Soft model of solidification with the order–disorder states competition

Abstract

A theoretical model is proposed that describes the kinetics of the formation and evolution of competing phases, one of which is a disordered system of topologically stable excitations (vortices) and the second one is an ordered (crystalline) phase. This model is intended to be the simplest model which can demonstrate such important characteristics of solidification process as a sensitivity to the cooling speed, natural appearance of the relaxation times of kinetic phase transformations, and particular features of the rapidly solidified systems. The model was studied numerically showing the crucial properties relevant to the obtained in the experiments on the amorphization in metals. In the present work, we derive a general form of the system's Hamiltonian and stochastic dynamical equations to describe the rapid solidification and a competing formation of amorphous and crystalline phases. The numerical study of the formation of both phases shows the competition of inherited phases during the simultaneous growth from nuclei. The cooling speed has a significant impact on the regimes of the phase formation. We find that solidification during fast cooling leads to the preferred selection of the disordered phase, then the subsequent evolution leads to the aging and to continuous transition to a solid ordered phase. Also, it is shown that further cooling leads to the spinodal decomposition, and the mobility of phases plays a significant role in the dynamics of the defects migration.