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 it s melt is developed. The sharp-interface limit of this model reduces to the continuum equations describing the Asaro-Tiller-Grinfeld instability. In a ddition, it allows the derivation of generalizations of these equations. Th e dynamics of extended systems are investigated via the phase-field approac h which contains an inherent lower length cutoff, thus avoiding cusp singul arities. General initial conditions lead to coarsening. For periodic states , this arises via a series of approximate period doublings, the beginning o f which can be demonstrated analytically. (C) 2001 Elsevier Science B.V, Al l rights reserved.