Numerical modeling of the phase transition kinetics for the sub-microsecond solidification of water under dynamic compression

Several landmark experimental studies on the solidification of liquid water to the high-pressure ice VII phase under multiple-shock and ramp dynamic compression have been carried out over the past two decades, yet modeling this rapid phase transition has proven challenging. The application of classical nucleation theory (CNT)-based approaches to rapid phase transition kinetics occurring under extreme temperatures and pressures presents a variety of new opportunities for predictive computational modeling. This work attempts to model the liquid water-ice VII phase transformation using a numerical discretization scheme to solve the Zel’dovich-Frenkel partial differential equation, an underlying CNT-based kinetic equation describing the statistical time-dependent behavior of solid cluster formation. One major result of this research is that the Zel’dovich-Frenkel equation is able to accurately determine---without the need for empirical scaling parameters---the duration of the induction time prior to the onset of the phase transformation.