Elastic attraction

The steady-state for diffusion-controlled recombination without interaction is given by equation (4.2.15), whereas its analog for the isotropic elastic attraction (g > 0) without tunnelling reads [59, 60]... 

Mobile H centres in alkali halides are known to aggregate in a form of complex hole centres [64] this process is stimulated by elastic attraction. It was estimated [65, 66] that for such similar defect attraction the elastic constant A is larger for a factor of 5 than that for dissimilar defects - F, H centres. Therefore, elastic interaction has to play a considerable role in the colloid formation in alkali halides observed at high temperatures [67]. In this Section following [68] we study effects of the elastic interaction in the kinetics of concentration decay whereas in Chapter 7 the concentration accumulation kinetics under permanent particle source will be discussed in detail. 

In conclusion of Section 6.3 we wish to stress that the elastic attraction of similar defects (reactants) leads to their dynamic aggregation which, in turn, reduces considerably the reaction rate. This effect is mostly pronounced for the intermediate times (dependent on the initial defect concentration and spatial distribution), when the effective radius of the interaction re = - JTX exceeds greatly the diffusion length = y/Dt. In this case the reaction kinetics is governed by the elastic interaction of both similar and dissimilar particles. A comparative study shows that for equal elastic constants A the elastic attraction of similar particles has greater impact on the kinetics than interaction of dissimilar particles. 

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). 

The formalism presented in Section 7.1 is generalized here by incorporating the elastic attraction between similar particles (defects) which causes... 

More information about these approaches and their advantages readers could find in [14, 15, 64, 65] in this Section 7.2 we focus on the further improvement of the microscopic approach to the defect aggregation via taking into account elastic attraction between point defects. 

The critical dose rate pc necessary for initiating the aggregation process is the smaller, the lower the temperature, the stronger elastic attraction of similar particles and the slower the diffusion (greater the activation energy for hopping). This conclusion is in a complete qualitive agreement with the results obtained recently in terms of a quite different mesoscopic approach [63-65],... 

Lastly, a decisive role of the elastic attraction between F centres in their agregation is seen in Fig. 7.14. For small attraction energy av (curve 1)... 

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