Phase changes and the equation of state of Zr

Abstract

The equation of state of Zr is investigated, with an emphasis on determining the phase diagram, and the correct sequence of phases along the shock Hugoniot. This investigation involves the creation of free energy functions for hcp, ω, and bcc phases. These free energies incorporate information from electronic structure theory, and allow a unified description of data on thermodynamic properties, equation of state, and phase changes. All the data and calculations are consistent with a Zr phase diagram in which the high temperature and high pressure bcc phases are a single continuous phase. The Hugoniot is interpreted as consisting of a metastable α (hcp) phase branch, an ω phase branch, and a β (bcc) phase branch. There are significant kinetic effects on the α–ω transition, so that, on the timescale of shock wave experiments, it is observed well above the equilibrium transition pressure. This parallels closely the behaviour of Ti. The presence of the second ω–β transition in Zr contrasts with Ti, which shows only one prominent phase transition on its Hugoniot. The Zr Hugoniot is estimated to intersect the ω–β phase boundary at P = 24 GPa and T = 585 K. It is expected that the ω–β transition will lead to shock splitting for pressures between 24 and 31 GPa.