A detailed study is made of the "conductivity plot" ($log\sigma T$ vs $T^{-1\mathrm{}}$) for the dc ionic conductivity, $\sigma$, of NaCl crystals doped with various divalent cation impurities. This plot, when examined over a range from the melting point down to -35°C, divides itself into a number of distinct regions. Below the intrinsic range is the region in which the cation-vacancy concentration is equal to the impurity concentration. Below this range the plot steepens due to the occurrence of vacancy-impurity association, after which it again steepens (for slowly cooled samples) due to impurity precipitation. At still lower temperatures, (below about 100°C), the plot returns to a slope characteristic of the association reaction. Finally, by "quenching" a sample to -60°C (at 30°C/min), the association reaction may be frozen and an abnormally high conductivity observed below 0°C. From an analysis of the data for quenched samples, a value for the activation energy for motion of a cation vacancy in NaCl, of ${0.79}_6$±0.02 ev, is obtained. The isothermal annealing of the quenched-in vacancies is also studied and found to obey essentially first-order kinetics, rather than the second-order kinetics characteristic of direct recombination.

• Received 26 December 1961

DOI:https://doi.org/10.1103/PhysRev.126.1367