Use of Cellular Automata for Modelling of the Carbon Nanolayer Growth on a Light Alloy Substrate

Abstract

Carbon deposition forming a nanolayer on a light alloy substrate is a physico-chemical process of the discrete type in all of its aspects. Thus, use of cellular automata, intrinsic discrete, as a mathematical tool for modelling, is fully justified. We adopted two-dimensional (i.e. surface), two-layer automation with Moore vicinity of a cell, for modelling of the carbon deposition process, starting from bonding to the light alloy substrate, leading through layer growth and finishing at the phase transition process, converting graphite into diamond form. To achieve this, we related the transition probabilities of the automaton with the Lennard-Jones potentials for carbon and metal atoms, as well as the physico-chemical conditions in the reaction environment gaseous hydrocarbons density and their particles energy distribution (Maxwell). Taking it into account allowed us to establish an automation time scale of about 1s per calculations run, which has resulted in a simulated layer thickness growth rate well matched with observed results. Using of the two-layer automation allowed us to make some survey into the mechanism of the graphite/diamond transition in the real environmental conditions we met. This demanded further thorough investigations to properly model the spatial structure of mutually interleaved areas of the graphite and diamond type carbon, giving not only a flat-surface but also a vertical structure. The overall surface morphology of the simulated nanolayer we have compared with those of AFM survey performed on real samples, observing relatively good matching in terms of statistical parameters of the surface.