The Rate Theory and Mean Field Approximation

The RDT is frequently but inappropriately called ‘the rate theory.’ This is due to the misunderstanding of the role of the transition state theory (TST) or (chemical reaction) RT (see Laidler and King38 and Hanggi et at39 for reviews) in the RDT. The TST is a seminal scientific contribution of the twentieth cen­tury. It provides recipes for calculating reaction rates between individual species of the types which are ubiquitous in chemistry and physics. It made major contributions to the fields of chemical kinetics, diffu­sion in solids, homogeneous nucleation, and electri­cal transport, to name a few. TST provides a simple way of formulating reaction rates and gives a unique insight into how processes occur. It has survived considerable criticisms and after almost 75 years has not been replaced by any general treatment compa­rable in simplicity and accuracy. The RDT uses TST as a tool for describing reactions involving radiation — produced defects, but cannot be reduced to it. This is true for both the mean-field models discussed here, and the kinetic Monte Carlo (kMC) models that are also used to simulate radiation effects (see Chapter 1.14, Kinetic Monte Carlo Simulations of Irradia­tion Effects).

The use of the name RT also created an incorrect identification of the RDT with the models that emerged in the very beginning, which assumed the production of only FPs and 3D migrating PDs to be the only mobile species, that is, FP3DM. It failed to appreciate the importance of numerous contradicting experimental data and, hence, to produce significant contribution to the understanding of neutron irra­diation phenomena (see Barashev and Golubov35 and Section 1.13.6). A common perception that the RDT in general is identical to the FP3DM has devel­oped over the years. So, the powerful method was rejected because of the name of the futile model. This caused serious damage to the development of RDT during the last 15 years or so. Many research proposals that included it as an essential part, were rejected, while simulations, for example, by the kMC etc. were aimed at substituting the RDT. The simula­tions can, of course, be useful in obtaining information on processes on relatively small time and length scales but cannot replace the RDT in the large — scale predictions. The RDT and any of its future developments will necessarily use TST.

An important approximation used in the theory is the MFA. The idea is to replace all interactions in a

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Interaction of energetic particles with a solid target is a complex process. A detailed description is beyond the scope of the present paper (Robinson41). However, the primary damage produced in collision events is the main input to the RDT and is briefly introduced here. Energetic particles create primary knock-on (or recoil) atoms (PKAs) by scattering either incident radiation (electrons, neutrons, protons) or accelerated ions. Part of the kinetic energy, EPKa, transmitted to the PKA is lost to the electron excitation. The remaining energy, called the damage energy, Td, is dissipated in elastic collisions between atoms. If the Td exceeds a threshold displacement energy, Ed, for the target material, vacancy-interstitial (or Frenkel) pairs are produced. The total number of displaced atoms is proportional to the damage energy in a model proposed by Norgett et at42 and known as the NRT standard

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