Effective Volumes of Vacancies of Divalent Ions and Their Diffusion Coefficients in Alkali Halides

Photoelastic effects induced by divalent ions ${\mathrm{Sr}}^{++}$ and ${\mathrm{Ba}}^{++}$ diffused into KCl have been observed and measured experimentally. The theoretical analysis allows the calculations of the diffusion coefficients $D\left({\mathrm{Sr}}^{++}\right)=9.0\mathrm{}\times {10}^{-5\mathrm{}}{e}^{-\frac{0.77}{\mathrm{kT}}}$ ${\mathrm{cm}}^2$/sec and $D\left({\mathrm{Ba}}^{++}\right)=2.5\mathrm{}\times {10}^{-2\mathrm{}}{e}^{\frac{1.1}{\mathrm{kT}}}$ ${\mathrm{cm}}^2$/sec, and of volume changes due to impurity-vacancy complexes. By following the thermal dissociation of these complexes, it was possible to conclude that the isolated vacancy causes a lattice expansion larger than the contraction due to the isolated divalent ion.