Plane-wave pseudopotential study for the structural stability of Hf: The role of spin-orbit interaction

With the use of density functional theory, first-principles calculation has been performed to investigate the structural stability of Hf. In this context, Hf has several characteristics, including the openness of its omega structure in the sequence hcp→omega→bcc with elevated pressure, its tight-binding d-bands near the Fermi level and the possible requirement of relativistic correction (spin-orbit coupling, SO) for its relatively high atomic number. To decouple these characters and reproduce the equilibrium transformation pressures of hcp→omega as well as omega→bcc, we treat Hf with (I) local density approximation (LDA) without and (II) with SO coupling, (III) generalized gradient approximation (GGA) without and (IV) with SO coupling. Our plane-wave pseudopotential calculation with GGA and SO interaction results in transformation pressures much closer to the experiment compared to the previous linear muffin-tin orbit calculations. Furthermore, we discuss the dependence of lattice parameters and the transformation pressure on SO coupling. The effect of SO on the correlation of d-band occupancy and the structural stability is also revealed.