K. Funke

Ion transport in fast ion conductors: spectra and models

In fast ion conductors, the dynamics of the hopping motion of the mobile ions determines the shape of their hopping conductivity spectra. Therefore, analysis of complete conductivity spectra is a useful tool for extracting details of the correlated and relaxational hopping behaviour of the ions. The paper shows how this is done on the basis of the jump relaxation model. Furthermore, the model is reconsidered and extended, with a view to describe not only crystalline but also glassy electrolytes.

Dynamics of mobile ions in crystals, glasses and melts

Abstract In crystalline, glassy and molten electrolytes, the dynamics of the mobile ions is best studied by taking conductivity spectra, i.e., by measuring ionic conductivities in the entire range from dc to far-infrared frequencies. Experimental conductivity spectra are reviewed and discussed, with particular emphasis on their high-frequency plateaux and their low-frequency scaling properties. The concept of mismatch and relaxation (CMR) is shown to provide a general basis for understanding the spectra in terms of the ion dynamics. The conductivity spectra of crystalline fast ion conductors are, e.g., explained by the jump relaxation model, which builds on the CMR. In glassy electrolytes, the mobile ions encounter different kinds of site, and the jump relaxation model has to be modified accordingly. Formulating the CMR without reference to the existence of fixed sites yields a description of the ion dynamics in simple molten salts. The model is thus able to reproduce both the conductivity spectra of fragile molten salts and the characteristic temperature dependence of their dc values. The remarkable low-frequency scaling behaviour of glassy electrolytes is considered a manifestation of the particular long-time properties of the CMR.

Ionic glasses : History and challenges

We review the history of glass technology and glass science and discuss, from a personal point of view, the great challenges in the physics and chemistry of ionic glasses.

Information on the absolute length scales of ion transport processes in glasses from electrical conductivity and tracer diffusion data

We show that absolute values for the time-dependent mean-square displacement of mobile ions in glasses can be obtained from a combined analysis of electrical conductivity and tracer diffusion data. By applying this method to sodium germanate glasses of different compositions, we find that the distances the ions cover in characteristic stages of the transport process increase considerably with decreasing sodium oxide content. At low sodium oxide contents, we observe a linear relation between the transport distances and the interionic separation distances, while this relation is lost at high sodium oxide contents. The same is found to be true for other alkali ion conducting glassy systems. The analysis of this effect is important for discriminating between the influence of the network structure and of the interionic Coulomb interactions on the ion dynamics.

Ionic motion in materials with disordered structures: conductivity spectra and the concept of mismatch and relaxation

Solid electrolytes with disordered structures, both crystalline and glassy, as well as supercooled ionic melts, exhibit surprisingly similar features in their conductivity spectra, σ(ν). This finding suggests that the dynamics of the mobile ions in the different systems should be governed by similar rules. Examples are given in this study, including new results on γ-RbAg4I5, β-AgI, and several glassy electrolytes. In spite of their overall similarity, however, the spectra also display characteristic differences in their shapes and in their scaling behaviour, the latter feature causing, e.g., Arrhenius or non-Arrhenius temperature dependences of the dc conductivity. The observed characteristics of the spectra, both the common and the more specific ones, are well reproduced with the help of two coupled rate equations describing the evolution of the ion dynamics with time. This treatment is based on the jump relaxation model, and is called the concept of mismatch and relaxation (CMR).

Debye-Hückel-type relaxation processes in solid ionic conductors: The model

Abstract The present model deals with the interactions among the mobile charged defects in a solid electrolyte and their effects on the microscopic and macroscopic transport properties. Two competing relaxation processes are considered after each “initial forward” hop of a charged defect: the backward hop of the defect and the forward motion of the surrounding “defect cloud”. The model yields those properties of solid electrolytes known as “universal dielectric response”, i.e., the power-law behavior of the frequency dependent conductivity and the occurrence of almost circular arcs in the complex-conductivity plane, with centers displaced below the real axis.

A unified site relaxation model for ion mobility in glassy materials

Abstract The unified site relaxation model combines key features of the earlier dynamic structure and jump relaxation models, and provides a coherent model of ionic transport processes in glassy materials. The essential idea is that mobile ions hop backwards and forwards many times before: (i) the Coulomb field is relaxed and (ii) the ‘target site’ adjusts itself to the needs of its new occupant. The other mobile ions and the network of the glass are both involved in this (unified) relaxation process. Manifestations of site relaxation are seen in the frequency dependence of the conductivity, in mechanical loss spectra and in many d.c. ‘anomalies’ such as the mixed cation effect.

Concept of mismatch and relaxation derived from conductivity spectra of solid electrolytes

Abstract Below the microwave regime, conductivity spectra of crystalline ionic conductors like RbAg 4 I 5 and others display remarkably uniform characteristics. Depending on the ranges of temperature and frequency, these may be approximated in terms of UDR (universal dynamic response) and NCL (nearly constant loss) behaviour, while a plateau is observed at millimetre wave frequencies. All these features are consistently described by a new non-power-law, non-KWW master curve. Its formal structure is shown to be equivalent to a proportionality of the rates of relaxation via the single- and many-particle routes. This is the essence of the concept of mismatch and relaxation (CMR).

Jump relaxation in solid ionic conductors

Correlated forward-backward hopping sequences of individual mobile charged defects are the elementary processes of jump relaxation in solid ionic conductors. The phenomenon is due to the repulsive interaction between defects. The microscopic dynamics of the relaxation is described in a simple model which yields in particular the frequency spectrum of the hopping motion. With the help of this function, it is possible to explain the experimental manifestations of the “universal dynamic response”, including the well-known arcs in the complex planes of conductivity and permittivity, the power-law frequency dependence of the ionic conductivity, as well as the non-BPP-type behaviour of spin-lattice relaxation times and the broad components of quasielastic neutron scattering spectra.

First and Second Universalities: Expeditions Towards and Beyond

Abstract Understanding the mechanisms of translational and localised ionic movements in disordered materials has seen intense activity spanning several decades. This article attempts to convey a concise overview of our contribution to this field over the period from 2005 to 2010 and to place it in its broad context.