Radha D. Banhatti

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).

Characterization of the complex ion dynamics in lithium silicate glasses via computer simulations

We present results of molecular dynamics simulations on lithium metasilicate over a broad range of temperatures for which the silicate network is frozen but the lithium ions can still be equilibrated. The lithium dynamics is studied via the analysis of different correlation functions. The activation energy for the lithium mobility agrees very well with experimental data. The correlation of the dynamics of adjacent ions is weak. At low temperatures the dynamics can be separated into local vibrational dynamics and hopping events between adjacent lithium sites. The derivative of the mean square displacement displays several characteristic time regimes. They can be directly mapped onto respective frequency regimes for the conductivity. In particular it is possible to identify time regimes dominated by localized dynamics and long-range dynamics, respectively. The question of time–temperature superposition is discussed for the mean square displacement and the incoherent scattering function.

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.

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.

Structure and dynamics of lithium silicate melts: molecular dynamics simulations

We present molecular dynamics simulations of lithium silicate melts (Li2O)x(SiO2)1−x with Li2O concentrations x = 0.01, x = 0.1 and x = 0.5 in equilibrium conditions for temperatures down to 1500 K. The partial pair correlation functions are determined and compared with recent experimental data. The dynamics of the individual species is characterized ia the mean square displacement. From the temperature dependence of the long-time diffusion constant we extract information about its activation energy. Interestingly, for x = 0.5 the extrapolation of the diffusion constant to temperatures below 700 K shows good agreement with experimental tracer diffusion data. In agreement with experiment, the length scale beyond which the dynamics becomes diffusive systematically varies with lithium concentration. Analysis of the van Hove self correlation function reveals how the occurrence of hopping processes as well as the presence of dynamic heterogeneities at low temperatures is correlated with the Li2O concentration.

Anion Rotation and Cation Transport in the Rotor Phase α -Sodium Orthophosphate: Paddle-Wheel Mechanism Redefined in View of New Experimental Results

The high-temperature phase of sodium ortho-phosphate, α -Na3PO4, is characterized by a dynamic rotational disorder of its polyatomic anions and, at the same time, by a considerable translational mobility of its cations. During the past decade, there has been considerable controversy about the question of whether both kinds of motion are dynamically coupled. To resolve this issue we have probed anionic and cationic motion individually over a wide range of experimental time scales. Coherent quasielastic neutron scattering as well as temperature-dependent 17O NMR lineshape and relaxation spectroscopy serve to characterize the rotational motion of the anions, whereas the cation motion is probed by high-frequency conductivity and 23Na NMR relaxation measurements. On the picosecond timescale, the combined interpretation of the neutron scattering and electrical conductivity data suggests strong dynamic coupling between the rotation of the phosphate groups about one of the four threefold P-O axes and the spatial fluctuations of nearby sodium ions. On more extended timescales, the NMR data indicate an additional, slower process, corresponding to dynamic jump reorientations of the C3 axis of rotation. This process appears to be coupled to the translational Na+ transport dynamics as suggested by a strong correspondence between the 17O and 23Na NMR relaxation characteristics and the electrical conductivities in the dc plateau region. The Na+ transport process can be viewed as highly correlated, not unlike the chain mechanism observed in AgBr.

Insights into Ion-Network Interactions and Ion Transport in Glass

Zusammenfassung We discuss the origins of mixed-former effects in borophosphate glasses of general composition: Li0.5BO1.75:(1−x)LiPO3 and 0.4 Na2O:0.6 [xB2O3:(1−x)P2O5], and show how these effects relate to changing ion-network interactions. In particular for the latter system, we analyse the permittivity spectra using the MIGRATION concept. The results show that the increase in the calculated “cage length” (spatial extent of localised ion motion) in the mixed former region correlates well with the increased abundance of the BO4 tetrahedra. We propose that more local cation sites are created and fast electronic bond-switching processes open up these sites to facilitate macroscopic transport. This picture of ion transport independent of network dynamics accounts for all favourable effects observed in mixed former glasses such as increase in ion mobility, rise in Tg and improvement in chemical durability.

Non-Arrhenius viscosity related to short-time ion dynamics in a fragile molten salt

The equation T x sigmaDC(T) = alpha x exp[--(E*/kappa(B)T)--gamma x exp(E*/kappa(B)T)] has been used to understand the non-Arrhenius behaviour of the DC conductivity in supercooled glass-forming melts. Here, alpha, gamma and E* are parameters, E* denoting the activation energy for an elementary displacive step. Unlike the empirical VTF relation, our equation provides a link between the long-time and the short-time ion dynamics as observed in broad-band conductivity spectra. Surprisingly, the same equation with the same value of E* but different gamma successfully describes the fluidity (inverse viscosity) of a fragile glass-forming melt. This opens up the possibility of relating non-Arrhenius viscosities to short-time properties, which is in agreement with recent experimental and computer-simulation results.

From Ostwald′s Times to Solid State Ionics: Migration and Localised Hopping of Silver Ions in Crystalline Rubidium Silver Iodide

Abstract Since Ostwald′s times, the concepts of ionic motion in condensed matter have been extended to comprise systems with increasingly complex dynamic properties. Today, one of the central problems in the field of SOLID STATE IONICS consists in finding simple, yet relevant rules for the correlated hopping motion of the mobile ions in structurally disordered ionic materials. Rubidium silver iodide, RbAg4I5, belongs to this class of materials. To analyse the hopping dynamics of the mobile silver ions in the three phases of RbAg4I5, we have taken conductivity spectra at frequencies up to the far infrared. Also, a simple set of rules for the development of the ion dynamics with time has been provided by the MIGRATION concept, the acronym standing for MIsmatch Generated Relaxation for the Accommodation and Transport of IONs. In the phases α and β, an increasing tendency for correlated forward-backward hopping is observed as the temperature is decreased from 298K to 129K. At the first-order β-γ phase transition at 121.8K, the number of translationally mobile silver ions is found to be markedly reduced. The conductivity spectra of the different phases of RbAg4I5 are well explained by the MIGRATION concept as long as the angular frequency does not exceed the elementary hopping rate of the mobile silver ions. At higher frequencies, an additional dynamic feature is encountered, which is superimposed onto the MIGRATION-type conductivity. This feature, which shows a nearly constant loss (NCL) behaviour, becomes increasingly pronounced as the temperature is lowered. It is caused by a strictly localised motion of interacting silver ions. In our model treatment for the MIGRATION and NCL parts of the dynamic conductivity, the potentially translational and the strictly localised ionic hopping motion are best described with a single elementary hopping rate. Consequently, this rate marks the beginning of the NCL behaviour on the angular frequency scale. This observation is in agreement with earlier results obtained by Leon et al. on solid lithium-ion conductors.

Backward correlations and dynamic heterogeneities: A computer study of ion dynamics

We analyze the correlated back and forth dynamics and dynamic heterogeneities, i.e., the presence of fast and slow ions, for a lithium metasilicate system via computer simulations. For this purpose we define, in analogy to previous work in the field of glass transition, appropriate three-time correlation functions. They contain information about the dynamics during two successive time intervals. First we apply them to simple model systems in order to clarify their information content. Afterwards we use this formalism to analyze the lithium trajectories. A strong back-dragging effect is observed, which also fulfills the time-temperature superposition principle. Furthermore, it turns out that the back-dragging effect is long ranged and exceeds the nearest-neighbor position. In contrast, the strength of the dynamic heterogeneities does not fulfill the time-temperature superposition principle. The lower the temperature, the stronger the mobility difference between fast and slow ions. The results are then compared with the simple model systems considered here as well as with some lattice models of ion dynamics.