Diffusion and collective motions in liquid metals

Abstract

Collective oscillations in thermal equilibrium are shown to represent only a small fraction of the degrees of freedom of a liquid metal, the important fraction being associated to uncorrelated motions of the atoms. The present paper, however, justifies the basic interest for these oscillations in the theory of diffusion. In fact, they can be explained in the framework of a collective coordinate formulation, where the relevant Fourier components of the pair potential are only those corresponding to the wavevectors of the collective modes. Since the matrix elements for atomic scattering processes are proportional to the Fourier coefficients, it follows that, in this formulation, the only important processes are collisions where the wavevector change of an atom is a wavevector of the collective modes. A reduction in the number of these modes, as produced by a temperature rise, implies a reduction in the scattering processes and, subsequently, of the resistance presented by the liquid to the motion of a diffusing atom. This explains the strong rise with temperature of the self-diffusion coefficient, as recently observed in liquid lithium. Perturbation theory can be used to account for those Fourier components, which have been neglected in the above formulation. In this case, the results are fully consistent with the theory of diffusion developed earlier [M. Omini, Phil. Mag. 86 1643 (2006)].