Determination of Vacancy Jump Frequencies from Dielectric Loss Measurements onNi++-Doped NaCl Crystals

Small divalent cation impurities such as Co, Mg, Mn, Ni, etc.,in alkali halide crystals give two dielectric relaxation peaks, as they are associated with the nearest-neighbor (nn) and the next-nearest-neighbor (nnn) vacancies. NaCl: ${\mathrm{Ni}}^{++}$ crystals give peaks at frequencies (in Hz) of $(3.69\mathrm{}\pm 0.37)\times {10}^{11}{e}^{-0.62\mathrm{}\pm 0.06\frac{\mathrm{eV}}{\mathrm{kT}}}$ and $(2.84\mathrm{}\pm 0.28)\times {10}^{11}{e}^{\frac{-(0.55\mathrm{}\pm 0.05\mathrm{eV})}{\mathrm{kT}}}$. The jump frequencies ${\omega }_0 ({\omega }_0={\omega }_1+{\omega }_2)$, ${\omega }_3$, and ${\omega }_4$ are expressed in terms of the positions of the two peaks and the ratio of the heights of the two peaks. ${\omega }_1$, ${\omega }_2$, ${\omega }_3$, and ${\omega }_4$ are the field-free jump frequencies of the cation vacancy defined by (i)${\omega }_1$, nn → nn; (ii) ${\omega }_2$, nn → impurity; (iii) ${\omega }_3$, nnn → nn; and (iv) ${\omega }_2$, nn → nnn. At 80°C, the values of jump frequencies ${\omega }_0$, ${\omega }_3$, and ${\omega }_4$ were found to be (1.54±0.17) ×${10}^4$, (1.19±0.18) ×${10}^3$, and (1.20±0.20) ×${10}^3$ Hz, respectively. It is seen that ${\omega }_0>{\omega }_3$, ${\omega }_4$ and that ${\omega }_3$ and ${\omega }_4$ are almost equal in magnitude. From the latter fact it is concluded that the concentration of nn and nnn vacancies is almost equal. The relative values of ${\omega }_0$, ${\omega }_3$, and ${\omega }_4$ are consistent with the earlier results...