On the Representativity of Electrode Microstructure Parameters and Their Electrochemical Response for Lithium Ion Batteries
Authors: Usseglio-Viretta Francois L. E. , Colclasure Andrew M. , Allen Jeffery M. , Finegan Donal P. , Graf Peter , Smith Kandler 
Published: August 2024

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the microstructure analysis. A microstructure scale electrochemical model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell [1]. To evaluate the representativeness, and thus relevance, of these model predictions, a coupled representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response [2].
Electrode microstructure parameters representativeness has been first quantified using the representative volume element (RVE) methodology [3]. The RVE major flaw is that ultimately it can only conclude if a FOV contains representative subvolumes of the FOV, but not if the FOV itself is representative of the electrode volume. Analysis can conclude negatively (“FOV is not representative”), but not positively (“FOV is representative”). One major contribution of this work was to quantify the convergence of the RVE size with the FOV, to actually investigate the FOV representativeness and thus partly remedy this intrinsic limitation. The analysis determined that performing a standard RVE calculation, without exploring its FOV convergence, is likely to strongly underestimate the actual RVE size (cf. Fig. 1). The new RVE methodology has been automated in the NREL open-source Microstructure Analysis Toolbox (MATBOX) and is available to the battery community* [4].
Representativeness of microstructure parameters is however only an intermediate step, as the end-results of an electrochemical model are performances predictions. Indeed, what is the practical consequence of a given deviation for a microstructure parameter? The microstructure parameter deviation propagations to the 3D microstructure scale electrochemical response have been then quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Such deviation propagation analysis is analogous to error propagation analysis and is necessary to determine the relevance of microstructure scale model predictions for macroscale predictions. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Therefore, we introduced the novel concept of electrochemical RVE (eRVE) that is a function of the operating conditions (thus defined as a dynamic RVE), with an increasing dependence with the C-rate. Representativity analysis of the investigated cell determined a FOV of 144.4 ×154.4 µm2 is large enough to establish a convergence on the representative section areas for low to intermediate C-rate (≤2.5C), but not large enough to conclude for higher rates.
This work aims to emphasize the importance of representativity analysis for LIB electrode microstructures, as it is required to estimate the error, and thus the relevance, of microstructure parameters intended to be used in macroscale models. The methodology and results can help researchers to select the relevant imaging and associated FOV required to provide accurate enough microstructure parameters.

*New features will be released after article [2] publication.

[1] F. L. E. Usseglio-Viretta, A. M. Colclasure, J. Allen, D. P. Finegan, P. Graf, K. Smith, Microstructure Scale Lithium-ion Battery Modeling, Part I: on lithium plating prediction and heterogeneity, in preparation.
[2] F. L. E. Usseglio-Viretta, A. M. Colclasure, J. Allen, P. Graf, K. Smith, Microstructure Scale Lithium-ion Battery Modeling, Part II: on the representativity of microstructure parameters and electrochemical response, in preparation.
[3] T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. of Solids and Structures, 40 (2003) 3647–3679.
[4] F. L. E. Usseglio-Viretta, P. Patel, E. Bernhardt, A. Mistry, P. P. Mukherjee, J. Allen, S. J. Cooper, J. Laurencin, K. Smith, MATBOX: An Open-source Microstructure Analysis Toolbox for microstructure generation, segmentation, characterization, visualization, correlation, and meshing, SoftwareX, 17 (2022) 100915.

Figure 1