Understanding the Li Disorder and Migration in Cubic Garnet Ionic Conductors through Diffraction Techniques and Computer Modeling
Authors: Wang Yuxing , Klenk Matt , Lai Wei 
Published: February 2020

Solid-state lithium ionic conductors have received much attention recently as the issues associated with liquid electrolyte materials were increasingly recognized. Lithium garnet ionic conductors emerged as the most promising candidate in the oxide system owing to their high conductivity and good chemical and thermal stability [1, 2]. Majority of the research done on this family of compounds focused on the characterization of transport properties on a wide range of compositions with different doping strategy [3, 4], leaving a void of knowledge on the conduction mechanism. The limited number of structural studies [5, 6] typically employed a single technique. The lack of cross-check with other techniques left the findings vulnerable to challenges on the ground of limitations of individual technique.
To understand local Li disorder and conduction pathway, we applied various diffraction and computational techniques to the lithium garnet oxides. The model material Li5La3Ta2O12 was picked because of its relative simplicity. Diffraction based techniques employed in this study include Rietveld refinement using time-of-flight neutron powder diffraction data, pair distribution analysis using total scattering data and maximum entropy analysis using constant wavelength neutron diffraction data. Static and dynamic structures were modeled with energy minimization method and molecular dynamics using conventional interatomic potentials. Rietveld refinement results revealed large anisotropic displacement factors on both tetrahedral and octahedral Li sites, suggesting strong positional disorder. Nuclear density map as calculated from maximum entropy analysis added more details to the lithium distribution. We adopted the iterative algorithm to minimize the structural biases. At low levels, the densities at the tetrahedral and octahedral sites connected, indicating the conduction pathway. This was confirmed by the modeled static structure where low energy state positions were represented by nuclear density maps obtained using a statistical approach. Pair distribution function analysis using reverse Monte Carlo modeling provided experimental evidence of the local structures and Li disorders. The positional disorders of both Li sites were further confirmed and the occupancies were in good agreement with Rietveld refinement results. Note that this is the first PDF analysis on garnet compounds so far and we proved that useful information can be extracted with this method despite the challenges as posed by the structural complexity and small scattering contribution from Li. Finally, the MD modeling simulated the conduction pathway of Li which is consistent with the indication of other techniques. To sum up, all the techniques tell one consistent story: positional disorders are so strong that the Li ions in Li-stuffed garnet compounds can be consider as composing an amorphous phase (i.e., having no symmetry at all) within a high symmetry framework; both tetrahedral and octahedral sites are involved in the conduction and the conduction pathway can be represented by connecting neighboring tetrahedral and octahedral Li sites.

Figure 1. Nuclear density maps generated by (a) Rietveld refinement, (b) maximum entropy method, (c) energy minimization, (d) molecular dynamics; (e) experimental and fitted pair distribution functions.
Acknowledgement
This work is supported by the Ceramics Program of National Science Foundation (DMR-1206356). We are grateful to Spallation Neutron Sourse at ORNL, Lujan Neutron Scattering Center at LANL and NIST Center for Neutron Research for making all facilities available. We wish to acknowledge the Michigan State University High Performance Computing Center and the Institute for Cyber-Enabled Research for access to their computing resources.
References
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