Generating multi-scale NMC particles with radial grain architectures using spatial stochastics and GANs

TL;DR

The paper tackles the challenge of linking particle-level morphology and inner grain architecture to Li-ion cathode performance by developing a two-scale, stereological generative framework. It combines a spherical-harmonics-based outer-shell model for 3D particle shapes with a GBPD-based inner-grain tessellation model, calibrated via a GAN-driven stereological fitting procedure that learns from 2D EBSD data and 3D nano-CT data. The approach enables rapid generation of statistically representative 3D NMC811 particles and provides a public dataset of simulated morphologies suitable for chemo-mechanical simulations. This work advances material characterization by enabling fully virtual testing of multi-scale microstructures, with potential to inform electrode design and degradation modeling at scale. It also demonstrates how 2D measurements can robustly constrain 3D microstructures through differentiable, interpretable tessellations and targeted data augmentation.

Abstract

Understanding structure-property relationships of Li-ion battery cathodes is crucial for optimizing rate-performance and cycle-life resilience. However, correlating the morphology of cathode particles, such as in NMC811, and their inner grain architecture with electrode performance is challenging, particularly, due to the significant length-scale difference between grain and particle sizes. Experimentally, it is currently not feasible to image such a high number of particles with full granular detail to achieve representivity. A second challenge is that sufficiently high-resolution 3D imaging techniques remain expensive and are sparsely available at research institutions. To address these challenges, a stereological generative adversarial network (GAN)-based model fitting approach is presented that can generate representative 3D information from 2D data, enabling characterization of materials in 3D using cost-effective 2D data. Once calibrated, this multi-scale model is able to rapidly generate virtual cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations. A large dataset of simulated particles with inner grain architecture has been made publicly available.

Figures (11)

• Figure 1: Subsequent data-preprocessing steps for modeling the outer shell of NMC particles: a) Planar section of 3D nano-CT data. b) Segmentation of the planar section shown in a). c) 3D rendering of voxel-based particle representation. d) Star-shaped representation of particles displayed in c). e) Spherical harmonics-based representation of particles shown in d). f) simulated particles generated by the stochastic outer shell model (explained in Section \ref{['sec:outer_shell']} below).
• Figure 2: Orientation of grain planar sections: The orientation angle $\alpha$ of a grain is computed via its first principal component $v_1$ and its center $c$ (first column from the left). The angle distribution of each EBSD planar section is determined by kernel density estimation, using symmetric boundary conditions. The curves in black correspond to retained data, whereas the gray curves correspond to neglected data (third column). Two exemplary grain architectures of retained and neglected planar section data are shown (second and fourth columns).
• Figure 3: Empirical distance correlation coefficient (edcc) between $a_{00}$ and $a_{\ell m}$ of nano-CT data (left), and plots of further exemplary data with corresponding empirical correlation coefficients (right), where the values above the plots are the edcc and the Pearson correlation coefficient, respectively. Values of edcc that are close to 0 and 1 indicate weak and strong dependence, respectively.
• Figure 4: Distribution of spherical harmonics coefficients: The blue histograms depict the distributions of coefficients $a_{\ell m}$ across different orders $\ell$, while the red curves represent the probability densities of the fitted parametric distributions. In particular, for the case where $\ell=0$, a log-normal distribution is fitted, while in the other cases, Student's t distributions are used.
• Figure 5: Architectures of neural networks: a) Fully connected architecture of marker generator $G_\mathrm{net}$ being part of $G$. b) Convolutional architecture of discriminator $D$. The numbers above the arrows and bars correspond to the dimensions of respective inputs/outputs and convolutional layers.