Dielectric Relaxation Due to Impurity-Vacancy Complexes in NaCl Crystals

Abstract

Sodium-ion vacancies are introduced into sodium chloride crystals by the addition of the following divalent cation impurities: ${\mathrm{Mg}}^{++}$, ${\mathrm{Mn}}^{++}$, ${\mathrm{Ca}}^{++}$, ${\mathrm{Zn}}^{++}$, ${\mathrm{Cd}}^{++}$, and ${\mathrm{Sr}}^{++}$. Below 150°C, the virtual negative charge of a cation vacancy binds the majority of the vacancies to the divalent impurity ions to form complexes. The reorientation of these dipolar complexes is observed in the present experiments as a transient dielectric polarization current occurring immediately after the application of a dc electric field. Below 0°C, the dominant effect is an exponential "fast polarization" due to complexes in which the vacancy is in the nearest sodium-ion site to the impurity ion (except for the case of NaCl: ${\mathrm{Mg}}^{++}$). Also observed is a "very fast polarization" which may be interpreted as due to next-nearest-neighbor impurity-vacancy complexes, plus a "slow polarization" ascribed to vacancies jumping between more distant bound sites. By combining the present measurements with earlier ac measurements, one can obtain particularly accurate values for the jump activation energies of vacancies occupying the nearest-neighbor site to ${\mathrm{Ca}}^{++}$ and ${\mathrm{Mn}}^{++}$ ions in a NaCl crystal. The energies obtained for these two cases are 0.702±0.010 ev and 0.680±0.010 ev, respectively. From the manner in which the relaxation time at a given temperature varies with the radius of the impurity ion, the dominant jump mechanisms can be inferred. The major reason for the decrease in relaxation time with decreasing radius of the impurity ion appears to be the strong dependence of the jump rate of the impurity ion on ionic radius.