from 0 to 3 Mbar; two of them are bcc to rh(u)-a low pressure (0.3 Mbar) thermodynamic transition found from Gibbs free energies being equal (not observed) and a higher pressure (0.65 Mbar) instability transition when the bcc phase becomes unstable (observed).