First-principles study of Zr phase stability and its influence on the equation of state

We conducted static and dynamic first-principles calculations to investigate the energetic and mechanical phase stability of the α, ω, and β phases of pure zirconium. The static calculations provided insights into the total energy dependence of the α and ω phases on their c/a ratio, transformation pressures from α to ω and from ω to β, single-crystal elastic constants and polycrystalline elastic properties. The energetic stability of each phase was evaluated by comparing their total energies, while transformation pressures were derived from the Gibbs free energies of the phases. Mechanical stability and ductility across different pressure ranges were assessed using elastic properties. We also evaluated the shock Hugoniots for all phases using the Murnaghan equation of state (EOS), fitted to E(V) data obtained from static calculations as their cold curves. Deviations in the theoretical shock Hugoniots of the β phase compared to published experimental data were observed. To resolve this, we used quantum molecular dynamics (QMD) simulations to estimate the E(V) data for the β phase. Fitting a Murnaghan EOS to this QMD-generated data and using it as the cold curve resulted in shock Hugoniots that perfectly matched experimental results. This improvement can be attributed to QMD’s ability to explore a wide range of atomic configurations, unlike static calculations that rely on fixed atomic arrangements, thereby producing more accurate E(V) data for mechanically unstable phases.