Predicting Effective Transport Properties of Randomly Oriented Polycrystalline Li-Ion Battery Electrodes
Authors: Hoffman Robert M. , Taghikhani Kasra , Berger John R. , Kee Robert J. 
Published: August 2024

Widely practiced Li-ion battery models, such as pseudo-two-dimensional (P2D) models [1-3], use representative spherical electrode particles with assumed isotropic transport properties. Electrode particles, such as NMC, are typically composites that are comprised of numerous randomly oriented crystallites. Each of the single-crystal primary particles that compose secondary particle can have strongly anisotropic transport properties that affect the intercalation process. The empirically approximated effective properties (e.g., diffusion coefficients) as reported in literature vary by as much as six orders of magnitude. In many cases, the effective diffusion coefficients are determined as a part of a parameter-fitting procedure to represent battery polarization measurements.
The present approach develops both analytical and computational homogenization methods that derive effective properties based upon the intrinsic single-crystal properties of the crystallites. Homogenization techniques are computationally effective methods to predict macroscale behavior based on microscale properties.
As illustrated in Fig. 1, the computational approach begins by assembling over 1000 randomly oriented single-crystal primary particles, with each crystallite having anisotropic properties associated with the crystal lattice. The dodecahedron-shaped primary particles are tightly assembled into a secondary particle that is approximately spherical. A three-dimensional finite-element model predicts transient Li-intercalation fractions throughout a secondary particle during charge or discharge processes. In graphite, the transverse and normal diffusion coefficients differ by approximately six orders of magnitude. Based on the cut plane in Fig. 1, and despite extreme anisotropy within the crystallites, the homogenized macroscopic behavior is nearly isotropic.
The analytical approach extends a self-consistent method (SCM) for polycrystalline materials first presented by Ponte-Castañeda and Willis [4], which mathematically combines tensors describing diffusion pathways for every primary particle. The present study considers the concentration-dependent and anisotropic diffusion parameters collected by Persson et al. [5] and Zhou et al. [6] for graphite and NMC, respectively. Another homogenization method is the use of an orientation distribution function (ODF) [7], which predicts the effective diffusion parameters based on the statistical average of every possible primary particle orientation. Fig. 2 shows the predicted effective diffusion coefficients bounded by Hashin-Shtrikman bounds for anisotropic composites proposed by Willis [8] and the experimentally determined diffusion coefficients. The predicted effective diffusion coefficients are lower than the experimentally determined values in transverse direction but are significantly larger than the values in the normal direction. Additionally, the in-plane diffusion dominates the curvature of the predicted effective properties.
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Figure 1