Defects accumulation

Consider now the fluctuations of the order parameter in the system possessing the chemical reaction this problem could be perfectly illustrated by computer simulations on lattices. We start with the bimolecular A + B -y 0 reaction discussed above, and first of all froze particle diffusion. Let the recombination event happen instantly when a pair AB of dissimilar particles occupies the nearest lattice sites (assume lattice to be squared). Immobile particles enter into reaction as a result of their creation with the equal probabilities in empty lattice sites from time to time a newly created particle A(B) finds itself nearby pre-created B(A) and they recombine. (Since this recombination event is instant, the creation rate is of no importance.) This model describes, in particular, Frenkel defect accumulation in solids under... 

During their diffusive walks, H centres can either approach their own F centres to within the distance r ro and recombine with them in the course of the so-called geminate (monomolecular) reaction or leave them behind in their random walks. Some of these H centres recombine with foreign F centres, thus participating in bimolecular reactions. The rest of the H centres become trapped by impurities, dislocations, or aggregate in the form of immobile dimer H2 centres thus going out of the secondary reactions as shown in Fig. 3.4. In other words, the survival probability of the geminate pairs (F centres) directly defines the defect accumulation efficiency and thus, a material s sensitivity to radiation. 

In the last decades, both experimental data [2, 51] and theoretical studies [52-56] revealed the effect of the statistical similar defect aggregation under defect accumulation (permanent particle source). It means that the initial random mixture of defects of two kinds A and B during bimolecular reaction is... 

As it was said in Section 3.1, the survival probability of the geminate pairs oj 1 [ oo) directly defines the efficiency of the Frenkel defect accumulation in solids. Let us assume that the concentration of radiation-created defects is n. Then after a transient period during which mobile interstitials recombine with their geminate partners or leave them thus surviving, we have nacc of stable defects obeying the relation nacc = rjn, where r = cu(oo) is accumulation efficiency, which could be identified with the survival probability of a single mobile interstitial (provided that different geminate pairs do not mix). 

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 + B — 0, if the relative distance between dissimilar particles is less than some critical distance 7 0. 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 (d= 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). 

To get the reference point for many-particle effects in defect accumulation, the saturation concentration, n(t —> oo) could be taken from equation (7.1.58) with Uo < 1, i.e., in the linear approximation neglecting many-particle effects... 

Results of computer simulations of defect accumulation in a two-dimensional crystal of length L. The area of the recombination zone is lx l, the number of accumulated defects is N [113]... 

Equation (3) is the most widely used in analyzing experimental curves, since its form is intuitively clear the rate of the defect accumulation is determined by the fraction of free volume of the crystal not occupied by previously created defects, without taking account of the overlap of the annihilation volumes of similar defects. Evidently it is applicable only in the initial stage of accumulation kinetics at relatively low concentrations of defects, nvo superposition approximation corresponds to the first two terms of expansion (2) in powers of nvo-... 

The kinetic equations for diffusion-controlled defect accumulation are presented in the rest of the Table 7.6. Equations (7)—(11) are approximations of the kinetics of accumulation that are not substantiated theoretically in any way but give curves with saturation, which qualitatively resemble the form of equations (1) to (5). 

We note in conclusion that taking account of correlation of defects in genetic pairs, formation of pairs of new defects (e.g., owing to the tunnelling mechanism of recombination), and of radiation-induced disclocation loops, etc., substantially complicate the development of rigorous and universal theory of the kinetics of defect accumulation. The temperature dependence of the efficiency of defect accumulation contains substantial information on the correlation within genetic pairs and on the nature of their interaction [119, 124] and is also of great theoretical importance. 

The kinetics of defect accumulation requires further theoretical studies at temperatures at which they become mobile. The creation under the action of radiation of an ordered structure from the accumulation of radiation defects is an effect akin to those discussed in the theory of self-organization of structures - synergetics [14]. 

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