Attempt Frequencies for Solid-State Ionic Conductivity from Statistical Analyses of Steady-State and Biased Molecular Dynamics Simulations

The attempt frequency characterizes the fundamental initiation of ionic transport. As such, it is an important parameter for both material design and coarse-grained methods, such as Monte Carlo simulations, attempting to approximate the practical performance of ionic conductors. The question of whether the attempt frequency corresponds to a well-defined vibration or to an ensemble-averaged quantity retains relevance despite decades of experimental and computational research. Here, we offer two methods of determining the vibrational attempt frequency from large-scale classical molecular dynamics simulations for fast ion-conducting materials with well-defined lattice sites, using β- and β”-aluminas as examples [1]. First, the statistics of hopping events bear signatures of their vibrational origin: ions are most likely to commit hops at well-defined periods of time, which empirically define the attempt frequency. Second, we simulate an excitation of ionic motion mimicking a pump-probe experiment: the attempt frequency can be distinguished by an anisotropic response of the material to its resonant excitation [1]. We find that parts of the vibrational density of states contribute unevenly to ion hops: some are nearly inactive, while others are responsible for the majority of hopping events. Furthermore, in materials with interstitialcy or knock-on hopping mechanisms, distinct frequencies can be responsible for initiating distinct mechanisms of hopping.<br/> <br/>[1] The Persistence of Memory in Ionic Conduction Probed by Nonlinear Optics, A.D. Poletayev, M.C. Hoffmann, J.A. Dawson, S.W. Teitelbaum, M. Trigo, M.S. Islam, A.M. Lindenberg, pre-print available at arXiv:2110.06522.