Source-linked AI summary
Cracking predictions of lithium-ion battery electrodes by X-ray computed tomography and modelling
Adam M. Boyce, Emilio Martínez-Pañeda, Aaron Wade, Ye Shui Zhang, Josh J. Bailey, Thomas M. M. Heenan, Dan J. L. Brett, Paul R. Shearing
TL;DR
Fracture contributes to capacity fade and reduced battery lifespan, but prior fracture analysis of image-based electrodes was limited to a single idealized particle. This study combines CT imaging, electro-chemo-mechanical modeling, and phase-field fracture to predict damage in a realistic electrode, with the model predicting significant fracture within the electrode.
Problem
Prior fracture analysis of image-based electrodes was limited to a single idealized particle, despite electrode cracking contributing to capacity fade and reduced battery lifespan.
Source: §1 · pp. 2, 5Method
The study combines advanced imaging, electro-chemo-mechanical modeling, and a phase-field fracture framework to predict damage in a realistic electrode.
Source: §1 · p. 5Results
The model predicts significant fracture within an electrode.
Source: §5 · p. 19Takeaways & Limitations
The framework extends fracture prediction from idealized particles to an entire realistic electrode.
Source: §1 · p. 5Individual-particle fracture observations are not explored in detail, limiting the depth of particle-level interpretation.
Source: §5.6 · p. 32
Abstract
from arXiv · showhide
Fracture of lithium-ion battery electrodes is found to contribute to capacity fade and reduce the lifespan of a battery. Traditional fracture models for batteries are restricted to consideration of a single, idealised particle; here, advanced X-ray computed tomography (CT) imaging, an electro-chemo-mechanical model and a phase field fracture framework are combined to predict the void-driven fracture in the electrode particles of a realistic battery electrode microstructure. The electrode is shown to exhibit a highly heterogeneous electrochemical and fracture response that depends on the particle size and distance from the separator/current collector. The model enables prediction of increased cracking due to enlarged cycling voltage windows, cracking susceptibility as a function of electrode thickness, and damage sensitivity to discharge rate. This framework provides a platform that facilitates a deeper understanding of electrode fracture and enables the design of next-generation electrodes with higher capacities and improved degradation characteristics.
1. Introduction
Electrode fracture can degrade battery capacity and lifespan, while prior fracture analysis of image-based electrodes was limited to a single idealized particle. This study combines 3D X-ray CT imaging, electro-chemo-mechanical modeling, and phase-field fracture to predict damage in a realistic electrode.
1. Introduction
- Pre-existing voids and cracks promote particle fracture, which can disintegrate particles and reduce usable energy-storage volume.Cracked surfaces can also accumulate SEI, while particle or electrode disconnection can cause electrical isolation.Source: §1 · pp. 2–3
- Fracture can begin within primary particles, at grain boundaries, or at pre-existing defects; this study focuses on large synthesis- and manufacturing-related voids and cracks.The authors regard these defects as likely drivers of much electrode damage because they are typically larger than primary-particle and grain-boundary features.Source: §1 · p. 3
- Electro-chemo-mechanical interactions and electrode heterogeneity make realistic, microstructure-level fracture prediction important for understanding degradation.The introduction notes comparatively little work combining electro-chemo models with mechanics at the image-based micro-scale.Source: §1 · pp. 2, 4
- The proposed framework combines 3D X-ray CT imaging, electro-chemo-mechanical modeling, and phase-field fracture to predict damage across an entire realistic electrode.The study moves beyond the single-idealized-particle limit of prior image-based electrode fracture analysis.Source: §1 · p. 5
- The authors present the framework as a means to study how electrode morphology, particle position, and cycling relate to fracture, supporting design of higher-capacity electrodes with improved degradation characteristics.The modeled electrode includes active particles, the PVDF-carbon-binder composite, and interactions with the current collector.Source: §1 · p. 5
2. Theoretical framework
This section presents a coupled electrochemical, mechanical, and phase-field fracture framework for an X-ray CT-based electrode microstructure, including charge transfer and carbon binder domain transport. It also specifies boundary conditions at the current collector, separator, and particle interfaces, along with initial-state and insulation assumptions.
