Frenkel pair

We have, in this case, both a vacancy associated with an interstitial atom. Using the approach shown in 2.5.18., we have  

Minimizing the free energy as before, we can write for the Frenkel pairs  

Note that AF applies to both interstitial and vacancy sites. Using 2.5.23. and 2.5.24., we can get the fraction of Frenkel defects as  

---

The process responsible for initiating RES follows from the earlier discussion of radiation damage in graphite. Specifically, in a displacement event a Frenkel pair... 

Note that we can use the same statistical mechanical approach to calculate SchottslQi" pairs, Frenkel pairs, divancies (which are associated vacancies), impurity-vacancy complexes, and line dislocation-point defect complexes. 

In this case, the Frenkel pair diffusion, i.e.- Vai + Ali3+, predominates and is fester than any other possible mechanism. 

FIGURE 5.1 Schematic illustration of intrinsic point defects in a crystal of composition MX (a) Schottky pair, (b) perfect crystal, and (c) Frenkel pair. 

Most of the irregular SE s formed by irradiation interact with impurities that are the native irregular SE s of the crystal. Impurities interact with the irradiation products either by their stress field or, if heterovalent, by the electrostatic (Coulomb) field. Photolysis (radiolysis) is found in other than halide crystals as well. In oxides, the production of Frenkel pairs under photon irradiation is negligible. This has been ascribed to the fact that the reaction O2- +0" = 02 is endothermic, whereas the reaction X- +X = is exothermic. 

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

For the exciton mechanism of defect production in alkali halides the Frenkel pairs of well correlated defects are known to be created [35], the mean distance between defects inside these pairs is much smaller than that between different pairs. The geminate pair distribution function could often be approximated as... 

If both components of the Frenkel pair (v, i) are mobile and no other reaction but annihilation occur, the tendency to generation-recombination... 

A cation vacancy may be paired with a nearby cation interstitial. This is called a Frenkel pair. An example is the formation of Zn+2 vacancies and Zn+2 interstitials in ZnO. This is illustrated in Figure 5.2B. In principle, paired anion vacancies and interstitials are possible, but this is less likely because of the larger size of the anions. 

Figure 7. Scheme of ES-mechanism of Frenkel-pair formation induced by exciton selftrapping into quasi-molecular state. 

Increase of the stable Frenkel-pair concentration under irradiation of the samples is saturated (Fig.6) when the trapping of excitons at defects exceeds the exciton self-trapping in the perfect lattice. Further long-time irradiation of the samples results in an aggregation of vacancies and interstitials, which results in decrease of intensity of defect subbands (Fig.6e). 

The ES-mechanism of Frenkel-pair formation as a result of excitation of Rydberg atomic states was confirmed by recent molecular dynamics calculations [28,29]. After the bubble formation the surrounding ground state atoms appear to have moved to the second shell. It was found that the second-nearest neighboring vacancy-interstitial pairs could create the permanent defects, which remain in the lattice after exciton annihilation (Fig.Sb) [29],... 

In all RGS selective excitation of excitons by photons of energies below the band-gap energy Eg results in accumulation of Frenkel-pairs, which is a direct proof of the excitonic nature of the ES-mechanism of defect formation. 

Atomic cryocrystals which are widely used as inert matrices in the matrix isolated spectroscopy become non-inert after excitation of an electronic subsystem. Local elastic and inelastic lattice deformation around trapped electronic excitations, population of antibonding electronic states during relaxation of the molecular-like centers, and excitation of the Rydberg states of guest species are the moving force of Frenkel-pairs formation in the bulk and desorption of atoms and molecules from the surface of the condensed rare gases. Even a tiny probability of exciton or electron-hole pair creation in the multiphoton processes under, e.g., laser irradiation has to be taken into account as it may considerably alter the energy relaxation pathways. 

Similarly, in thermal equilibrium, some ionic crystals at a temperature above absolute zero enclose a certain number of Frenkel pair defects, that is, anion and cation interstitials in the structure. Since the concentration of Frenkel pair defects at equilibrium at an absolute temperature, T, obeys the mass action law, then [16]... 

There are two types of lattice defects that occur in all real crystals and at very high concentration in irradiated crystals. These are known as point defects and line defects. Point defects occur as the result of displacements of atoms from their normal lattice sites. The displaced atoms usually occupy sites that are not in the lattice framework they are then known as interstitials. The empty lattice site left behind by the interstitial is called a vacancy. Avacancy produced by displacement of an anion or cation, along with its interstitial ion, is called a Frenkel pair, or simply a... 

Fig. 3 displays the changes in the introduction rate of the vacancy-oxygen complex with the irradiation temperature. The introduction rates of the VO and C -Oi centers increase about twice upon raising the irradiation temperature from 350 to 685 K. An analysis of all the available results on the effect of irradiation temperature on introduction rates of radiation induced centers allows us to suggest that the observed increase of t] in the range of 350-685 K can be associated with suppression of the annihilation rate of Frenkel pairs with the temperature increase. 

We mentioned above the collision cascade producing displaced atoms in a solid target. If we consider a single collision event in a crystalline solid, we can see that this displacement of atoms leads to the preferential formation of point defects. The most important types of point defects are a single vacancy (one atom or ion is missing), a single interstitial (an additional atom), a vacancy-interstitial pair (Frenkel pair). 

---