Cascading crystallographic transitions α → ω → β → β’→ β" and melting curve of elemental zirconium

Abstract

Precise fitting of the experimental data analyzed separately for each identified crystallographic phase (α, ω, β, β′and β") yield different bulk moduli Bo and Bo’ and different zero pressure volumes (Vo) than those claimed in the literature. Special attention is given to the bcc phases indicating cascading transitions β → β’→ β” associated with volume collapse. The present analysis reveals the existence of a bcc-β′ phase which is reported here for the first time. It is shown that the first order volume collapse at ~58 GPa (β → β′) is followed by a moderate transition to the bcc-β” phase. The β′ phase is stable up to 110 GPa. Above 110 GPa the bcc-β” is dominant and stable up to ~220 GPa. The derived bcc-β" bulk moduli are confirmed by the Lindemann-Gilvarry criterion as Bo and Bo’ simultaneously fit both the P–V EOS and the P-T melting data points (combined approach). The calculated melting curve of elemental Zr, taking into account the thermal pressure Poth shift and the elevated melting Tmo’ at Poth, yield very good fit of the experimental melting data permitting a safe extrapolation to high pressures and temperatures. In addition, the combined approach lead to direct determination of the Grüneisen parameter γo, needed for applying the approximated Lindemann-Gilvarry melting formula.It is shown the DFT (QMD) simulations and the non-hydrostatic thermodynamic formalism for solid mediums mismatch the experimental melting data.