Phase transitions in high-purity zirconium under dynamic compression

We present results from ramp compression experiments on high-purity Zr that show the ?? ??, ?? ??, as well as reverse ?? ?? phase transitions. Simulations with a multiphase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic ?? ?? transition occurs ???9 GPa above the equilibrium phase boundary, the ?? ?? transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ??-?? line at P = 29.2 GPa, and T = 490 K. The thermodynamic path in the interior of the sample lies ???100 K above the isentrope at the point of the ?? ?? transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the nonequilibrium ?? ?? transition. The inferred rate of the ?? ?? 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 sji has the same effect on the nucleation rate as a pressure increase ??P = c???ijsji/(???V/V ), where c is a geometric constant ???1 and ???ij are the transformation shear strains. The small fractional volume change ???V/V ??? 0.1 at the ?? ?? transition amplifies the effect of shear stress, and we estimate that for this case ??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.