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 mu m-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. (C) 2011 Elsevier B.V. All rights reserved.