Defect energetics for self-diffusion in sodium

Abstract

Recent data on self-diffusion and the isotope effect in sodium indicate clearly the existence of at least two operating defect mechanisms. This paper investigates the possibility of vacancy, divacancy, and interstitial mechanisms by calculating the diffusion energetics for the vacancy-type defects and estimating the same for interstitials based on other calculations. The aim is to search for a combined mechanism which can be used to interpret the available data on defect studies. The validity of choosing pseudopotentials for defect calculations is tested by using three potentials with different exchange and correlation corrections in the dielectric function of the conduction electrons. There is about a 15% variation in the results for vacancy and divacancy. Our energetic results indicate that a combined vacancy and divacancy mechanism can be used to account for most of the data obtained in diffusion, isotope effect, and dilatometric measurements. The available theoretical and experimental results do not seem to favor, but cannot completely rule out, the interstitial mechanism. It is suggested that the question is not likely to be resolved by further energetic calculations due to the lack of reliable interatomic potentials at close ranges; instead, experiments designed for detecting interstitials and dynamical calculations of K are needed. © 1973 The American Physical Society.