Vacancies interaction among

In previous sections it has been assumed that the enthalpies and entropies of defect formation are independent of composition. However, if there is interaction among the defects, this assumption is no longer valid. If the degree of interaction among defects is not negligible, additional terms for interaction enthalpy and entropy between defects must be introduced into Eq. (77). In terms of the mass action law, this means that activities and activity coefficients must be used instead of concentrations. For example, let us consider the formation of X vacancies [Eq. (29)] ... 

The phonon-interaction and boundary-scattering process establish the general shape of the conductivity curve for a perfect crystalline dielectric. Further scattering may occur at internal lattice imperfections such as vacancies, interstitial atoms, impurity atoms (among which may be included isotopes of the primary constituents), and dislocations. These added resistances have the effect of lowering and flattening the conductivity curve and, in the limit of a glassy or disordered solid, lead to a curve without a maximum. 

---