OPEN source IMage based PArallelisable Linear Algebra

1. OPEN source IMage based PArallelisable Linear Algebra James Le Houx, Denis Kramer

2. Contents • Introduction • Types of Battery Model • Overview of Li-ion battery • Motivation • Newman Pseudo 2D • Bruggeman Correlation • Methodology • Imaging • Postprocessing • OpenImpala • Overview, Results • Challenges • Conclusions

3. Introduction Battery Modelling Newman Pseudo 2D μm mm nm cm Atomistic Single Particle models Density Functional theory Equivalent circuit models

4. Introduction Overview of Lithium Ion Battery Load Charge Cu Current Collector Al Current Collector Discharge Separator Negative Electrode Positive Electrode Positive electrode active material Negative electrode active material Li-ion

5. Introduction Tortuosity Direction of Diffusion

6. Motivation Homogenised Newman Model Load Load Charge Charge Cu Current Collector Cu Current Collector Al Current Collector Al Current Collector Discharge Discharge Separator Negative Electrode Positive Electrode Separator Negative Electrode Positive Electrode Homogenised positive electrode Homogenisednegative electrode Li-ion Positive electrode active material Negative electrode active material Li-ion

7. Motivation Bruggeman Correlation ≠ Figure 1: SEM image of a commercial lithium iron phosphate electrode [1] [1]: 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 [2]: 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.

8. Motivation Tortuosity Factor Figure 1: Comparison of 8 different methods used to calculate tortuosity factor, the presented model is Taufactor [1] [1]: Cooper, S., Bertei, A., Shearing, P., Kilner, J. & Brandon, N. (2016) Taufactor: An open-source application for calculating tortuosity factors from tomographic data, SoftwareX vol. 5, pp. 203-210

9. Methodology Imaging Methods Voxel Size: 70nm Pixel Detector : 2048 x 2048 Figure 1: Photograph of the University of Southampton’s Zeiss 160 kVp Versa 510 [1] [1] Zeiss 160 kVp Versa 510, μVis, https://www.southampton.ac.uk/muvis/about/equipment/versa.page Date Accessed: 10/06/18

10. Methodology Image-Based Modelling • Obtain tomography of electrode structure Air TiO2 Carbon Polymer 50μm Figure 1: Individual tomographic slice of a TiO2 layer on a carbon polymer substrate, voxel size of 481nm

11. Methodology Image-Based Modelling • Obtain tomography of electrode structure • Threshold the data into regions of interest through post-processing 50μm Figure 1: Volumetric rendering of a thresholded TiO2 layer on a carbon polymer substrate, ~108 voxels, size of 481nm

12. Methodology Image-Based Modelling • Obtain tomography of electrode structure • Threshold the data into regions of interest through post-processing • Use segmented dataset in modelling Figure 1: Electrode data segmented into 2 phases; blue for liquid phase, red for solid phase

13. Motivation TauFactor Figure 1: Report generated from running TauFactor[1] [1]: Cooper, S., Bertei, A., Shearing, P., Kilner, J. & Brandon, N. (2016) Taufactor: An open-source application for calculating tortuosity factors from tomographic data, SoftwareX vol. 5, pp. 203-210

14. Methodology OpenImpala

15. Methodology OpenImpala

16. Methodology OpenImpala

17. Results Lithium Iron Phosphate CT Resolution Comparison Figure 1: 3D visualisation of the concentration gradient across an LFP electrode sample under steady state diffusive flow.

18. Results Scaling Results Figure 1: Time taken to solve diffusion equation on an LFP electrode ~3 x 107 voxels • Figure 2: Parallel efficiency to solve diffusion equation on an LFP electrode ~3 x 107voxels

19. Challenges Image Resolution Figure 1: CT of an LFP electrode detailing (a) the mounting, (b) the region of interest; 801 nm voxels scans of (c) raw data, (e) equalised and filtered data, and (g) 2-phase thresholded data; and 400 nm voxel scans (d), (f) and (h) of the same sub-volume

20. Challenges Image Resolution • Tortuosity in y direction is averaged at 1.52 • Tortuosities in x and z are averaged at 1.87 and 1.72 respectively Figure 1: Comparison of the variance of calculated direction averaged tortuosity factor for 6 subvolumes of the LFP electrode for 801 nm and 400 nm voxel size, and the Bruggeman method.

21. Future Work Where does this fit in? Newman Pseudo 2D μm mm nm cm Atomistic Single Particle models Density Functional theory Equivalent circuit models

22. Future Work Multiscale modelling Figure 1: A heterogeneous periodic microstructure, Ω0, featuring three distinct phases, and the corresponding homogenised material with effective transport properties [1]

23. Future Work Future Work • Development of OpenImpala to multi-physics capability • Comparison of accuracy to more established methods • Adaptive mesh functionality to improve speed of solution • Build up a userbase/ work out the needs of the community

24. Conclusions • OpenImpala provides a computational platform to determine transport properties from imaged microstructures • Early parallelisation results are very promising • There remain a number of challenges in the field, namely effect of image resolution and speed and accuracy of calculation

25. Mailing listopenimpala.kramergroup.scienceAny questions?