Isotope effects and defect energetics for diffusion in Na and NaCl

Abstract

The rate theory of Vineyard has been used to deduce an expression for the sharing of kinetic energy between a diffusing isotope at its saddle-point and the surrounding atoms in terms of the (imaginary) frequency of the localized vibration. The theory is explicitly applied to the case of Na diffusion in the Na sublattice of NaCl and provides a consistent explanation of the observed small sharing of kinetic energy when the vacancy mechanism of self-diffusion prevails. The theory has also been applied to Na metal and it is clear that it cannot provide a satisfactory explanation of the observed mass effect if a vacancy self-diffusion mechanism is assumed in this case. This situation is therefore explored further, by studying the migration energies for interstitial and vacancy diffusion processes using suitable pair potentials. In particular, we find that the stable interstitial configuration is a 〈111〉 crowdion with a very low migration energy (∼ 0·005 ev), whereas, with the same potentials, the vacancy migration energies are much larger (∼ 0·1 to 0·3 ev). It is this circumstance that makes it feasible that the interstitial mechanism could be favoured.The configurations of the split 〈110〉 interstitial and the 〈111〉 crowdin lie very close energetically and our proposal is that self-diffusion occurs predominantly via the crowdion, which, however, can frequently change direction via an intermediate 〈110〉 split interstitial configuration. The motion of more than one atom at the saddle-point then affords a ready explanation of the observed mass effect.The energetics suggest that vacancies will probably contribute appreciably to self-diffusion at higher temperatures. In addition, we have estimated a divacancy binding energy ∼ 0·03 ev, and divacancies may also be relevant in self-diffusion near to the melting point.