Solid State Nuclear Magnetic Resonance 22, 344–362 (2002) doi:10.1006/snmr.2002.0089 Two-Dimensional 109 AgNMRandRandom-WalkSimulationStudies ofSilverDynamicsinGlassySilverIonConductors M. Vogel, C. Brinkmann, H. Eckert, and A. Heuer 1 Institut f . ur Physikalische Chemie and SFB 458, Westf . alische Wilhelms-Universit . at, Schlossplatz 7, D 48149 M . unster, Germany FESTSCHRIFT IN HONOR OF PROFESSOR HANS-WOLFGANG SPIESS ON THE OCCASION OF HIS 60TH BIRTHDAY By applying one- and two-dimensional 109 Ag NMR, we demonstrate that silver diffusion in silver iodide/silver phosphate glasses is governed by a very broad, continuous distribution of correlation times Gðlg tÞ: As a consequence, over a wide temperature range, the 109 Ag NMR spectra can be described by a weighted superposition of a Gaussian and a Lorentzian where these line-shape components result from the slow and the fast silver ions in Gðlg tÞ; respectively. For the 109 Ag NMR two-time correlation functions F 2 ðtÞ; measured as a stimulated echo, a very stretched decay to F ss 2 ðt m Þ¼ 0 is observed. When fitting to a Kohlrausch function, exp½ðt=tÞ b ; a stretching parameter b  0:2 is found. The temperature dependence of the mean correlation time of silver dynamics is described by an Arrhenius law where the activation energy is consistent with the one reported for the dc conductivity s dc : In addition, it is shown that the effect of complex dynamical processes on NMR multi-time correlation functions can easily be calculated when performing random-walk simulations for schematic models such as the random-barrier model and the random-energy model. Based on these models it is possible to simulate various NMR observables and the mean square displacement, thus revealing the information content of multi-dimensional NMR experiments on solid ion conductors. # 2002 Elsevier Science (USA) 1. INTRODUCTION Solid materials with high ionic conductivity are technologically interesting for solid-state electrochemical devices such as batteries, fuel cells and chemical sensors [1]. Therefore, a large variety of solid ion conductors has been developed and several empirical rules have been established during the last decades relating composition and structure to ionic conductivity. For example, it is well known that the ionic conductivity increases rapidly when a network glass former is both modified by the addition of a metal oxide and doped with a metal halide salt. In this way, a room temperature dc conductivity s dc > 10 2 S=cm can be obtained. Further, it is clear that the macroscopic ionic diffusion results from thermally activated elementary jumps of mobile ions in a basically rigid matrix. However, a generally accepted theory for ion transport in solids is still missing. Thus, to come to an unambiguous decision on the various theoretical approaches experimental evidence on a microscopic level is required. In particular, it is important to address the origins 1 To whom correspondence should be addressed. 344 0926-2040/02 $35.00 # 2002 Elsevier Science (USA) All rights reserved.