A simple harmonic model as a caricature for mismatch and relaxation effects for ion hopping dynamics in solid electrolytes

We formulate a simple harmonic mean-field model with N+1 particles and analyse the relaxation processes following a jump of one of these particles. Either the particle can jump back (single-particle route) or the other N particles adjust themselves (multi-particle route). The dynamics of this model is solved analytically in the linear response regime. Furthermore we relate these results to a phenomenological approach by Funke and coworkers (concept of mismatch and relaxation: CMR) which has been successfully used to model conductivity spectra in the field of ion dynamics in solid electrolytes. Since the mean-field model contains the relevant ingredients of the CMR-approach, a comparison of the resulting rate equations with the CMR-equations becomes possible. Generalizations beyond the mean-field case are discussed.Comment: 28 pages, 9 figures, to be published in JC

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 in 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.Comment: to be published in Phys. Chem. Chem. Phy

Erforschung der Dynamik fester Ionenleiter mittels Computersimulationen am Beispiel von Lithiumsilikatgläsern

Im Rahmen der Dissertation wurden Molekulardynamiksimulationen ionenleitender Glaeser der Zusammensetzung x Li2O (1-x) SiO2 (x=0,5; 0,1) bei verschiedenen Temperaturen zwischen 640 K und 1240 K durchgefuehrt. Mittels geeigneter Zweizeitenkorrelationsfunktionen wurde die komplexe Ionendynamik charakterisiert. Eine wichtige Rolle kommt hierbei der Funktion w(t) = (d/dt) zu, die ueber die Theorie der linearen Antwort mit der frequenzabhaengigen Leitfaehigkeit sigma(nue) verbunden ist. Die Hin- und Rueckdynamik sowie dynamische Heterogenitaeten der Lithiumionen wurden mithilfe geeigneter Dreizeitenkorrelationsfunktionen untersucht. Die Arbeit beinhaltet zudem ein detailliertes Studium der Zusammenhaenge zwischen Netzwerk- und Lithiumdynamik. Beispielhaft hierfuer wird der "Schiebetuer"-Mechanismus vorgestellt. Schliesslich wurde die Ionendynamik unter dem Einfluss starker elektrischer Felder studiert