C. Cramer

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 nthe jump relaxation model, and is called the concept of mismatch and relaxation (CMR).

Ion dynamics in superionic chalcogenide glasses studied in large frequency and temperature ranges

Abstract Electrical conductivity measurements on silver thiogermanate glasses have been performed in extended temperature (20–600 K) and frequency (10 Hz–60 GHz) ranges. The data indicate the presence of three conductivity regimes: the d.c. regime with a deviation from Arrhenius law below the glass transition temperature, a dispersive region where σ ( ω )= A ω s 1 (where s 1 ≈0.5 and A is thermally activated with an activation energy E 1 ≈(1− s ) E d.c. ) and a third regime where σ ( ω )= B ω s 2 . At T 150 K) shows clearly a superlinear frequency dependence. Additional measurements are needed to clearly identify the temperature dependence of conductivity in this region.

Correlated ionic hopping processes in crystalline and glassy electrolytes resulting in MIGRATION-type and nearly-constant-loss-type conductivities

Solid electrolytes with disordered structures may be crystalline or glassy. Their complex ionic conductivity displays a characteristic frequency dependence. Modelling the dynamics of the mobile ions, we have developed the MIGRATION concept, the acronym standing for MIsmatch Generated Relaxation for the Accommodation and Transport of IONs. With the help of the MIGRATION concept it is possible to reproduce frequency-dependent experimental conductivities and permittivities including their scaling behaviour. Scaling is a property typically observed in and below the radio frequency regime. At sufficiently high frequencies and low temperatures, however, conductivity spectra of crystals and glasses are often found to contain a second component which displays the so-called nearly-constant-loss (NCL) behaviour. Suitably modifying the MIGRATION concept, we are able to explain this feature and to show that it is caused by a displacive or hopping ionic motion that stays completely localised. Here, as in the unmodified MIGRATION concept, interactions between the ions play an essential role. Experimentally, interesting differences are detected between the NCL-type dynamics in a crystalline and in a glassy ion conductor. In crystalline gamma-RbAg4I5 we find the same elementary rates for the MIGRATION-type and NCL-type hopping movements of the ions, suggesting identical barrier heights for the respective processes. On the other hand, the two rates are found to differ markedly from each other in glassy AgI-AgPO3, not only with regard to their absolute value but also in their temperature dependence. We suggest that the NCL effect in the glass results from dynamic localised displacements involving both the silver ions and negatively charged entities such as iodide ions and/or non-bridging oxygen ions.

Ionic and polaronic glassy conductors: conductivity spectra and implications for ionic hopping in glass

Complete conductivity spectra have been taken of a lithium ion and a polaron conducting glass. The former exhibits high-frequency plateaux in its hopping conductivities and two different power-law exponents in the dispersive regime. This is readily explained if ions, contrary to polarons, have a pronounced site preference. At the same time, this view also explains the well known differences in the dependence of carrier mobility on carrier concentration in the two types of glasses.

Ionic and polaronic hopping in glass

Abstract In this paper we present conductivity spectra of the ion conducting glasses B 2 O 3 · 0.56Li 2 O · 0.45LiBr and Ag 2 S · GeS 2 and of the polaron conducting glass 0.2P 2 O 5 · 0.8 (0.89V 2 O 5 · 0.11V 2 O 4 ), covering a frequency range of more than 13 decades. At frequencies below the onset of the vibrational motion the spectra of both ion conducting glasses clearly differ from those of the polaronic glass. The dispersive conductivity of 0.2P 2 O 5 · 0.8 (0.89V 2 O 5 · 0.11V 2 O 4 ) follows a simple power-law behavior, the exponent being smaller than one. In contrast, the conductivities of both ion conducting glasses show the existence of two power-law exponents; one is the Jonscher exponent, the other is larger than unity. The data are interpreted in terms of the ‘unified site relaxation model’.

