Competition Between Lithiation-Induced Stress and Concentration Gradients in 3D Geometries

A comprehensive understanding of electro-chemo-mechanical (ECM) phenomena in solid-state batteries (SSBs) requires not only theoretical models, but validation of the models by direct measurement in well-defined geometries. We will highlight a few intriguing results using 3D models of SSBs and measurements on thin film electrodes, which motivate novel methods for measuring local stress and Li concentration in situ. These results emphasize that the inclusion of ECM effects is essential in understanding the fluxes in 3D geometries.<br/> <br/>Using muti-physics modeling we have simulated the electrochemical behavior of a battery operating in the confined space of a nanopore. The 3D geometry produces large concentration gradients that affect the Li flux: rather than a conformal flux field, largely along the radial axis of the pore, the Li flows up and down the pore. However, the same geometry, when including electro-chemo-mechanical coupling, has entirely different behavior. Due to the stress gradients produced by the confined volume expansion of the cathode, the Li flux is further influenced, and achieves the fully conformal distribution that we expected from intuition.<br/> <br/>Experimentally, we have measured ECM coupling in two model systems using Si electrodes, whose electrochemical and mechanical properties are well known. We employed micro-Raman mapping to measure the shift in the Si peak, and ultimately translated that to a strain/stress profile in the electrode during lithiation. In single-crystal Si wafers we measured bi-axial stress maxima around 0.6 GPa, localized to the lithiation front, and post-mortem SEM shows lateral cracks that form at this same depth, causing delamination and breakdown the electrode. Furthermore, XPS depth profiles and EBSD cross sections show that the lithiation front is not sharp, as seen elsewhere in the literature. Due to ECM effects, the diffusion lengths in this experiment are 100x larger than predicted by concentration gradients alone.<br/> <br/>In subsequent experiments, using a square Si island approximately 10 µm on a side, dynamic stress profiles are measured. The Raman stress measurement is fast enough to be done in operando, allowing us to see transient stress states for comparison with models. Existing literature treated the cracking and delamination of these islands entirely from a mechanical perspective. Our ECM models, parameterized to the experimental observations, reveal that the origin of the failure is not simply mechanical, but due to a competition between Li concentration gradients and stress gradients.<br/> <br/>While the theory of ECM coupling is rather well studied, it's application in 3D geometries is not well explored. At the same time, validation of the theory is nascent in electrochemical systems, where material properties change dynamically with state of charge. Together, our models and experiments are providing the fundamental understanding of SSB performance required for next generation designs.