Statistical Thermodynamics of Defect Solids

1 Statistical Thermodynamics of Defect SoKds If a defect of any kind can be created in a crystalline solid by the expenditure of a finite amount of energy, 

For the fundamentals of statistical thermodynamics the reader is referred elsewhere (14) however, it is possible from a knowledge of classical thermodynamics and an acceptance of the manner in which the classical thermodynamic functions can be specified in terms of observable quantities to show how statistical theory can be usefully applied to the defect solid state. 

One requires to know the way in which ail the atoms or molecules of the system under discussion are distributed over all the possible energy states of all degrees of freedom of the system. The determination of these energy states is, of course, the fundamental problem of quantum-mechanics, and this will be discussed briefly for defect solids in the next section of this chapter. Once one knows this distribution, the thermodynamic functions may be deduced and the equilibrium conditions, expressed in terms of the appropriate thermodynamic functions, applied. 

The distribution of molecules among the accessible energy states is expressed in terms of the partition function, which is simply the sum, over all the energy states, of the terms which are the operative quantities determining the number of molecules in each state The partition function may then be written  

A convenient property of the partition function emerges if one makes the usual approximation that energies 

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