Ion dynamics in mixed alkali glasses

To study the ion dynamics in an amorphous mixed alkali system, frequency-dependent conductivities of 0.3[xLi2O·(1u2006−u2006x)Na2O]·0.7B2O3 glasses have been measured by impedance spectroscopy in a wide temperature range. The conductivities show a transition from their dc values into a dispersive regime where they increase continuously with frequency, tending towards a linear frequency dependence at sufficiently low temperatures. In addition to the “classical” mixed alkali effect, i.e. the occurrence of a minimum in the dc conductivity, we also observe the following new mixed alkali effect. In contrast to conductivity spectra of single cation glasses which follow the time-temperature superposition principle, featuring a temperature-invariant shape, the shapes of the conductivity spectra of the mixed alkali glasses studied here are found to change with ntemperature. To explain the effect, we suggest differently activated mobilities of the two different ionic species. The spectra are discussed in the framework of the concept of mismatch and relaxation (CMR).

Dynamics of mobile ions in crystals, glasses and melts, described by the concept of mismatch and relaxation

Abstract The concept of mismatch and relaxation (CMR) provides a model description for the dynamics of the hopping motion of ions in ion-conducting materials. The following applications are discussed. (i) In the crystalline fast ion conductor RbAg 4 I 5 the CMR is employed to analyse the gradual transition from random to nonrandom hopping that is found to occur below 298 K. (ii) When used to describe the ion dynamics in fragile supercooled melts, the CMR yields a new equation for the temperature dependence of the dc conductivity. (iii) In interacting dipole systems, the nearly-constant-loss (NCL) behaviour is reproduced by the CMR. (iv) After introduction of a structure-sensitive parameter, the CMR is able to fit experimental conductivity spectra that display significant differences in shape.

Dynamics of mobile ions in inorganic glasses

In order to study the ion dynamics of several inorganic glasses, we have taken conductivity spectra, extending from a few hertz up to the terahertz regime. At high frequencies the dynamic conductivity is governed by vibrational contributions, whereas ionic hopping sequences determine the low-frequency part of the spectra. In an intermediate frequency regime, both hopping and vibrational contributions do contribute to the dynamic conductivity. The shape of the vibrational conductivity is discussed for various glasses. Ionic hopping motion is brought into focus by removing the vibrational part from the total experimental spectra. The resulting spectra are discussed in terms of the concept of mismatch and relaxation.

Dynamics of mobile ions in single- and mixed-cation glasses

To study the ion dynamics of several inorganic glasses, including single- and mixed-cation glasses, we have determined conductivity spectra over wide ranges in frequency. In the case of the single-cation glasses, these spectra extend from a few hertz up to the terahertz regime. The spectra show a transition from their dc values to a dispersive regime where the conductivity increases continuously with frequency, tending towards a linear frequency dependence at sufficiently low temperatures. At high frequencies the dynamic conductivity is governed by vibrational contributions, whereas ionic hopping sequences determine the low-frequency part of the spectra. In an intermediate-frequency regime, both hopping and vibrational contributions contribute to the dynamic conductivity. The shape of the high-frequency conductivity spectra is discussed for various glasses. The low-frequency spectra are discussed in the framework of the concept of mismatch and relaxation.For the mixed-cation glasses where spectra have been taken by impedance spectroscopy, we report on a new kind of mixed-alkali effect. In contrast to conductivity spectra of single-cation glasses which follow the time–temperature superposition principle, featuring a temperature-invariant shape, the shapes of the conductivity spectra of the mixed-alkali glasses studied here are found to change with temperature. To explain this effect, we suggest differently activated mobilities of the two different ionic species.

Free volume anomalies in mixed-cation glasses revealed by positron annihilation lifetime spectroscopy (PALS)

PALS experiments reveal a minimum in ortho-positronium (o-Ps) lifetimes and a maximum in the corresponding intensities that emerge when mixed-cation (Li/Na) borate glasses are heated from ambient temperatures up to 473 K. These free volume anomalies appear to be a true manifestation of the mixed alkali effect (MAE). They are consistent with a mechanism of ion transport involving cooperation between hops of unlike cations, resulting in increased disturbance of the glass network. The result lends support to the dynamic structure model.