Alkali halides Frenkel defect

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

Frenkel defects on the anion sublattice show only anion migration and hence have fa close to 1. The alkali halides NaF, NaCl, NaBr, and KC1 in which Schottky defects prevail and in which the cations and anions are of similar sizes have both cation and anion contributions to ionic conductivity and show intermediate values of both anion and cation transport number. 

However, in the last two decades it has been shown experimentally [1,7, 8,12-14] and theoretically [15-18] that in many wide-gap insulators including alkali halides the primary mechanism of the Frenkel defect formation is subthreshold, i.e., lattice defects arise from the non-radiative decay of excitons whose formation energy is less than the forbidden gap of solids, typically 10 eV. These excitons are created easily by X-rays and UV light. Under ionic or electron beam irradiations the main portion of the incident particle... 

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... 

In many cases of interest tunnelling recombination of defects is accompanied by their elastic or Coulomb interaction, which is actual, e.g., for F, H and Vk, A0 pairs of the Frenkel defects in alkali halides, respectively. In these cases the equation defining the steady-state recombination profile is... 

Figure 7.15 shows the joint correlation function of similar defects in the region of concentration saturation as calculated from the results of the simulation. We see that the fraction of the close Frenkel defects (of the type of dimer F2-centres) exceeds by approximately threefold the value expected in the Poisson distribution, which agrees well with the analytical theory presented in Section 7.1 for the annihilation mechanism (see also [31, 111]) and with actual experiments for alkali halide crystals [13]. 

The experimental kinetics of accumulation of the Frenkel defects - F centres in alkali-halide crystals at liquid-helium temperatures - was studied in [17] and [40] within the framework of a model that yields a logarithmic dependence of the concentration of defects on the irradiation dose - equation (6) of Table 7.6). Although we criticized this relationship above, at low radiation doses it can be represented as a polynomial in powers of uqVq resembling equations (3) to (5). At the same time cogent arguments exist favoring the... 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

Ef corresponds to the enthalpy of formation of a defect pair Frenkel or Schottky, cf. Chapter 3). In an alkali halide, E( is typically about 3 eV implying a very low defect concentration, of the order of 10 at room temperature. E is the enthalpy of defect migration, usually several eV in dense structures, and / is the correlation or Haven factor. Its value varies between 0 and 1 and takes into account unfruitful attempts at transport in a given direction, caused by random jumps of mobile species and the particular geometry of each site. In other words, this factor takes into account the correlation effects (/ = 1 when correlations are absent). Usually / is of the order of 0.5-0.8 and plays a role in determining the transport mechanism. 

At this point let us briefly consider the formation of associates. The formation of associates between cation vacancies and divalent impurities in alkali halides has already been given as an example. Such reactions are homogeneous solid state reactions, and so the relaxation time for the formation of associates can be calculated in a completely analogous manner to the calculation of the relaxation time for the equilibration of Frenkel defects. The result of such calculations is precisely the same as the result given in eq. (6-5). It is only necessary, in the case of association, to replace the concentration c (eq) = in the denominator by the nearly constant concentration of the corresponding majority defect. In general, in the case of the formation of defect associates, we can conclude that the equilibrium concentration is attained rapidly compared to the time required by defect reactions which occur at sites of repeatable growth. 

To maintain charge neutrality, anion vacancies are normally compensated by cation interstitials (Frenkel defects), cation vacancies (Schottky defects), or by the vacancy caused by the substitution of a nonstoichiometric ion (cation with fewer electrons or anion with more electrons). Electron traps can be created by bombarding an alkali halide with radiation or neutrons to knock anions out of the lattice or by heating the material in the presence of the vapor of an alkali metal (for example, heating NaCl in a vapor of metallic Na). 

In some ionic crystals (primarily in halides of the alkali metals), there are vacancies in both the cationic and anionic positions (called Schottky defects—see Fig. 2.16). During transport, the ions (mostly of one sort) are shifted from a stable position to a neighbouring hole. The Schottky mechanism characterizes transport in important solid electrolytes such as Nernst mass (Zr02 doped with Y203 or with CaO). Thus, in the presence of 10 mol.% CaO, 5 per cent of the oxygen atoms in the lattice are replaced by vacancies. The presence of impurities also leads to the formation of Schottky defects. Most substances contain Frenkel and Schottky defects simultaneously, both influencing ion transport. 

Intrinsic point defects are deviations from the ideal structure caused by displacement or removal of lattice atoms [106,107], Possible intrinsic defects are vacancies, interstitials, and antisites. In ZnO these are denoted as Vzn and Vo, Zn and 0 , and as Zno and Ozn, respectively. There are also combinations of defects like neutral Schottky (cation and anion vacancy) and Frenkel (cation vacancy and cation interstitial) pairs, which are abundant in ionic compounds like alkali-metal halides [106,107], As a rule of thumb, the energy to create a defect depends on the difference in charge between the defect and the lattice site occupied by the defect, e.g., in ZnO a vacancy or an interstitial can carry a charge of 2 while an antisite can have a charge of 4. This makes vacancies and interstitials more likely in polar compounds and antisite defects less important [108-110]. On the contrary, antisite defects are more important in more covalently bonded compounds like the III-V semiconductors (see e.g., [Ill] and references therein). 

A major difference between crystals and fluids refers to the necessity of distinguishing between different sites. So the autoprotolysis in water could, just from a mass balance point of view, also be considered e.g. as a formation of a OH vacancy and a IT vacancy. In solids such a disorder is called Schottky disorder (S) and has to be well discerned from the Frenkel disorder (F). In the densely packed alkali metal halides in which the cations are not as polarizable as the Ag+, the formation of interstitial defects requires an unrealistically high energy and the dominating disorder is thus the Schottky reaction... 

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