A microscopic model for solidification

– 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 functionalsà la Landau. The system is composed by 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. A remarkable feature, observed in solidification processes, is the occurrence of different morphologies of the solid-liquid boundary, namely flat, cellular or dendritic, according to the initial undercooling, which acts as control parameter for the growth process. The theoretical models employed so far to study this kind of non equilibrium phase transformations represent at different degrees a coarse grained, mesoscopic picture of the underlying microscopic processes. They miss consequently an important point, i.e. the stochastic character of the thermal fluctuations and disregard the nucleation of the growing phase in the melt. It has also been argued [1] that small a thermal noise can account for the enhanced sidebranch activity during dendritic growth. The state of affairs is as follows: in the free boundary model [2] [3] the solidification process is formulated in terms of a sharp moving boundary, acting as a source for the diffusion field, while the thermodynamic information enters the model only via the boundary conditions; in the phase field model [4], instead, employing a local order parameter formulation, whose evolution