A Model for Phase Transitions Under Dynamic Compression

Abstract

An approach is described for simulating phase transitions among an arbitrary number of phases under dynamic compression. The time evolution of the phase fractions λi is governed by the master equation, which naturally incorporates the constraints ∑ iλi= 1 and 0 ≤ λi≤ 1. The rates are taken to be strongly nonlinear functions of the thermodynamic driving forces. The implementation of the method is described, and illustrative applications to phase transitions in Zr are shown. The relation of the model to irreversible thermodynamics is discussed. A modification for the case where domain growth limits the transformation rate is described. This variant gives sigmoidal transformation-time curves, with the second phase fraction proportional to t3 at early time.