A greyscale erosion algorithm for tomography (GREAT) to rapidly detect battery particle defects

The study addresses the challenge of early detection of micro-cracking and sub-particle defects in high-Ni NMC811 cathode particles, which drive capacity fade in Li-ion batteries. Ni-rich NMC materials offer high energy but suffer from structural instabilities, phase transitions, metal dissolution, gas release, and crack formation, exacerbated at higher upper cut-off voltages and fast charging due to lattice collapse and SOC heterogeneities. Conventional high-resolution imaging directly visualizes large cracks but is slow and yields poor statistics, and existing automated approaches generally require large, resolvable cracks. The research objective is to develop and apply a rapid tomography-based algorithm that infers sub-resolution defects via greyscale intensity analysis, enabling early, statistically robust detection of intra- and inter-particle damage and correlating it with electrochemical history and capacity losses.

Prior work has used X-ray CT extensively to study Li-ion electrodes, enabling non-destructive, 3D microstructure analysis. Automated crack detection methods have identified fractured particle pairs or used neural networks to detect broken particles, and studies have categorized damage across electrodes. However, these approaches generally detect only large defects resolvable at the scan resolution; micro-cracks below resolution remain elusive. Quantification precision improves with voxel resolution but at the expense of sample volume, necessitating trade-offs. There is thus a need for techniques that infer small-scale damage within larger volumes. Literature also documents degradation mechanisms in Ni-rich NMC, including phase transitions, transition metal dissolution, SEI-related effects, and crack initiation often from particle cores during high voltage and fast-charging operation. Existing morphology metrics like surface-area-to-volume often fail to distinguish early damage.

Materials and cells: Commercial NMC811 cathode sheets (NEI) were punched into 10 mm disks and assembled into seven graphite||NMC811 coin cells with Celgard separator and 1 M LiPF6 in EC:EMC (3:7), plus a pristine (uncycled) electrode. Assembly in Ar-filled glovebox. All cells underwent two formation cycles (CC C/20 to 4.2 V, CV hold until <C/40, CC discharge to 3 V, 10 min hold). Post-formation cycling varied by C-rate, upper cut-off voltage, and cycle number (see operational matrix). Discharge was at 1 C to 3 V; experimental temperature ~25 °C.

Electrochemical protocols: Eight electrode histories: pristine; control (0.5C to 4.2 V ×5); 2C to 4.2 V ×5; 5C to 4.2 V ×5; 0.5C to 4.3 V ×5; 0.5C to 4.4 V ×5; 0.5C to 4.5 V ×5; 0.5C to 4.2 V ×100. CV holds at end of charge until current < C/20. Formation capacities and subsequent capacity evolution recorded.

X-ray micro-CT acquisition: Zeiss Xradia 520 Versa at 120 kV, W anode (polychromatic beam with characteristic 58 keV W-Kα). Projections, exposure times, and isotropic voxel lengths ~0.18–0.217 µm depending on sample (e.g., pristine 50 s, 801 proj, 0.199 µm). Reconstructed via cone-beam FBP (Reconstructor Scout-and-Scan). ROIs: cycled samples ~140×140×35 µm³; pristine ~180×180×20 µm³ to reduce edge artefacts.

Segmentation and data export: Visualization and segmentation in Avizo. Threshold-based segmentation of NMC phase from binder/carbon/voids, with optional non-local means or Gaussian filtering. Exported 3DTIFF datasets: (1) raw greyscale tomogram; (2) binary mask of particles; (3) binary mask of pores/voids within ROI.

GREAT algorithm (greyscale erosion):

• Particle identification: scan tomogram voxels to label and index each particle uniquely (spatial indexing). Derive particle surface and compute morphology (surface area, volume). Calculate equivalent diameter from volume: d = (6·Volume/π)^(1/3).
• Surface-guided greyscale sampling: superimpose particle and pore masks on greyscale volume. For each particle, compute mean greyscale at its surface.
• Iterative morphological erosion: iteratively erode the particle mask n times, each step moving inward from the surface, collecting average greyscale at each radial shell, until core reached. Track surface area and volume at each iteration. High noise expected near core due to small voxel counts; core values treated cautiously.
• Normalization and profiling: For each particle, normalize greyscale at each radial shell by the particle’s surface greyscale, yielding g_norm(r). Compute differential intensity with respect to radius to assess radial gradients and mitigate absolute segmentation offsets.

Sensitivity analyses and binning:

• Segmentation sensitivity: Perform ±5% over/under-segmentation tests on pristine sample. Over-segmentation (pore mislabelled as particle) lowers apparent surface intensity, inflating normalized interior values; under-segmentation has opposite effect but smaller deviation. Recommendation: err slightly toward under-segmentation. Effects visualized for particle size bins.
• Particle size bounds: Evaluate three binning schemes (Small, Big, Hybrid bounds) balancing even particle distribution vs statistical power. Hybrid bounds used for main results. For each bound, average normalized greyscale across particles at each radial distance; compute standard deviations (typically ~1–2.5%). Note increased variability toward particle centers due to mixed sizes within bounds.

