Klaus Funke

Re-examination of published conductivity spectra for 2Ca (NO₃)₂∙3KNO₃ (CKN) in its molten and glassy states, in terms of the MIGRATION concept, has brought to light new links between elementary processes occurring within one picosecond and their successful outcomes, i.e. those which determine the DC conductivities. The starting point of this analysis is the transition at 378 K, which arises from a change from a decoupled to a coupled transport mechanism. Remarkably, while there is a change in the shape of the conductivity dispersion and a jump in its onset frequency, there is no change in the temperature dependence of DC conductivity. What emerges from the analysis is a surprising continuity in high-frequency behaviour, with the activation energy and volume for elementary displacements, E_ed and V_ed, remaining constant from 300 K in the glass up to 500 K in the melt. The ratio, E_ed/V_ed, turns out to be equal to our previously defined DC activation moduli for CKN, given by E_DC(T)/V_DC(T) and T_g/(dT_g/dp) for charge transport in the melt and structural relaxation at T_g, respectively. It seems that, at very short times, molten CKN behaves just like an elastic solid. The importance of elastic forces for ionic transport in CKN is corroborated by the finding that the published value of the high-frequency shear modulus of glassy CKN, G_¥, matches those of E_ed/V_ed and hence of both activation moduli. The detected continuity in the picosecond behaviour of CKN across the glass transition could provide a new link between fragile liquids and glassy materials in general.

Solid State Ionics has its roots essentially in Europe. First foundations were laid by Michael Faraday who discovered the solid electrolytes Ag2S and PbF2 and coined terms such as cation and anion, electrode and electrolyte. In the 19th and early 20th centuries, the main lines of development toward Solid State Ionics, pursued in Europe, concerned the linear laws of transport, structural analysis, disorder and entropy and the electrochemical storage and conversion of energy. Fundamental contributions were then made by Walther Nernst, who derived the Nernst equation and detected ionic conduction in heterovalently doped zirconia, which he utilized in his Nernst lamp. Another big step forward was the discovery of the extraordinary properties of alpha silver iodide in 1914. In the late 1920s and early 1930s, the concept of point defects was established by Yakov Il'ich Frenkel, Walter Schottky and Carl Wagner, including the development of point-defect thermodynamics by Schottky and Wagner. In terms of point defects, ionic (and electronic) transport in ionic crystals became easy to visualize. In an ‘evolving scheme of materials science’, point disorder precedes structural disorder, as displayed by the AgI-type solid electrolytes (and other ionic crystals), by ion-conducting glasses, polymer electrolytes and nano-composites. During the last few decades, much progress has been made in finding and investigating novel solid electrolytes and in using them for the preservation of our environment, in particular in advanced solid state battery systems, fuel cells and sensors. Since 1972, international conferences have been held in the field of Solid State Ionics, and the International Society for Solid State Ionics was founded at one of them, held at Garmisch-Partenkirchen, Germany, in 1987.

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.

At sufficiently low temperatures, disordered ionic materials display the well-known Nearly Constant Loss (NCL) effect, with ionic conductivities becoming approximately proportional to frequency and virtually independent of temperature. There is a broad consensus that the effect is a collective phenomenon, with many interacting ions participating, each of them performing some non-vibrational motion that remains strictly localised. The underlying many-particle dynamics have been analysed in Monte Carlo simulations and also by straightforward modelling. Both kinds of treatment predict that, with decreasing frequency, a frequency squared behaviour should become visible. Here, we report on the experimental detection of the squared to linear crossover in an NCL component of conductivity spectra of sodium borate glasses, xNa₂O·(1 − x) B₂O₃ with x = 0.05 and x = 0.1, at temperatures below 100 K. From the composition dependence of the effect it is obvious that it is caused by the sodium ions. We demonstrate that this behaviour corresponds to an almost trivial property of the mean square displacement of the confined, but locally mobile ions, which approaches a temperature-independent long-time value, reflecting the finite size of the accessible volume. In the log–log plot of measured conductivity versus frequency, the transition from slope two to slope one is rather gradual, reflecting the existence of different local neighbourhoods of the sodium ions.

Conductivity spectroscopy spans more than 17 decades on the frequency scale, ranging from a fraction of a mHz up to about 100 THz. It provides a time-resolved view of the dynamics of the mobile ions in materials with disordered structures, acting as a "microscope in time". It thus has the potential to elucidate the development from an individual ionic displacement or hop to macroscopic transport of mass and charge, i.e., from less than a picosecond up to minutes and hours. The experimental setups required to cover the entire frequency range are sketched in Fig. 1. Fig. 1 Schematic overview of techniques for the measurement of frequency-dependent conductivities. Linear response theory is essential for relating conductivity spectra to time-correlation functions, which reflect the basic aspects of the ion dynamics in the sample. As it turns out, it is possible to sketch the dynamics in terms of a set of rules which, at the same time, reproduce the experimental spectra. We present such rules, written in the form of simple rate equations. The rules constitute the so-called MIGRATION concept [1]. Recently, this model treatment has been successfully applied to reproduce and explain the "universal" properties displayed by conductivity spectra of ion-conducting materials with disordered structures. These properties include scaling and, even more importantly, those ubiquitous features that have come to be known as "first" and "second" universality, to be outlined below.

The frequency- and temperature-dependent shear fluidity, f(ν,T), of the ionic liquid [BMIm]BF₄ is presented and compared with its ionic conductivity, σ(ν,T). [BMIm]BF₄ is short for 1-butyl-3-methyl-imidazolium tetrafluoroborate. Its DC fluidity, f_DC(T), and DC conductivity, σ_DC(T), are non-Arrhenius and superimpose in an Arrhenius-type representation if the respective inverse temperature axes are made to differ by a small amount, Δ = (1/T^⊗− 1/T) > 0. The observed superposition suggests that f(ν,T) should display a frequency dependence similar to σ(ν,T^⊗). We have therefore measured f(ν,T) of [BMIm]BF₄ over five decades of frequency at different temperatures. The spectra thus obtained corroborate our expectations. We model our experimental results in terms of the MIGRATION concept and arrive at the conclusion that f(ν,T) and σ(ν,T^⊗) are Fourier transforms of quite similar time correlation functions.