Microscopic Studies of Clusters in Phase Transitions
Final rept. 1 Oct 1987-30 Sep 1990,
BOSTON UNIV MA
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The fractal properties of percolation clusters in the long range bond or meanfield limit were investigated via Monte Carlo simulations and by the use of scaling arguments. These investigations were undertaken because it is these meanfield structures that initiate nucleation near the spinodal. The key results were that the fractal dimension of such clusters is four independent of the dimension of the imbedding space and different from the Hausdorf dimension and that the density of these clusters is significantly less than the value predicted by the scaling of the order parameter as would be expected in systems that have hyperscaling. The nucleation process in crystallization is very poorly understood. It is known that there are spinodals in supercooled liquids in systems with long range interactions but the effect of such spinodals on the nucleation process has not been elucidated. We performed large scale molecular dynamics simulations to investigate this phenomenon. Unfortunately the precise definition of clusters available for the work on spinodal nucleation in Ising models is not as yet available for fluids so we developed phenomenological cluster definitions. Two conclusions emerged from this work.