Dielectric function and localized diffusion in ion conducting glasses

We present the three coupled rate equations of the mismatch generated relaxation for the accommodation and transport of ions (MIGRATION) concept that describe the ion dynamics in, for example, ion-conducting glasses and simultaneously yield scaled conductivity and permittivity spectra. Here, model spectra are compared with the experimental spectra of xNa2O·(1-x)GeO2 glasses for x=0.0513, 0.0902, 0.213. This allows us to estimate the long-time limit of the localized rms displacement, lim t → ∞ { < R 2 ( t ) > − 6 ⁢ D ⁢ t } 0.5 , which may be roughly interpreted as the average size of the ion cage before the dynamics become diffusive. For the three compositions considered, we obtain an approximate x−1/3 dependence of this quantity, which implies that the ion dynamics are largely governed by the Coulomb interactions between the mobile ions.