Finite Volume Modelling of Li-Ion Composite Cathodes Based on Micro-Scale X-Ray Computed Tomography
Authors: Le Houx James , Kramer Denis 
Published: May 2020

INTRODUCTION

Mathematical models have been used to simulate the physical and electrochemical processes occurring inside batteries in order to aid understanding and design. Newman et al. developed one of the most popular lithium ion battery models based on the porous electrode and concentrated solution theory. Newman’s pseudo-2D (P2D) model assumes that the porous electrode is made of equally sized, isotropic, homogenous spherical particles. It has been shown that battery electrodes are actually very heterogeneous structures [1] and therefore more complex approaches are required in order to fully characterise the transport processes occurring within the battery.
This work uses an open-source, data-driven, image-based modelling framework, OpenImpala, that is capable of modelling lithium-ion battery electrodes.

METHODOLOGY

A number of different imaging techniques are capable of providing electrode data, namely: scanning electron microscopy (SEM), focussed ion beam scanning (FIB) and x-ray computed tomography (CT). SEM techniques reach suitable resolutions (~0.5 nm) however they only provide 2D data, therefore they cannot capture the full 3D volume of the electrode. FIB scanning uses a beam of positively charged ions to mill away the surface of the target and so is a destructive method, therefore in-situ testing or re-testing of a battery would not be possible. State of the art CT scanners can achieve sub-micron resolutions whilst being a non-destructive method [2], for these reasons CT imaging was chosen.
Finite element based models have been used extensively to simulate lithium-ion batteries [3] however they have been shown to be computationally expensive to mesh the image data. Finite difference/volume schemes use a regularly discretised mesh and are usually quicker to implement, as the voxel dataset can be used directly, but they can result in approximation errors. Adaptive mesh refinement (AMR) is a technique used in finite difference and volumes schemes to refine or coarsen the grid around regions of sensitivity, both spatially and temporally. This is a technique that allows for quick implementation of the mesh whilst retaining accuracy.
The electrodes imaged were Lithium Iron Phosphate (LFP) samples on an aluminium foil substrate, originally made for a Lithium ion battery.
Two scans were performed using the Zeiss 160 kVp Versa 510 at the University of Southampton. The first with a 15 s exposure time and 2401 projections across an image angle of ±180°, using a 20x optical magnification to capture a voxel size of 801 nm.
The second with a 50 s exposure and 3201 projections, using a 40x optical magnification to capture a voxel size of 400 nm. Both used a voltage of 80 kV and a power of 6 W,the power was slightly higher than usual in order to better resolve the image. The two scans were both carried out on the same sample and using the same focal point, this is so they could be used as a direct comparison to see how porosity and tortuosity values changed with spatial resolution.

RESULTS AND DISCUSSION

It is found that the Bruggeman correlation significantly underestimates the tortuosity factor compared to the OpenImpala calculated results. It is also found that there is a larger stochastic variance in the 801 nm results, whereas the 400 nm results have a much smaller standard deviation.

CONCLUSIONS AND FUTURE WORK

This work has made use of a single-physics, image-driven computational model, OpenImpala. A comparison of resolution study was carried out to see how this affects results obtained, and these were then compared the Bruggeman relation. Work is ongoing to to fully expand the model to multi-physics simulations.

REFERENCES

1. Tjaden, B., Cooper, S. J., Brett, D. J., Kramer, D., & Shearing, P. R. (2016). On the origin and application of the Bruggeman correlation for analysing transport phenomena in electrochemical systems. Current opinion in chemical engineering, 12, 44-51.
2. Ojha, M., Le Houx, J., Mukkabla, R., Kramer, D., Wills, R. G. A., & Deepa, M. (2019). Lithium titanate/pyrenecarboxylic acid decorated carbon nanotubes hybrid-Alginate gel supercapacitor. Electrochimica Acta, 309, 253-263.
3. Kashkooli, A. (2016) Multiscale Modeling of lithium-ion battery electrodes based on nano-scale X-ray computed tomography, Journal of Power Sources 307 496-509