Modeling the Thermal Stability of the $\alpha/\omega$ Microstructure in Shocked Zr: Coupling between defect state and phase transformation

Under high pressure, Zr undergoes a transformation from its ambient equilibrium hexagonal close packed $\alpha$ phase to a simple hexagonal $\omega$ phase. Subsequent unloading to ambient conditions does not see a full reversal to the $\alpha$ phase, but rather a retainment of significant $\omega$. Previously, the thermal stability of the $\omega$ phase was investigated via in-situ synchrotron X-ray diffraction analysis of the isothermal annealing of Zr samples shocked to 8 and 10.5 GPa at temperatures 443, 463, 483, and 503 K. The phase volume fractions were tracked quantitatively and the dislocation densities were tracked semi-quantitatively. Trends included a rapid initial (transient) transformation rate from $\omega\to\alpha$ followed by a plateau to a new metastable state with lesser retained $\omega$ (asymptotic). A significant reduction in dislocation densities in the $\omega$ phase was observed prior to initiation of an earnest reverse transformation, leading to the hypothesis that the $\omega\to\alpha$ transformation from is being hindered by defects in the $\omega$ phase. As a continuation of this work, we present a temperature dependent model that couples the removal of dislocations in the $\omega$ phase and the reverse transformation via a barrier energy that is associated with the free energy of remaining dislocations. The reduction of dislocations in the $\omega$ phase occur as a sum of glide and climb controlled processes, both of which dictate the transient and asymptotic behavior of the annealing process respectively.