A microscopic model for solidification

¹ Dipartimento di Matematica e Fisica, Università di Camerino and Istituto Nazionale di Fisica della Materia, Unità di Camerino Via Madonna delle Carceri, I-62032, Camerino, Italy
² Dipartimento di Fisica, Università La Sapienza - Roma, Italy

Received: 2 February 1999
Accepted: 25 May 1999

Abstract

We present a novel picture of a non-isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more apparent than in existing approaches based on coarse-grained free-energy functionals à la Landau. The system is composed of a lattice of Potts spins, which change their state according to the stochastic dynamics proposed some time ago by Creutz. Such a method is extended to include the presence of latent heat and thermal conduction. Not only the model agrees with previous continuum treatments, but it allows to introduce in a consistent fashion the microscopic stochastic fluctuations. These play an important role in nucleating the growing solid phase in the melt. The approach is also very satisfactory from the quantitative point of view since the relevant growth regimes are fully characterized in terms of scaling exponents.