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The thermodynamic
equilibrium concentration of vacancies corresponds to the minimum value
of the Gibbs function as n is changed. The minimum
results from the balance between the enthalpy and entropy contributions.
(dGn/dn)T,p
= 0 = (d[G0+nHV- kT Ln{W}]/dn)T,p
� For large x, Stirling's approximation
gives:
ln x! = x ln x - x.
� Using this to differentiate
the above expression for G gives:
Hv - kT[Ln(N
- n0) - Ln(n0)] = 0
i.e. {n0/(N
- n0)}={n0 / N} = exp(- HV/kT)
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