Self-organization of nanometer periodic structures of clusters in solids

The formation of non-uniform spatial structures in irradiated solids (metals, semiconductors) is investigated, when the subsystem of nonequilibrium lattice defects (vacancies and interstitials) forms bonded states, nanoclusters. A set of kinetic equations is formulated which incorporates, (i) generation of point defects by radiation, (ii) their diffusion and recombination, (iii) mutual pairwise elastic interaction among defects, (iv) formation and growth of the nanoclusters of point defects, and (v) losses of the nanoclusters; due to removal from the nucleation Zone by diffusion. Linear stability analysis is used to show that, if the temperature (T) of medium is below a critical value (T-cr), due to the elastic interaction the homogeneous distribution of point defects and their clusters becomes unstable, and a periodic structure of a nanometer scale arises. The criterion of self-organization of the clusters and the dependence of a Super-lattice period on temperature of medium are determined analytically. The critical temperature for self-organization of periodic structures is governed by the dilatation volume of defects, by the potential energy of elastic interaction, and the concentration of defects. Estimations showed that the period of super-lattices may change in the range of (20-80) nm. Obtained results agree with the experimental data.