Thermodynamics

The concentration of a particular point defect in a solid is given by the expression $[D_{j}]=C e^{\frac{-G}{k_{B}T}}$. G is the Gibb's free energy, C is a prefactor, k$_{B}$ is the Boltzmann constant and T is the temperature. The Gibbs energy is $G=E_{form}+S_{form}T$ where E$_{form}$ is the energy of formation and S$_{form}$ is the entropy of formation. S$_{form}$ comes about because of the local strain around a defect and has been shown to be negligible compared to E$_{form}$. [8] The prefactor C is the number of sites in the volume at which the defect can sit. [1,9] Upon substitution, the concentration of defects can be rewritten

$$[D_{j}]=N_{sites} e^{\frac{-E_{form}}{k_{B}T}}$$ (1)