Frenkel defect pairs

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]... 

FIGURE 8.9. Distribution of the majority, Frenkel pair, defects near the grain boundaries between an SE (or an MIEC in which the majority charged defects are ionic), and a second phase. Specific example assumes M to be a mobile ion. (a) A(insulator)/MX(MIEC or SE). (b) Two different MIECs or SEs with a common mobile ion M. (c) Two grains of the same MIEC or SE material. (Adapted fi om Maier, J., in Recent Trends in Superionic Solids and Solid Electrolytes, Chandra, S. and Laskar, A., Eds., Academic Press, New York, 1989, 137.)... 

The number of Frenkel pair defects n depends on the number of regular positions in the crystal N and the number of interstitials N ... 

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. 

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. 

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... 

Equation (2.2.24) means homogeneous generation of particles A and B with the rate p (per unit time and volume), whereas (2.2.25) comes from the statistical independence of sources of a different-kind particles. Physical analog of this model is accumulation of the complementary Frenkel radiation defects in solids. Note that depending on the irradiation type and chemical nature of solids (metal or insulator), dissimilar Frenkel defects could be either spatially correlated in the so-called geminate pairs (see Chapter 3) or distributed at random. We will focus our attention on the latter case. 

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... 

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. 

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... 

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). 

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

Ceria Ceria (CeO2) is similar to zirconia and, in pure form, has the fluorite structure (see Chapters 2 and 9). The dominant point defects are anion Frenkel pairs and, like zirconia, ceria can be doped with rare earth cations to increase the concentration of anion vacancies and increase the oxygen ion conductivity. There is considerable interest in the application of ceria in SOFCs, as it has a higher conductivity than zirconia and can therefore operate at lower temperatures [127]. Unlike zirconia, ceria is readily reduced at elevated temperatures, resulting in the loss... 

Presence of these interstices provides to the fluorite stmcture extremely specific features. In UO2 particularly, it allows for placement of some radioactive decay products, these sites are responsible for existence of hyperstoichiometric UO2+X phase, where the extra oxygen ions fill the empty interstitial sites in the fluorite lattice etc. First case is extremely important in radiation damaged UO2. Second one is cmcial in oxidation of pure UO2 in atmospheric conditions. Diffusion of atmospheric oxygen into the bulk of crystal brings excess oxygens into empty interstices. These become filled more or less randomly only at low x, at higher concentration of extra anions they form different types of clusters, including so-called 2 2 2 Willis dimers Willis), tetra- and pentameric defects clusters of cuboctahedral symmetry Allen and Tempest). Last defects appear due to interaction of extra anions with intrinsic crystal FP defects (anion Frenkel pairs, i.e. anion vacancies and anion interstitials). 

Mechanisms of formation of these defects in pure and damaged UO2 are different. In pure UO2, oxygen Frenkel pairs (OFP) defects appear spontaneously as thermally induced excitations of anionic crystalline sublattice, in damaged dioxide they normally produced by fast fission products. 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

As indirect evidence of the presence of perfect LO in amorphous Fe-B and Pd-Si alloys, there serve the data on the threshold energy of defect formation under electron irradiation at low temperatures. Distinct thresholds of defect formation appear to exist, which are very close to the thresholds of Frenkel pairs formation in corresponding crystals [6.45,46]. 

For Si, there are three types of native defects the vacancy, the interstitial, and the interstitialcy. The vacancy, V, is an empty lattice site. Depending on the configuration of the unsatisfied bonds due to the missing atom, a vacancy in Si can be either neutral, negatively or positively charged. A vacancy is also referred to as a Schottky defect. A Si atom residing in the interstices of the Si lattice is defined as a self-interstitial. A Frenkel pair is a vacancy-interstitial pair formed when an atom is displaced from a lattice site to an interstitial site. An interstitialcy... 

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