Mechanisms of microstructural pattern formation in irradiated solids

Metals and alloys under irradiation with energetic particles such as electrons, neutrons, or ions are open dissipative systems far from thermodynamic equilibrium. The continuous production, diffusion, and annihilation of point defects result in microstructural changes in the irradiated materials. Under proper conditions, self organization of the microstructure is experimentally observed. Examples are the void lattice, periodic concentration fluctuations of dislocation loops, and irradiation induced homogeneous precipitation in undersaturated alloys. The theoretical description rests on a coupling of the point defects with the microstructure by nonlinear reactions. In general, a complicated reaction scheme has to be investigated. In practice, however, a simplified reaction model is applicable from which the minimum requirements for self organization can be derived by using a linear stability analysis. In a special case of the reaction scheme it is possible to evaluate exact stationary solutions of the appropriate diffusion reaction equations. They show the stabilizing effect of the annihilation of the point defects by recombination and at neutral sinks against pattern formation. A stability diagram for irradiation induced periodic structures is developed that gives the temperature and displacement range where self organization of loop arrangement is possible, and that is in good accordance with the experimental result