Statistical fluctuations in two-dimensional nucleation and growth processes

Abstract

A Monte Carlo numerical method was used to study the stochastic fluctuations in the rate of coverage of an electrode, by a layer which forms via a nucleation and growth mechanism. Numbers of nuclei from 10 to approximately 200 were examined. The fluctuations were found to be proportional to the inverse square root of the number of growth centres. The constants of proportionality were 0.38 and 0.70 for the cases of instantaneous and progressive nucleation respectively. The extra degree of freedom inherent in the time dependence of the number of nuclei in the progressive case led to a substantial increase in the level of the stochastic fluctuations. The magnitudes of the fluctuations are compared with other work reported in the literature. It was also shown that the electrode edge hinders layer growth and its influence also is proportional to the inverse square root of the number of growth centres. The constants of proportionality were 0.33 and 0.49 for instantaneous and progressive nucleation respectively. Again the case of progressive nucleation displayed the greater sensitivity to the effect.