Analytical calculation of the velocity auto-correlation function in ionic solids from a simple model

Since the prime fluctuation-dissipation theorems, it is possible to consider a frequency dependent ionic diffusion coefficient which is directly proportional to the Fourier transform of the velocity auto-correlation function. To explain the velocity auto-correlation function obtained by the inverse Fourier transform of the experimental data, we propose a microscopic model, physically realistic, based on classical considerations. We demonstrate by means of a complete analytical calculation that this model allows us to recover the experimental behavior. Thanks to this model, it is possible to extract some parameters, such as the relaxation frequency, which are associated with constants that characterize the ionic motion. Further, this calculation gives a physical meaning to both ionic diffusion and polarization, without necessarily referring to the concept of hopping conductivity. (C) 2002 Elsevier Science B.V. All rights reserved.