Equilibrium Concentration of Frenkel Defects Derived from Configurational Entropy

3 Equilibrium Concentration of Frenkel Defects Derived from Configurational Entropy 

The calculation of the number of Frenkel defects in a crystal proceeds along lines parallel to those above. The introduction of Frenkel defects causes the Gibbs energy of the crystal to change by an amount AGp  

In a crystal of overall composition MX, suppose that nP is the number of Frenkel defects in the crystal at a temperature T (K), that is, there are n, interstitials distributed over Ni interstitial sites and nP vacant atom sites present, distributed over N possible atom sites. 

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 

Similarly, the number of ways of distributing the nP interstitial atoms over the N, available interstitial positions in the crystal is 

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