Small deviation from stoichiometry. II. Imbalanced Frenkel defects

4 Small deviation from stoichiometry. II. Imbalanced Frenkel defects 

As noted above, the existence of anion vacancies is considered to be very rare except in special compounds such as (see Table 1.7 below). 

Consider a crystal Mj X which contains both metal vacancies and interstitial metal atoms in low concentration, i.e. M occupies lattice points in N lattice sites of metal, X occupies N in N lattice sites (generally, N, N, but in this calculation we assume = Nf and, moreover, interstitial M occupies in Na, where a is a constant which is fixed by crystal structure. If the conditions N N — N ), (N — N ), N are satisfied, it is not necessary to take the interaction energy between defects, as mentioned below, into consideration. The free energy of the crystal may be written as 

The chemical potentials of metal atoms, both in the regular and in the interstitial sites, and that of the anions in the regular sites are obtained from eqn (1.68) as 

Comparing this with eqn (1.57), it immediately follows that Na = Nj, eV + eV = fip. An intrinsic disorder parameter C , as a measure of the disorder of metal atoms at the stoichiometric composition, is defined as (by use of 

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