Nonstoichiometry —Equilibria with External Phases

If the concentrations of each type of point defect in a conjugate pair are not equivalent, the crystal becomes nonstoichiometric. If there is an excess of M vacancies, X interstitials, or X substitutionals, the compound will have a surplus of X (or deficiency of M) over the ideal stoichiometric composition. This condition will be referred to as a positive deviation from stoichiometry. Conversely, for a negative deviation from stoichiometry, X vacancies, M interstitials, or M 

The formula for a nonstoichiometric compound may be written where 6, the degree of deviation from stoichiometry, may be positive or negative. In terms of defect concentrations, 8 may be expressed as follows  

The concentrations of point defects, and therefore the direction and degree of nonstoichiometry, are determined by the thermodynamic activities of external phases in equilibrium with the nonstoichiometric compound. For example, the concentration of X vacancies may be controlled by maintaining the crystal in equilibrium with another phase containing X at a definite activity. The external phase may be X2 gas (e.g., O2). The equation for formation of X vacancies then may be written 

The pressure of X2 gas will then determine the activity and concentration of vacancies. 

The concentration of X vacancies may also be controlled by the activity of the M component in an external phase. For example. 

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In most experimental work on nonstoichiometric compounds the extent of nonstoichiometry usually is determined by the pressure of the nonmetal gas in equilibrium with the crystal. Therefore, the remaining discussion in this section will be in terms of X2 gas and the activity of the X component. However, it should be kept in mind that equivalent relationships can be obtained for the M component, and that the external phase need not be X2 gas but may be any compound containing the X component. 

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