Phase-field approach to crystal growth in the presence of strain

A phase-field model for the dynamics of a strained solid in contact with its melt is developed. The sharp-interface limit of this model reduces to the continuum equations describing the Asaro–Tiller–Grinfeld instability. In addition, it allows the derivation of generalizations of these equations. The dynamics of extended systems are investigated via the phase-field approach which contains an inherent lower length cutoff, thus avoiding cusp singularities. General initial conditions lead to coarsening. For periodic states, this arises via a series of approximate period doublings, the beginning of which can be demonstrated analytically.