2. Theoretical framework
- The framework is applied to an image-based 3D electrode domain comprising active material, carbon binder, and electrolyte-filled micropores.The schematic distinguishes electron and lithium-ion flow in the half-cell.Source: §2 · p. 5, Figure 1 · p. 6
2.1 Electrolyte: electrochemical and transport formulation
- The electrolyte model accounts for lithium-ion diffusion, electric-field-driven migration, non-steady-state transport, and ionic current from conductivity and electrochemical activity.It assumes a binary 1:1 electrolyte with equal positive-ion and counterion concentrations and imposes charge conservation.Source: §2.1 · pp. 6–7
2.2 Active material: electro-chemo-mechanical and transport formulation
- Active-particle mechanics use small-strain, isotropic linear elasticity, while lithiation-induced strain contributes a hydrostatic stress state.The model describes stress through mechanical equilibrium and Hooke’s law.Source: §2.2 · pp. 7–8
2.2.1 Phase field fracture formulation
- The phase-field formulation predicts cracking by balancing elastic strain energy against fracture-surface energy, with a length scale characterizing the fracture process zone.A phase-field variable distinguishes cracked from uncracked material and represents stiffness degradation.Source: §2.2.1 · pp. 8–9
2.2.2 Solid-state transport
- Solid-state lithium flux follows Fick’s first law modified by hydrostatic stress, with transient particle transport, charge conservation, and electronic conduction also represented.Source: §2.2.2 · pp. 9–10
2.2.3 Charge transfer reaction
- Interfacial lithium insertion is modeled as a Butler–Volmer charge-transfer reaction, with diffusion-induced hydrostatic stress included in the overpotential.Source: §2.2.3 · pp. 10–11
2.3 Carbon binder domain: electrical, transport and mechanical formulation
- The carbon binder domain is assigned effective ionic and electronic transport properties, with bulk properties scaled by a porosity factor of 0.276.Its mechanics are assumed isotropic and linearly elastic under small strains, with perfect contact at particle and current-collector interfaces.Source: §2.3 · p. 11
2.4 Boundary and initial conditions
- At the current collector, the model applies a 1C-based current density and clamps displacement, while other surfaces remain mechanically free.The 1C current is calculated from active-material volume and the maximum accepted lithium quantity.Source: §2.4 · p. 12
- At the separator, electrolyte-salt flux, ionic current, and zero potential are prescribed, while electronic current is blocked across the separator–electrode interface.This interface condition permits only ionic current to cross between the separator and heterogeneous electrode.Source: §2.4 · p. 12
- At electrolyte–particle interfaces, lithium fluxes and current densities are prescribed to represent charge transfer between electrolyte and active particles.Source: §2.4 · p. 12
- The electrode starts with prescribed active-material and electrolyte concentrations in an unstressed state, and external domain surfaces are electrically and species-flux insulating.Source: §2.4 · p. 13
3. Experimental methods
The experimental methods describe preparation of an NMC622 cathode and acquisition of a 3D X-ray CT image for image-based modeling.
3.1 Electrode manufacture
- The cathode slurry consisted of NMC622, PVDF, and C65, had approximately 60 wt.% solids, and was doctor-blade coated onto approximately 16 µm aluminum foil.Source: §3.1 · p. 13
- PVDF and C65 powders were pre-dried at 120 °C in a vacuum oven over 12 h; the PVDF/NMP binder solution was mixed at 2000 rpm for 15 min until homogeneous.Source: §3.1 · p. 13
3.2 Image acquisition
- The NMC622 sample was laser-machined before lab-based X-ray micro-CT acquisition and reconstruction.Imaging used 601 projections at 20× magnification and yielded a voxel size of 0.371 µm.Source: §3.2 · p. 14
4. Numerical methods
The numerical workflow converts CT images into a meshed three-phase electrode and applies coupled electro-chemo-mechanical and phase-field fracture models across multiple discharge, thickness, and voltage-window cases.
4.1 Image processing
- The CT image was segmented into particles, carbon binder, and pores, yielding volume fractions of 51.3%, 35.5%, and 13.2%, respectively.The region of interest spans the full 89 µm electrode thickness and measures 50 µm by 50 µm in-plane.Source: §4.1 · p. 14
4.2 Finite element implementation
- The segmented volume was meshed with approximately 3.6 million linear tetrahedral elements, with 400 nm elements in regions of interest to support mesh convergence.The stated element size is 4.5 times smaller than the phase-field length scale.Source: §4.2 · p. 15
- The coupled transport, electrode-kinetics, and deformation equations were solved sequentially, with a history field enforcing damage irreversibility.The implementation used COMSOL Multiphysics and second-order backward Euler time stepping.Source: §4.2 · p. 15
4.3 Material models
- NMC622 was modeled as an isotropic linear-elastic solid with brittle failure, while its solid-state diffusivity depended nonlinearly on lithium concentration.The carbon binder was treated as an electronically conductive linear-elastic material.Source: §4.3 · p. 17
- The model used LiPF6 electrolyte with salt-concentration-dependent properties and treated the aluminum current collector as an electronically conductive, linear-elastic solid with conductivity K=3.7×10^7 S m−1.Source: §4.3 · p. 17
4.4 Simulation details
- The test cases examined discharge rates of 1C, 3C, 6C, and 9C from pristine states, electrode thickness at 6C, and voltage windows with multicycle charging and discharging at 6C.The discharge-rate cases were single discharges without prior cycling history.Source: §4.4 · p. 19
5. Results and discussion
This section examines simulated void-driven fracture across particle size, electrode position, discharge rate, thickness, and cycling, relating concentration and stress gradients to cracking, capacity fade, and lithium removal. It also describes depth-dependent cracking, damage localization at the collector interface, and particle-scale damage progression.
