Frenkel defect formation

The Gibbs energy, AGcf, is often replaced by the enthalpy of Frenkel defect formation, AHcP, as described above, to give... 

It is important that the complete diagram displays prominently information about the assumptions made. Thus, the assumption that Schottky defect formation was preferred to the formation of electronic defects is explicitly stated in the form Ks > Ke (Fig. 7.9e). As Frenkel defect formation has been ignored altogether, it is also possible to write Ks > Ke > > Kt , where A p represents the equilibrium constant for the formation of Frenkel defects in MX. 

Interstitial sites are defined as those that would usually be empty in an ideal structure. Occasionally in real structures, ions may be displaced from their lattice sites into interstitial sites Frenkel defect formation). Once this happens, the ions in interstitial sites can often hop into adjacent interstitial sites. These hops may be one stage in a long range conduction process. A schematic example is shown in Fig. 2.1(h) a small number of Na ions are displaced into the tetrahedral interstitial sites and can subsequently hop into adjacent tetrahedral sites. It should be noted, however, that while a small number of Frenkel defects may form in NaCl, conduction is primarily by means of vacancies whereas in some other structures, e.g. AgCl, Frenkel defects do predominate. 

The first reaction is a site exchange reaction and so does not alter the number of lattice sites. The second reaction describes the formation of a complete lattice molecule M. An example of the first type of reaction (exchange reaction, Eqn. (2.59)) is the so-called Frenkel defect formation reaction in AX (e.g., in silver halides, see Fig. 1-2)... 

Let us apply Eqn. (4.143) to the homogeneous Frenkel defect formation reaction Aa+V = A +VA, which describes the formation of intrinsic majority defects in... 

The activation energy for self-diffusivity of the Ag cations by the interstitialcy mechanisms is the sum of one-half the Frenkel defect formation enthalpy and the activation enthalpy for migration,... 

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... 

This is an important result because it predicts that the defect concentrations in stoichiometric oxides or compounds for which the Schottky or Frenkel defect formation energies are much greater than 3 eV will most likely be dominated by impurities. 

The enthalpy of formation of a Frenkel defect in silver bromide, AgBr, is 1.81 x 10 J. Estimate the fraction of interstitial silver atoms owing to Frenkel defect formation in a crystal of AgBr at 300 K. 

Hosono, H., Kawazoe, H., and Matsunami, N., Experimental evidence for Frenkel defect formation in amorphous SiOj by electronic excitation, Phys. Rev. Lett. 80, 317 (1998). 

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