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The kinetics of F-center aggregation under irradiation: many-particle effects in ionic solids

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The accumulation kinetics of primary Frenkel defects created in solids under permanent irradiation is calculated using the microscopic formalism of many-particle densities. It is based on the Kirkwood superposition approximation for three-particle densities as described in our previous paper p. N. Kuzovkov and E. A. Kotomin, Physica Scripta 47, 585 (1993)l. This formalism is generalized in this paper by incorporating the elastic attraction between similar defects (called in ionic solids F-centers) which causes their efficient aggregation. It is shown that the aggregation process starts only if the dose rate and elastic attraction energy exceed certain critical values; it also happpens in the limited temperature interval, in agreement with experimental data known for NaCl crystals. Results obtained are compared with those of the mesoscopic approach. 1. Introduction The irradiation of solids of any nature (metals, semiconductors, insulators) with high-energy particles or electrons produces Frenkel defects-pairs of interstitial atoms and vacancies [ 1-71. In alkali halides, MeX, primary Frenklel defects - F and H centers - are neutral defects with respect to the crystalline lattice; they are anion vacancy with trapped electron and X; quasimolecule formed by Xo atom with a regular X- anion, respectively. Both in metals and ionic solids vacancies are slowly mobile, whereas interstitials start to migrate at much lower temperature, typically about 30 K in alkali halides [3]. Therefore, even at moderate temperatures, the process of radiation-induced defect accumulation is diffusion-controlled. Numerous studies - both theoretical and experimental - were devoted in particular to the kinetics of F-center accumulation in alkali halides under irradiation [8-211. Of special interest in recent years was the kinetics of defect aggregation in the form of colloids; in alkali halides irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles of several nm in size were observed [21]. Several theoretical formalisms were developed for describing this phenomenon, which could be classified into three general categories : (i) macroscopic theory [22-241, which is based on the rate equations for macroscopic defect concentrations; (ii) mesoscopic theory [25-271 operating with space-dependent local concentrations of point defects, and lastly (iii) microscopic theory [28-301 based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of