Dynamics of positive-ion vacancies in x-irradiated NaCl by positron annihilation

A fraction of thermalized positrons in a NaCl crystal can be trapped in crystal defects to form annihilation or $A$ centers. This fraction is found to increase after x irradiation of the crystal. The increase is measured through the coincidence count rate of the two 0.51-MeV positron-electron-annihilation $\ensuremath{\gamma}$ quanta emerging from NaCl single crystals in exactly opposite directions. Isothermal annealing at various temperatures $T$ between 55 and 185 \ifmmode^\circ\else\textdegree\fi{}C always increases the count rate further, in time intervals ranging, respectively, from ${10}^{2}$ to 10 min. When $Tg100$ \ifmmode^\circ\else\textdegree\fi{}C, the count rate as a function of time passes through a pronounced maximum and diminishes slowly (in ${10}^{3}$ to ${10}^{2}$ min) toward the count rate of the annealed crystal. The activation energy for the rate of increase is 0.4 eV, and for the decrease 1.2 eV. Both values coincide with the activation energies for the rise and decline of the ionic conductivity in isothermal anneals at $T\ensuremath{\ge}130$ \ifmmode^\circ\else\textdegree\fi{}C. To the extent that the dominant $A$ centers are positrons trapped in mobile or immobile positive-ion vacancies, and that the dominant charge carriers in ionic conductivity are the mobile positive-ion vacancies, our data support the long-held conjecture that x irradiation creates vacancies and that during incipient periods of annealing additional vacancies are released from radiation-induced vacancy aggregates. The positive-ion vacancy-diffusion constant is deduced to be 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{cm}}^{2}$/sec, corresponding to a mobility \ensuremath{\sim} ${10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{2}$/V sec, by Einstein's relation. The ubiquitous initial rise in our count rates implies that the initial drop in conductivity for isothermal anneals at moderate temperatures, $T\ensuremath{\lesssim}100$ \ifmmode^\circ\else\textdegree\fi{}C, is caused not by the neutralization of positive-ion vacancies but by their immobilization through complex formation. The decline at long anneal times in both our count rates and the conductivities, with identical activation energies, signifies the slow formation of positive-ion-vacancy sinks leading to the complete annealing of the radiation-induced defects so observed.