Monte Carlo simulations of pattern formation at solid/solid interfaces
Abstract
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 Boltzmann-ansatz. 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 εAA, εAB and εBB. 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 TC (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 ΔεC= εAA-εBB is observed, above which the phase boundary becomes morphologically unstable if the more mobile phase is the growing one. In this case ΔεC is dependent on temperature, the boundary conditions and the external driving force. With increasing Δε 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 TC (complete miscibility of AX and BX) where we find instabilities of diffusion fronts.