Traitement en champ moyen et par méthode de Monte-Carlo de la diffusion dans les composés d'adsorption et d'intercalation

Abstract

We will focus in this work on some simple lattice gas models and we will show how the mean field kinetic equations an Monte-Carlo calculations allow to make contact between the microscopie lattice model and macroscopie physics. Indeed, mean field kinetic equations are a valuable tool to study the dynamics of lattice gas model. They can be derived as an approximation to the complete master equation of the system. The advantage of this approach is that one can obtain quite simple analytical expressions, for interesting quantities which are usually introduced phenomenologically. We review several methods to obtain such equations. For order-disorder transitions, studied in the framework of repulsive lattice gas, we build, in the case of square and tringular lattices, a set of coupled equations on for the mean concentration, a second for occupation differences between the two or three sublattices issued from the symmetry breaking due to ordering. The study is done especially in the intercalation compounds with triangular structure such as seen as repulsive particules jumping on a fixed host lattice. Taking into account the division of governing the dynamics of each sublattice. Finnaly, the lattice models may be similated by Monte Carlo method. The advantage of this approach is that all correlations in space and time are preserved, and that fluctuations are automatically incorporated; however, for the same reasons, an analytical treatment is very difficult and approximations are very necessaries, like mean field approach.