Pattern formation in cation-conducting crystalline solids (A,B)X due to instabilities of phase boundaries is investigated by computer simulations using an appropriate two-dimensional, two-phase model system AX\BX, in which a directed vacancy flux causes the growth of one of the phases. Below the critical temperature, T-C, the phase boundary roughens but remains morphologically stable unless the more mobile phase is the growing phase. Then a critical parameter Delta epsilon(C) = epsilon(AA) = epsilon(BB) (epsilon(ij) : repulsive interaction energies) exists above which the phase boundary becomes morphologically unstable.