Modification of Bragg-Williams approximation applied in Jackson’s model of crystal growth

Abstract

Results of Monte Carlo simulations for single-layer solid-fluid interface were compared with Bragg-Williams approximation, which describes the number of bonds between solid and fluid cells in Jackson's crystal growth model. The comparison shows that Bragg-Williams approximation produces much higher values than those resulting from simulations. The use of better approximations based on the results of the simulation does not lead directly to improvement of predictions given by Jackson’s model, but rather reveals further problems. In particular, the estimation of entropy seems to be also very overvalued. Monte Carlo simulations were used also to investigate the number of stable states of a single boundary layer for various crystal growth conditions. The results obtained differ significantly from those resulting from the analysis of free energy minima in Jackson’s model, but are in good agreement with the results of multi-layer simulations.