Diffusion of Impurity Ions in Ionic Crystals. Treatment of the Diffusion Equations for Concentration Dependent Diffusion Coefficients

The equations for the diffusion of divalent ions into alkali halide crystals have been investigated for the case where the thermally produced vacancies and the vacancies added by the impurity are both to be taken into account. The concentration dependence on the diffusion coefficient is then given by $$D_{\mathrm{(C)}}{\mathrm{=D}}_s{\text{α C[1+(1+2β/C}}^2{\text{)(1+4β/C}}^2{)}^{\text{−1/2}},$$ where D_s, α, and β are constants at constant temperature. Fick's second law is numerically treated for the initial conditions of the thin deposited layer. The diffusion profiles calculated for trial values of the specific activity of ⁴⁵Ca are in good agreement with the experimental profiles of diffusion of Ca^{+ +} into NaCl single crystals.