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

摘要

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.