Kinetics of thin film coalescence due to crystallite surface migration

Abstract

The kinetics of mobility coalescence in a thin discontinuous film are investigated provided that the deposition is completed and the process proceeds in a pure form. The analysis is made on the basis of the mathematical formalism developed by Smoluchowski for description of the colloid rapid coagulation. The two limiting cases of diffusion and merging controlled coalescence are considered under the assumption that the crystallite surface diffusion coefficient and the merging rate constant are power functions of the crystallite radius r of the type r s ( s = const.). It is shown that after elapsing of a sufficiently long time from the onset of the process the crystallite size distribution function Z takes a universal, self-preserving shape and an approximate analytic expression for Z is found. Formulae are also obtained for the time dependences of the dispersion of Z, the mean radius of the crystallites, their total number, their total exposed area and the total substrate area covered by them. It turns out that all these quantities are simple power functions of time t of the type t w , the value of w being dependent only on s. Finally, the theoretical results are compared with existing experimental data.