Separate migration and formation energies of vacancies in aluminum measured by NMR

After a rapid change in temperature of a crystalline solid, the rate of vacancy motion changes immediately while the concentration of vacancies changes more slowly. We report NMR diffusion measurements on pure aluminum foil done at constant vacancy concentration by rapid rf heating from a constant preparation temperature. Thus, the temperature dependence of the diffusion yields the migration energy $E_M$. Our results for $E_M$, 0.71 and 0.66 eV, are in good agreement with the accepted value. The experiment reported here should be applicable to all kinds of solids, provided a means of rapid heating or cooling is available.