Stresses Due to Intercalation in Layered and Non-Spherical Lithium Storage Particles
Authors: Purkayastha Rajlakshmi , McMeeking Robert 
Published: February 2020

With an increase of the scope of use of the Lithium Ion batteries from small electronic devices to large automobiles, there has been a concomitant effort to increase both the capacity and lifetime of these energy storage devices. While newer materials such as silicon show a dramatic increase in energy densities and capacities, the large strains and resulting stresses within these particles lead to comminution and degradation of the particle. Experimental studies have shown that combining these materials with carbon nanotubes can help reduce these strains, mostly by using geometry to constrain the volumetric change of silicon particles. These, and other studies, highlight an important point: the effect of geometry on the intercalation of lithium ions into storage particles and the stress generated as a result are not very well understood. The goal of our current work is to study the effect of morphology of these storage particles on the stresses that are generated within.
In our previous work [1,2] we developed a coupled stress-diffusion model for lithium intercalation into a storage particle due to the volumetric expansion of the particle. We identified three non-dimensional parameters that govern the stress response of these particles, the non-dimensionalized current, the non-dimensionalized partial molar volume and the maximum lithiation strain. Our work shows that the effect of the stress on the concentration within the particle can be quite significant and we identified certain combinations of material parameters that would lead to a decrease in the maximum stresses in these particles. We now take this idea one step further by introducing the bilayer spherical particle. This particle consists of an inner sphere, which is coated with a layer of a second material. Our results show that by controlling the rate of diffusion within the layers certain material combinations can be beneficial for the inner sphere. We also conduct a basic fracture mechanics study in order to identify the material parameters at which we particle degradation would be most likely.
Due to computational considerations most models of intercalation particles tend to look at spherical particles. However most storage particles used in battery electrodes tend to be irregular in shape with sharp edges and extended aspect ratios. The change of the relative surface area to the volume of the particle can lead to a change in the stress response of the particle for the same material parameters. In order to study the effect of these edges on the stress response, we perform a parameter study on cubic particles as well as ellipsoidal particles with different aspect ratios. Our results show that a change in material properties can lead to differences in both the value of maximum stress as well as its location in the particle, due to the interplay of diffusion and stress responses. Our model highlights the fact that if storage particle geometry could be controlled by using the appropriate manufacturing techniques, then the stress response of the lithium intercalation particles can be improved.

R Purkayastha, R.M McMeeking ‘A Linearized Model of Lithium Ion Batteries and Maps for their Performance and Failure’, Journal of Applied Mechanics, 79 (2012) 031021.1 – 031021.16

R. Purkayastha, R.M. McMeeking, ‘A Parameter Study of Intercalation of Lithium into Storage Particles in a Lithium-Ion Battery’ Computational Materials Science, 80 (2013) 2-14