Effects of Cell Size and Structure on Li+Diffusion in Llzo: Insights into the Nature of Grain Boundary Diffusion
Authors: Grieder Andrew , Heo Tae Wook , Akhade Sneha A , Wood Brandon C. , Adelstein Nicole 
Published: February 2020

The garnet Li7La3Zr2O­12is a promising candidate as a solid electrolyte due to its stability and fast lithium diffusion. Grain boundaries have been shown to impede Li+conductivity in Li7La3Zr2O­12.1To investigate the origin of slow grain boundary diffusion a lithium deficient system Li6.75La3Zr2O­12(LLZO) was studied. An LLZO system with Frenkel defects, and an amorphous system were used as proxies for the grain boundary diffusion in classical molecular dynamics (CMD) simulations. CMD simulations were performed on a variety of cell densities in crystalline and disordered LLZO systems, especially because the grain boundary is likely to be less dense than the bulk. There are a wide range of misorientation angles so disordered systems were used as a proxy for diffusion in the grain boundaries instead of simulating highly symmetric grain boundaries. We find that the disordered system has pockets with more free volume that trap Li-ions, slowing diffusion. Results from the crystalline simulations confirm that lower density and thus more free volume decreases the rate of diffusion.
Activation energies and diffusion pre-factors were extracted from Arrhenius plots of diffusion at temperatures ranging from 500 K to 2000 K for systems with volumes ranging from 92% to 108% of the experimental cell density. The activation energies were found to decrease for higher density cells even though one could expect bottleneck effects at the transition state for Li+ diffusion. The activation energies for the disordered systems were found to be higher than the ordered systems. The pre-factor and activation energy of the ordered system increase abruptly when cell density is 94% of the experimental cell density.
To correlate the probability of diffusion events with higher density, Voronoi analysis using zeo++2and site analysis module Sitator3were used to quantify the size of pockets and transition state geometries.Voronoi analysis on the non-lithium sublattice reveals activation energy increases with larger diffusion channels. Site type analysis shows a correlation between long lithium residence times and larger site volumes. These results confirm that when lithium has more free volume it has slower diffusion. Furthermore, grain boundaries with densities less than crystalline LLZO can act as Li+traps slowing diffusion.
Activation energies and diffusion coefficients were used as inputs to a phase-field model of polycrystalline LLZO that determines the effective diffusion with bulk and grain boundary contributions. The effects of microstructure on effective diffusion were investigated by varying grain size, percent of grain boundaries, and grain shape. The results from different microstructures provides insight into diffusion around and through grain boundaries for the LLZO system.
(1) Tenhaeff, W. E.; Rangasamy, E.; Wang, Y.; Sokolov, A. P.; Wolfenstine, J.; Sakamoto, J.; Dudney, N. J. Resolving the Grain Boundary and Lattice Impedance of Hot-Pressed Li 7La 3Zr 2O 12Garnet Electrolytes. ChemElectroChem
2014,1(2), 375–378. https://doi.org/10.1002/celc.201300022.
(2) Willems, T. F.; Rycroft, C. H.; Kazi, M.; Meza, J. C.; Haranczyk, M. Algorithms and Tools for High-Throughput Geometry-Based Analysis of Crystalline Porous Materials. Microporous and Mesoporous Materials
2012, 149(1), 134–141. https://doi.org/10.1016/j.micromeso.2011.08.020.
(3) Kahle, L.; Musaelian, A.; Marzari, N.; Kozinsky, B. Unsupervised Landmark Analysis for Jump Detection in Molecular Dynamics Simulations. arXiv:1902.02107 [cond-mat]
2019.