Monte Carlo simulations of pattern formation at solid/solid interfaces

Pattern-formation processes at solid/solid interfaces are investigated by Monte Carlo simulations using an appropriate two-dimensional model system AX/BX with an initially planar, coherent interface. The motion of cations A and B occurs via vacancies in the regular cation sublattice, and the jump frequencies of both A and B are described by a simple Boltzmannansatz. Therefore, the jump frequency is a function of temperature and the nearest neighbourhood of each cation, whose influence is determined by repulsive pairwise interaction energies epsilon(AA), epsilon(AB) and epsilon(BB). Using appropriate boundary conditions, a directed vacancy flux and, therefore, the growth of one or both phases is caused. In this way an external force, e.g. an external electric field, in a real experiment is simulated. Below a critical temperature T-C (limited miscibility between AX and BX), the phase boundary roughens but remains morphologically stable if the less mobile phase is the growing phase. In comparison, a critical parameter Delta epsilon(C) = epsilon(AA) - epsilon(BB) is observed, above which the phase boundary becomes morphologically unstable if the more mobile phase is the growing one. In this case Delta epsilon(C) is dependent on temperature, the boundary conditions and the external driving force. With increasing Delta epsilon a transition from finger-like to branched structures is observed. In exceptional cases the latter can be described as fractals. Similar results are obtained at temperatures above T-C (complete miscibility of AX and EX) where we find instabilities of diffusion fronts.