Diffusion processes in a liquid mixture of lithium isotopes

Abstract

The quantum mechanical theory of diffusion, as recently developed for liquid metals [M. Omini, Phil. Mag. 86 1643 (2006); Phil. Mag. 87 5249 (2007)], is now presented in a final version that improves and clarifies the original formulation. The new formulation uses a convergent variational method to solve the transport equation and confirms, through a rigorous analysis, the validity of the approximations introduced in the quoted papers. As a consequence, all previous calculations, concerning the self diffusion coefficients of liquid lithium isotopes, are automatically confirmed. The possibility of obtaining, as a limit of a convergent procedure, the true solution of the transport equation allows a reliable prediction of all isotope effects. In particular, it provides numerical values for the interdiffusion coefficients of ⁶Li and ⁷Li, which were not explicitly deduced in the previous works. The total consistency of these values with those measured by Feinauer et al. [Phys. Condens. Matter 6 L355 (1994)] further supports the theory. It is concluded that the whole set of experimental data on liquid lithium, as provided by the above authors, is theoretically explained within the experimental uncertainties.

Keywords:

• interdiffusion coefficients
• liquid lithium
• isotope effect
• phonons in liquids
• quantum theory of diffusion

Acknowledgment

The manuscript has been prepared with the cooperation and the constant encouragement of my wife, to whom all my gratitude is addressed.

Notes

Note

1. It is worth explaining why no configurational entropy was associated to the oscillators, described by ξ. The condition ξ < 1, as deduced in 2, is consistent with a picture where N′ξ solid-like atoms present a Mott oscillator in the first shell of neighbours, and N′(1 − ξ) solid-like atoms do not. There are many ways to realise a distribution of this kind. For instance, in the case N′ = 8, ξ = 1/4, two different ways are represented by the symbols a b c* d e f* g h and a b* c d e f* g h, where each letter refers to a solid-like atom and the star denotes the corresponding presence of a Mott oscillator in the first shell of neighbours. However, the latter symbol is obtained from the former by interchanging letters b and c. Since all the N′ atoms are treated as identical particles, such an interchange cannot produce any detectable effect, so that the two ways are indistinguishable. More generally, owing to the equivalence of all the ways through which the above distribution can be realised, the absence of any term of configurational entropy is justified.