First principles investigations of the structural stability and thermal dynamical properties of metal Ba under high pressure

The stabilities and the thermal dynamical properties of the three high-pressure phases of Ba (Ba-I, Ba-II and Ba-V) are investigated systemically by first principles method. Our results show that all the three phase meet the criteria of mechanical and dynamical stabilities at 0 K. With pressure increasing, the phonon frequencies in Ba-I and Ba-II phases become softened, whereas the Ba-V phase exhibits the hardening of phonon frequencies. Although both Ba-II and Ba-V phase are the same hcp structures, they show different elastic anisotropies under high pressure. We also find that Ba-II phase at higher pressure still meets the mechanical stability criterion, but does not meet the dynamical stability criterion. The absence of dynamical stability may be the reason for the transition from Ball phase to Ba-IV phase. We also calculate and make comparisons of sound velocity, Debye temperature, bulk modulus and shear modulus etc between Ba-II and Ba-V phases, showing that Ba possesses the thermal dynamical properties under high pressure.