  We study the thermally activated, slow conversion of the hysteretically
retained $\omega$ phase into stable $\alpha$ phase in recovered samples of
shocked zirconium. The $\omega$-phase decays in time following an algebraic
law, unlike the predictions of the nucleation-growth framework for first order
transitions, and residual volume fractions of phases and dislocation densities
are related by a power law. We propose an explanation for the annealing
mechanism through coupled dynamics of dislocations and phase change. We find
that the long-time behavior is controlled by the interplay of dislocations,
shear fluctuations, and remnant volume fractions of phases, which lead to an
algebraic decay in time. For late time, thermally activated quantities such as
the dislocation mobility and nucleation rate set the timescale and control the
algebraic behavior, respectively. At high enough temperatures this behavior is
effectively indistinguishable from standard Avrami kinetics.
