Energetics of divacancy diffusion in sodium

Abstract

The deviation of the self-diffusion coefficient from the normal Arrhenius temperature- and pressure-dependences observed at high temperatures in sodium have been investigated by considering contributions from divacancy diffusion. To determine the stable configuration and the migration path for divacancies, we have calculated quite extensively the energetics for divacancy formation and migration. The first, second and fourth neighbour divacancies are found to be stable, with highest binding energy for the second neighbour. The migration steps are most probably the exchange jumps between the first and second neighbour divacancies. It is found that these two exchange jumps have the same saddle-point configuration, therefore it would not be possible to distinguish their contributions to the self-diffusion coefficient. However, due to the different starting configurations, these two divacancies have different migration energies. Consequently, the contributions from two divacancies are manifested in the temperature- dependence of the correlation factor. The divacancy correlation factor has been calculated according to the established migration path. Based on the correlation factors for monovacancy and divacancy diffusion, we have estimated fΔK and compared with isotope effect measurements. By choosing a constant ΔK of 0 6 the majority of the data can be accounted for except for temperatures very close to the melting point. It is felt that more understanding on ΔK for both monovacancy and divacancy is required in order to explain the observed isotope effects. © 1972, Taylor & Francis Group, LLC. All rights reserved.