Effects of electrode particle morphology on stress generation in silicon during lithium insertion

We study the effects of particle morphology and size on stress generation during Li insertion into Si particles using a fully coupled diffusion-elasticity model implemented in a finite element formulation. The model includes electrochemical reaction kinetics through a Butler–Volmer equation, concentration-dependent material properties, and surface elasticity. Focusing on two idealized geometries (hollow spheres and cylinders), we simulate stresses during Li insertion in Si. These systems describe a wide variety of morphologies that have been fabricated and studied experimentally, including particles, nanowires, nanotubes, and porous solids. We find that stresses generated in solid particles during Li insertion decrease as particle radii decrease from μm-scale, but reach a minimum at about 150 nm. Surface stresses then begin to dominate the stress states as the particle size continues to decrease. The minimum occurs at larger radii for hollow particles. We also find that hollow particles experience lower stresses than solid ones, but our results suggest that there is not a significant difference in maximum stress magnitudes for spherical and cylindrical particles. Studying the influence of concentration-dependent elastic moduli we find that while they can significantly influence stress generation for potentiostatic insertion, their role is minimal when surface reaction kinetics are considered.

► A fully coupled diffusion-elasticity 3D finite element model for battery electrodes is developed.
► Stress generation during first insertion of Li into Si is considered.
► Influence of concentration dependent elastic constants is studied.
► Influence of surface stress is studied and its role on the stress evolution discussed.
► Optimal morphologies and particle sizes are identified.