Phenomenological kinetics of Frenkel defect recombination and accumulation in ionic solids

Abstract

This review deals with the theoretical study of the kinetics of the A t €3 + 0 bimolecular reaction between point Frenkel defects in irradiated solids. Three different approaches are discussed: macroscopic, mesoscopic and microscopic, and their advantages and shortcomings are analysed. Special attention is paid to the formalism of many-point particle densities and its application in the study of the effects of defect-density fluctuations. The kinetics of all recombination regimes are considered in detail, including static reactions, correlated annealing, diffusion-and hoppingcontrolled reactions, and aggregation of immobile defects under the conditions of a permanent defect source (irradiation). Problems rarely discussed in the literature are emphasized: transient kinetics; effects of long-range hop lengths and of defect interaction; cooperative phenomena at high defect densities and for long reaction times; and accuracy of Kirkwood's superposition approximation. Theory is illustrated by relevant experimental data for ionic crystals.

Comment on: “Energetics and Kinetics of Thermal Ionization Models of MALDI” by Richard Knochenmuss. J. Am. Soc. Mass Spectrom. 25, 1521–1527 (2014)

“…In fact, "black sphere" model was developed to calculate the kinetics of Frenkel defect recombination and accumulation in ionic solids [19]. This model is not suitable for the calculation of ion-ion recombination in the gas plume.…”

Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals

“…where the diffusion-controlled reaction rate K is proportional to the mutual diffusion coefficient D [39] 4 K DR = π (4) and, thus, depends exponentially on the defect migration energy E a , D = D 0 exp(-E a /kT), whereas R is the recombination radius. In our case of F, H defects, E a is the migration energy of a more mobile defect (an H center).…”

Application of Bogolyubov’s theory of weakly nonideal Bose gases to theA+A,A+B,B+Breaction-diffusion system

“…(84) suggests that WBGA is somewhat equivalent to the additive expansion of correlation functions. It has been argued that such additive approximation is inferior to the Kirkwood superposition approximation [4,5]. This in turn explains why WBGA fails to describe the A+A reaction.…”

“…It is interesting to note that equation above is very close to the shortened Kirkwood superposition approximation discussed in refs. [4,5]. Using approximation above to decouple three body density, and particular form for σ AA xy used throughout this section, gives following equations of motion,…”

“…The nature of the asymptotics of A+B reaction when initial number of A and B particles is equal has been hotly debated for decades. For example, Smoluchowskii approach predicts d/2 decay exponent [4,5,9]. Field theoretic RG method predicts correct d/4 decay for 3 < d < 4 [21], while for other dimensions nothing can be said in the RG framework.…”