Modeling the α / ω thermal stability in shocked Zr: A coupling between dislocation removal and phase transformation

Under high pressure, Zr undergoes a transformation from its ambient equilibrium hexagonal close packed α phase to a simple hexagonal ω phase. Subsequent unloading to ambient conditions does not see a full reversal to the α phase, but rather a retainment of significant ω. Previously, the thermal stability of the ω 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 [25]. The phase volume fractions were tracked quantitatively and the dislocation densities were tracked semi-quantitatively. Trends included a rapid initial (transient) transformation rate from ω → α followed by a plateau to a new metastable state with lesser retained ω (asymptotic). A significant reduction in dislocation densities in the ω phase was observed prior to initiation of an earnest reverse transformation, leading to the hypothesis that the ω → α transformation from is being hindered by defects in the ω phase. As a continuation of this work, we present a temperature dependent model that couples the removal of dislocations in the ω 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 ω phase occurs as a sum of glide and climb controlled processes, both of which dictate the transient and asymptotic behavior of the annealing process respectively.