Equilibrium Population of Schottky Defects in a Crystal

A Schottky defect in a crystal consists of a cation and anion vacancy combination that ensures overall electroneutrality in the crystal (Section 1.9). The estimation of the configurational entropy change in creating a population of Schottky defects in a crystal can be obtained in the same way as that of a population of vacancies in a monatomic crystal. The method follows that given in Section 2.1 for the equilibrium concentration of vacancies in a monatomic crystal and is set out in detail in Supplementary Material S4. 

Because Schottky defects are present as equilibrium species, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX  

The Gibbs energy, AGs, is often replaced by the enthalpy of Schottky defect formation, AHs, as in previous sections, to give 

Remember that these formulas only apply to materials with a composition MX. 

Some values for the enthalpy of formation of Schottky defects in alkali halides of formula MX that adopt the sodium chloride structure are given in Table 2.1. The experimental determination of these values (obtained mostly from diffusion or ionic conductivity data (Chapters 5 and 6) is not easy, and there is a large scatter of values in the literature. The most reliable data are for the easily purified alkali halides. Currently, values for defect formation energies are more often obtained from calculations (Section 2.10). 

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