Compositional patterning in systems driven by competing dynamics of different length scale

We study an alloy system where short-ranged, thermally driven diffusion com petes with externally imposed, finite-ranged, athermal atomic exchanges, as is the case in alloys under irradiation. Using a Cahn-Hilliard-type approa ch, we show that when the range of these exchanges exceeds a critical value labyrinthine concentration patterns at a mesoscopic scale can be stabilize d. Furthermore, these steady-state patterns appear only for a window of the frequency of forced exchanges. Our results suggest that ion beams may prov ide a novel route to stabilize and tune the size of nanoscale structural fe atures in materials.