The kinetics of defect accumulation under irradiation

Great fleas have lesser fleas upon their backs to bite them. And lesser fleas have lesser still. And so ad infinitum. 

In this Chapter the kinetics of the Frenkel defect accumulation under permanent particle source (irradiation) is discussed with special emphasis on many-particle effects. Defect accumulation is restricted by their diffusion and annihilation, A -f B —J 0, if the relative distance between dissimilar particles is less than some critical distance ro- The formalism of many-point particle densities based on Kirkwood s superposition approximation, other analytical approaches and finally, computer simulations are analyzed in detail. Pattern formation and particle self-organization, as well as the dependence of the saturation concentration after a prolonged irradiation upon spatial dimension (J = 1,2, 3), defect mobility and the initial correlation within geminate pairs are analyzed. Special attention is paid to the conditions of aggregate formation caused by the elastic attraction of particles (defects). 

The irradiation of all kinds of solids produces pairs of the point Frenkel defects hereafter denoted just AB-vacancies, v, and interstitial atoms, i, which usually are well correlated spatially [1-10]. In many ionic crystals these Frenkel defects are the so-called F and H centres discussed in Chapter 3. The function of the initial distribution of complementary defects - v, i pairs (called also geminate) over relative distances depends strongly not only on the particular mechanism of defect creation but also on the particular irradiation kind (e.g.. X-rays or photons) [9]. Under creation of v,i pair an interstitial 

In the last several decades, both experimental data and theoretical studies [5, 9, 13-15] have revealed the effect of similar defect aggregation in the course of the bimolecular A-l-B — 0 reaction under permanent particle source (irradiation) - the phenomenon similar to that discussed in previous Chapters for the diffusion-controlled concentration decay. Radiation-induced aggregation of similar defects being observed experimentally at 4 K after prolonged X-ray irradiation [16] via both anomalously high for random distribution concentration of dimer F2 centres (two nearest F centres) and directly in the electronic microscope [17], permits to accumulate defect concentrations whose saturation value exceed by several times that of the Poisson distribution. 

At low temperatures dissimilar-defect segregation arises under permanent particle source due to local fluctuations of particle (defect) densities. Radiation-induced production by a change of two or more similar defects (say. A) nearby creates a germ of their aggregate which is more stable and has a greater chance to survive rather than two isolated defects A since the probability that two or more defects B will be created statistically in the same 

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