Thermodynamics of Vacancy Formation

As stated above, point defects can be characterized by thermodynamics. Though processes, like the formation of point defects, are associated with positive entropy. 

The component of the aforementioned entropy is the configurational entropy , which is related to W on the basis of statistical mechanics as  

For large numbers, the logarithm of the factorial may be approximated by Stirling s relation  

Equation (3.1) gives the free energy to form n defects where Ep refers to one defect. Substituting for S in the free energy Eqs. (3.1) from (3.6) and taking the derivative, with respect to the number of defects to get the minimum, results in  

This relation indicates that at absolute zero the concentration of defects is zero and with increasing temperature, the number of defects increases rapidly. The radiation of specimens largely increases its defect concentration. In the derivation of Eq. (3.9), only the configurational entropy was used and all the other entropy terms were neglected. Therefore, Eq. (3.9) is usually given as  

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