April 23, 2021

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Atomic Modeling

   Philipp Maass specializes in the use of theoretical modeling and simulation techniques to examine the atomic level details of ion dynamics in ion conducting glasses. His group has developed new analytical schemes to combine percolation concepts with theories for dispersive ion transport in glasses and has expertise in various computer simulation techniques of disordered materials. Maass’ students will model and simulate these MGF glasses with the goal of developing detailed atomic level understanding of the structures and dynamics of the ion motions in these glasses.

      In the theoretical modeling, a multi-scale approach will be used to bridge time scales from picoseconds, where vibrational motions of the network and mobile ions govern the dynamics, to microseconds, where thermally activated jump processes of the mobile ions determine the long-range transport properties. We will use XRD (CMU) and ND (Chalmers) data to generate glass structures by RMC modeling to perform a bond-valence analysis identify of diffusion pathways for the mobile ions. This will be followed in close connection with the experiments, using them as input and test for the modeling and providing results and predictions for comparison with measurements.

       The multi-scale approach starts with ab-initio calculations of small clusters of the glass compositions. Geometrical optimizations for clusters of ~100 network and modifying ions are now possible based on electronic ground state calculations on our massive parallel computing cluster MaPaCC at Ilmenau. In a recent collaboration with the group at Chalmers, where a research student of the PI stayed 5 months at Gothenburg and carried out both Raman measurements and electronic structure calculations for special glass systems, it was shown that geometrical optimization of cluster structures with the software “Gaussian” gave vibrational properties that compared well with Raman and IR spectra. These provide a very sensitive validation test. Analogous calculations will be done for all ternary MGF systems prepared at ISU. Optimized cluster geometries will be validated by comparison with the IR and Raman spectra (ISU) and the structural information obtained from NMR (Munster). In the next step, the validated cluster configurations will be used to systematically develop potential models for MD simulations. In the literature, good results have been obtained for alkali network glasses when applying potential models that are composed of Coulomb interactions associated with fractional charges and Born-Mayer repulsive terms between all distinct pairs of ions in the system. In a few cases, additional three-body terms have been used to reproduce correctly the fraction of trigonal and tetrahedral borate units. Optimal parameter sets in such potential models for MGF systems have not been calculated yet. We will determine them by fitting the electronic energy landscape of the optimized cluster configurations for collective displacements along their normal mode directions and by comparison with structural data (as well as elastic constants) of corresponding crystal structures where these are available.

       Based on the potential models, MD simulations will be conducted for the MGF glasses. Structure factors calculated from equilibrated configurations will be compared with the XRD (CMU) and ND (Chalmers) data. This will determine if the intermediate range order is well captured by the potential models. Because of computational limits, calculations of the ion dynamics based on MD simulation are restricted to temperatures not too far below Tg. Diffusion coefficients of the mobile ions (Li and Na) and associated conductivity spectra (Munster) can be compared to the results from impedance spectroscopy (ISU) and radioactive tracer measurements (Cornell).  It is expected that the MGFE may be well reproduced through the careful development of the relevant potential models. To explore the underlying mechanisms of the MGFE, a subsequent analysis of the sites and diffusion paths of the mobile ions in the simulations will be performed. In this way, the local number density of the mobile ions will be determined. Connected regions (sites) of high number density as well as diffusion pathways (critical paths) are identified by applying methods borrowed from percolation theory. These regions will be compared with corresponding regions obtained from RMC models (Chalmers) in connection with bond valence analyses. Both sites and diffusion pathways can be further characterized with respect to their energetics. Using the information thus obtained we will be able to study the origin of the MGFE in detail. For example, we can investigate if preferred pathways with enhanced mobility are emerging at spaces with mixed local environments of network former units (“mixed interfacial regions”).  

      The dependence of the enhancement effect on the mixing ratio may then be attributed to the formation of percolating paths of these mixed interfacial regions. Alternatively, the MGFE may be caused by changes in site and barrier energies for jump processes on a local scale. It is possible that the different behaviors found for the mixing of network forming cations and of network forming anions are related to different mechanisms. For the study of such questions valuable information is provided also by impedance spectroscopy (ISU and Münster), where the strength of the MGFE is quantified by its dependence on frequency.

     In the last step of the multi-scale approach, effective jump models on a coarse grained scale will be developed based on the energetics and topology of the ionic sites and diffusion paths identified in the MD simulations These coarse-grained models have several benefits: (i) They allow the study of ionic transport behavior at low temperatures by MC simulations of the hopping motion of the mobile ions.  (ii) They reduce the complexity of the problem to a few essential features and are simple enough to apply analytical methods, as, for example, effective medium theories for the calculation of dispersive transport properties and percolation theory for the calculation of activation energies of long-range ion mobilities (a combination of these methods provides a unified analytical description of the ion dynamics at long and short times. Simple laws will be explored and reasoned in this way , e.g. the decrease of the conductivity activation energy with increasing modifier content and universal scaling features in conductivity spectra. (iii) They allow the characterization of specific materials properties in terms of only a few key parameters, here the MGFE will be the focus in this proposal.  Ilmenau will support one post-doctoral fellow and two undergraduate students to carry out their research.