5. Results and discussion
- At 6C, small central voids drive extensive fracture: many exceed the 0.49 μm transition flaw size, and cracks can extend to particle surfaces or form disk-like cracks.The model predicts significant electrode fracture, including complete fracture of particles.Source: §5 · pp. 19–20
5.3 Influence of electrode thickness
- At 6C, the 89 μm electrode has 38% less usable capacity than the 44.5 μm electrode, while the thinner electrode shows severe cracking throughout its microstructure.The thinner electrode has less-pronounced electrode-level lithium-concentration gradients, but particle-level gradients remain and cause fracture.Source: §5 · p. 20, §5.3 · pp. 25–26, Figure 5 · p. 25
5.1 General observations: first discharge
- At 6C, cracking initiates around 20% discharge in large particles near the separator, where transport-limited concentration and stress gradients promote fracture and damage peaks near the separator.Particle size affects gradient severity, and voids act as stress raisers; as discharge proceeds, fracture advances through inner electrode regions, while damage is lowest near the current collector.Source: §5.1 · pp. 22–23
5.2 Influence of discharge rate
- Cracking increases with discharge rate: 1C shows no obvious particle cracking, whereas 9C produces severe cracking in both particles and connecting struts.Intermediate rates show increasing cracking, attributed to greater lithium-concentration heterogeneity and corresponding hydrostatic-stress variation.Source: §5.2 · p. 23, Figure 4 · p. 24
5.4 Influence of cycling and depth of charge/discharge
- Capacity loss occurs after the first cycle and may be attributed to significant polarisation, represented by a sharp voltage increase that reduces the cycling voltage window and limits opportunity to remove or insert.The passages also note that polarisation is greater during charge.Source: §5.4 · p. 26
- Lithium accumulation and increasingly homogeneous concentration profiles lower diffusion gradients, accompanying progressively shorter charge and discharge half-cycles and capacity fade.A wider voltage window allows greater lithiation and delithiation and higher storage capacity, but cycling still reduces capacity, though less than in the narrower-window case.Source: §5.4 · pp. 26–27
- In both cases (I) and (II), most damage occurs within the first cycle; at greater depth of discharge (2.8 V in Case II), a larger degree of cracking is observed, with most additional crack growth in the first charge.Source: §5.4 · p. 29
5.5 Damage at the current collector-particle interface
- Particle expansion creates tensile stress at the collector interface, where stress concentrations can damage NMC particles and potentially detach them, electrically isolating the electrode.The model assumes perfect particle–collector attachment and does not capture aluminium post-yield behavior or bond strength.Source: §5.5 · pp. 30–31
- Current collector–particle interface cracking is more likely at lower discharge rates, while at high rates it appears in later cycles as lithium accumulates in adjacent particles.Greater lithium-concentration and hydrostatic-stress heterogeneity at higher rates is associated with the absence of interface cracking in earlier cycles.Source: §5.5 · p. 31
5.6 Observations on individual particle fracture
- At 6C, cracks initiate at voids under central triaxial tension, coalesce into a disk-like void, and then branch.Cracks arrest before reaching the surface while outer regions remain compressive; delithiation during charging creates tensile surface stresses that can promote further propagation.Source: §5.6 · p. 31, Figure 8 · p. 33
6. Conclusion
The coupled imaging, electro-chemo-mechanical, and phase-field framework predicts void-driven damage during early cycling in a realistic lithium-ion battery microstructure. Damage varies by location and electrochemical response, with design implications for particle size, electrode thickness, and cycling voltage window.
6. Conclusion
- The framework predicts void-driven damage in a realistic lithium-ion battery microstructure during early-stage cycling across cycling rates, electrode thicknesses, and voltage windows.It combines advanced imaging with electrochemistry, mechanics, and phase-field fracture.Source: §6 · p. 34
- Damage is location-dependent and linked to heterogeneous electrochemical response from slow diffusion in the electrolyte and active material; most void-induced damage occurs in the first cycle, followed by structural relaxation.Source: §6 · p. 34
- For thick electrodes, slow particle diffusion limits performance and promotes damage, suggesting smaller particles near the separator and microstructure grading for higher capacity and improved degradation characteristics.Source: §6 · p. 34
- The voltage window must be limited because cracking is more likely when electrodes operate at its charge and discharge extremes.Source: §6 · p. 34
- The framework provides information about battery characteristics and a foundation for improved electrode microstructures and operational boundary conditions that preserve performance.Source: §6 · p. 34
CRediT author contribution statement
The statement assigns conceptualization, methods, software, investigation, data, analysis, writing, supervision, project administration, and funding roles across the listed authors.
CRediT author contribution statement
- Adam M. Boyce is credited with conceptualization, methodology, software, investigation, data curation, formal analysis, and the original draft.Source: CRediT author contribution statement · p. 35
- Emilio Martínez-Pañeda, Aaron Wade, Ye Shui Zhang, Josh J. Bailey, and Thomas M. M. Heenan are credited with conceptualization or methods, software or investigation, and review and editing as listed.Emilio Martínez-Pañeda: conceptualization, software, and review and editing; Aaron Wade and Ye Shui Zhang: methodology, investigation, and review and editing; Josh J. Bailey and Thomas M. M. Heenan: investigation and review and editing.Source: CRediT author contribution statement · p. 35
- Dan J. L. Brett and Paul R. Shearing are credited with supervision, project administration, funding acquisition, and review and editing.Source: CRediT author contribution statement · p. 35