Phase transitions in high-purity zirconium under dynamic compression

We present results from ramp compression experiments on high-purity Zr that show the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}, \ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$, as well as reverse $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\omega}$ phase transitions. Simulations with a multiphase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition occurs $\ensuremath{\sim}9\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ above the equilibrium phase boundary, the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$ transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\beta}$ line at $P=29.2\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, and $T=490\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The thermodynamic path in the interior of the sample lies $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ above the isentrope at the point of the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$ transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the nonequilibrium $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition. The inferred rate of the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress ${s}_{ji}$ has the same effect on the nucleation rate as a pressure increase $\ensuremath{\delta}P=c{\ensuremath{\epsilon}}_{ij}{s}_{ji}/(\mathrm{\ensuremath{\Delta}}V/V),$ where $c$ is a geometric constant $\ensuremath{\sim}1$ and ${\ensuremath{\epsilon}}_{ij}$ are the transformation shear strains. The small fractional volume change $\mathrm{\ensuremath{\Delta}}V/V\ensuremath{\approx}0.1$ at the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition amplifies the effect of shear stress, and we estimate that for this case $\ensuremath{\delta}P$ is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.