Effets des transitions ordre-désordre sur la dynamique des systèmes inhomogènes

Abstract

We examine thoroughly the dynamics of diffusion process of mobile particles with repulsive interactions in inhomogeneous systems, especially in the intercalation compounds with triangular structure such as LixTiS₂. The study is done by using the lattice gas model in the mean field approach. Taking into account the division of the traingular lattice into three interpentrating sublattices, we derive three master equations govering the dynamics of each sublattice. In order to quantify the order in the system and to characterize the order-disorder transition we consider order parameters which represent the difference between the occupation of the different sublattices. The representation of the orde parameter as a function of te average concentration shows two maxima at critical concentrations which go up with an increase of the interaction energy. We have also been interested by the evolvement of the ordered structure within the system, especially by its universal bahaviour. Hence, we investigated the spatio-temporel dependency of the ordered region as well as the evolution of the interface between ordered and disordered regions. So in a first part we have analysed the effect of the appearance of the ordered region on the structure of the diffusion front (lengh σf, withth Nf) and its dynamics. At last, we have brought forward the diffusion coefficent behaviour which shows fine structures at the critical point that correspond to the transition from one phase to another.