Frenkel defect configurational entropy

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

S4.3 Equilibrium Concentration of Frenkel Defects Derived from Configurational Entropy... 

The configurational entropy change, A.Sf, due to the distribution of the defects over the available positions, can be determined by using the Boltzmann equation. The number of ways of distributing the nP vacancies that have been created over the N available positions in the atom array affected by Frenkel defects is... 

Atoms vibrate about their mean positions in solids. An increase in vibrational energy increases their amplitude and the frequency of their vibrations. Defects such as Schottky and Frenkel are produced by the movement of atoms from their original positions. All the aforementioned processes increase the internal energy of the material and the configurational entropy. 

The first basic disorder type to be discussed is the Frenkel disorder. Here a few cations have left their regular positions, on accoimt of the favourable configurational entropy (thermal influence), thus leaving behind vacancies, and now occupy interstitial sites. Such defects typically occur in the cationic sublattice and preferentially in cases of high polarizabihty, such as in the Ag" " sublattices of the silver halides AgCl, AgBr and Agl (see Section 5.2). 

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