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

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