Relationship between Mass Action Law and Statistical Thermodynamics

Relationship between Mass Action Law and Statistical Thermodynamics 

The total free energy of a crystal MXj containing point defects may be written as follows  

Let us assume that the concentrations of all defects other than Schottky defects are negligible. Then Eq. (77) can be written (using Stirling s approximation) 

If we consider M vacancies to be formed by addition of X atoms to the crystal, the total number of sites increases, and therefore N is not constant. Consequently, in obtaining idG/dNyf ) from Eq. (78), we must utilize the fact that BN/dNy = 1, since 

The mass action law equations for the other intrinsic defects can be derived in a similar manner from Eq. (77). 

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