Three-dimensional modeling of commercial battery anode microstructures

A three-dimensional theoretical and numerical framework was developed to understand the processing-induced randomness and microstructural interactions of rechargeable lithium-ion batteries. By starting from graphite anode microstructures extracted from X-ray tomography data the effects of the individual features on the electrochemical and mechanical reliability during galvanostatic recharge are quantified. Spatially resolved electrochemical calculations show that for dense porous electrodes: a) spatially connected porosity combined with internal surface roughness increases the macroscopic capacity of the cell; b) isolated porosity decreases the local conductivity, diffusivity, and charge capacity of the system; and c) fully dense regions are effective obstacles for charge transport at large C-rates. A combined statistical and visualization analysis identifies surface morphological features with a small radius of curvature and porosity bundles as favorable locations for dendritic growth. Simulations also show that lithium accumulation induces low electrochemical potential values and compressive stresses in those surfaces exposed to spatially connected porosity, while tensile stresses develop in surfaces exposed to electrochemically isolated porosity and fully dense regions, which in turn, favor crack initiation. The crystallographic anisotropy of graphite favors stress localization at grain corners and boundaries, particularly for large grain boundary misorientations. Simulations demonstrate that battery reliability can be improved by controlling the radius of curvature of features and the minimization of the occurrence of pore bundles. The acquired scientific experiences were abstracted into an analytical framework to validate and extend widely accepted porosity-tortuosity relations. The proposed framework enables the derivation of analytical expressions by starting from the volume fractions of the constitutive components. Experimentally measured tortuosities are rationalized through the relation developed herein, τ=1/(ϵυ)1/2 in the Bruggemann limit