A model of independently growing crystallites for describing the kinetics of formation of pyrographite

A kinetic model of the formation and growth of two-dimensional pyrographite crystallites during pyrotytic decomposition of carbon-containing gas on a heated surface is formulated. It is based on the assumption that the nuclei of crystallites form at the boundaries between crystallites of the substrate, and the boundaries of the growing crystallites contact one another only at the moment of completion of theformation of the layer. An integral equation was derived for the size-distribution junction of the crystallites, the moments of which are the number of growing crystallites and their total perimeter and area per unit surface. The asymptotic solution obtained with the use of the small parameter of the problem (Tesner number) made it possible to calculate the filling time of the layer, average size, and perimeter of the boundaries of the joined crystallites. It is shown that stabilization of the indicated parameters occurs as a result oflayerwise filling of the surface with crystallites. The relations between the stabilized values of the parameters and the qualitative character of their dependence on the conditions of conducting pyrotysis mainly correspond to the simple kinetic model proposed earlier by Tesner and to the experimental results obtained by him.