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.

Ab Initio Study of Advanced Metallic Nuclear Fuels for Fast Breeder Reactors

“…According to the FPLMTO calculations, the   and    phase transitions in Zr take place at 33 and 268 kbar, respectively, which are in a good accord with experimental measurements [9,42]. Within the EMTO formalism [28], the total-energy, E tot , can be expressed as the sum of two contributions: E tot = E b + E M , where E b consists of all "local" (band-structure) contributions, E b = E s + E intra + E xc , such as the kinetic energy of non-interacting electron gas, E s , the intra-cell electrostatic energy, E intra , which is due to the electron-electron and electron-ion Coulomb interactions, and the exchange and correlation energy, E xc .…”

“…It is well established that under compression zirconium metal undergoes the following phase transformations: -Zr (hcp)  -Zr (C32)  -Zr (bcc) [9,42]. According to the FPLMTO calculations, the   and    phase transitions in Zr take place at 33 and 268 kbar, respectively, which are in a good accord with experimental measurements [9,42].…”

Analysis and modeling of laser ramps and shocks in tiitatium and zirconium with phase transitions

“…1). The Zr EOS also included 4 phases (α, β , ω, and liquid), then 4 binary mixtures and a single triple point, and is consistent with the 3-phase EOS by Greeff [7] (Fig. 2).…”

The shock and spall response of three industrially important hexagonal close-packed metals: magnesium, titanium and zirconium

“…It is known that Zr moves from the HCP α phase through a hexagonal with a three atom basis/hex-3 ω phase to the BCC β phase at elevated pressures [85][86][87]. Greeff [86] established a high strain-rate phase diagram and Hugoniot equation of state which clearly illustrated the transition through these three phases. In particular, under shock loading conditions, zirconium has been observed to undergo an α-ω phase transformation across a range of pressures from 2.3 to 8.5 GPa.…”