Auxiliary analyses: Particle size distributions and surface area-to-volume (SAV) ratios computed; these conventional metrics assessed for discriminative power.

Data processing outputs: (1) Particle morphology file (surface area, volume, ID); (2) Greyscale erosion data (per-particle normalized radial intensity). Per-bound averages and differential profiles plotted and analyzed. Throughput achieved of approximately 1400 particles/day.

• Throughput and capability: GREAT quantified inter- and intra-particle density variations for hundreds to thousands of particles per dataset (~1400 particles/day), a ~10× improvement over conventional nano-CT analysis (~130 particles/day), enabling statistically robust correlations to electrochemistry.
• Sub-surface layer: All samples show a sub-surface region (~2.0–2.5 µm from surface) with elevated normalized intensity, attributed primarily to partial volume effects from primary particle roughness; this layer diminishes with cycling, indicating surface smoothing.
• Conventional metrics non-discriminative: Particle size distributions and surface-area-to-volume ratios were similar across conditions and did not reliably distinguish damaged vs pristine particles.
• Radial intensity decay indicates defects: Normalized intensity generally decreases from surface toward core; values below unity imply internal low-density features (cracks/voids). Differential profiles show earlier and stronger negative gradients in more degraded samples.
• Size dependence: Smaller particles exhibit higher normalized intensities and less radial decay, indicating greater resistance to micro-crack formation, likely due to more uniform SOC and reduced internal stress.
• Cycling condition effects: • Pristine shows highest normalized intensities and slowest decay across sizes. • Control (0.5C, 4.2 V ×5) shows reduced intensities vs pristine, indicating some defect formation. • 2C (4.2 V ×5) similar to control with modest additional decay; minimal added degradation. • 5C (4.2 V ×5) displays notable decreases for large particles (intensity < 1), but smaller particles remain relatively intact; overall degradation only slightly worse than control. • 4.3 V (×5) slightly more damage than control, especially at cores. • 4.4 V (×5) broad degradation across sizes; second-worst overall intensities when considering all particles; some regions below surface intensity. • 4.5 V (×5) strong degradation in large particles with early and deep negative gradients; smaller particles less affected. • 100 cycles (0.5C, 4.2 V ×100) consistently lowest intensities and largest radial variations among small particles, indicating widespread internal degradation.
• Core integrity metric: Average core normalized intensities rank pristine highest; samples with greatest capacity fade (100 cycles, 4.4 V, 4.5 V/5C for large particles) show lowest core intensities. Trends robust even under under-segmentation tests.
• Correlation to electrochemistry: Lower normalized intensities (especially at cores) correlate with larger capacity losses. Example capacities (Table 3): • Control: 196 → 139 mAh g⁻1 (29% loss) • 2C: 202 → 142 mAh g⁻1 (30% loss) • 5C: 198 → 129 mAh g⁻1 (35% loss) • 4.3 V: 196 → 139 mAh g⁻1 (29% loss) • 4.4 V: 182 → 100 mAh g⁻1 (45% loss) • 4.5 V: 202 → 121 mAh g⁻1 (40% loss) • 100 cycles: 195 → 114 mAh g⁻1 (42% loss)
• Mechanistic insight: Damage often initiates near particle cores; high voltage operation (c-lattice collapse) and fast charging (SOC heterogeneities) drive micro-crack generation. GREAT infers sub-resolution cracks via reduced greyscale, enabling early detection before full fracture.

The GREAT algorithm addresses the need for early, statistically robust detection of sub-resolution intra-particle defects in Ni-rich NMC cathodes. By leveraging greyscale attenuation profiles and iterative erosion, it infers density deficits associated with micro-cracks that are not directly resolvable at micro-CT voxel sizes. The observed reductions in normalized intensity—particularly at particle cores and in the differential decay rates—track with increasingly aggressive cycling histories and align with electrochemical capacity fade, supporting the hypothesis that micro-crack formation contributes to performance loss. The method clarifies that traditional morphology metrics (e.g., SAV) and size distributions are insufficient to capture early-stage damage. Size-dependent resilience is evident: smaller particles maintain higher intensities and shallower radial gradients, consistent with reduced chemo-mechanical stress from more uniform SOC. The results suggest that high-voltage cycling (4.4–4.5 V) and extended cycling (100 cycles) produce significant intra-particle damage across sizes, while high C-rate (5C) predominantly impacts larger particles. Overall, GREAT provides a quantitative, high-throughput integrity metric that bridges microstructural degradation and electrochemical performance, enabling earlier fault detection and more representative materials statistics.

This work introduces GREAT, a greyscale erosion tomography algorithm that rapidly quantifies intra- and inter-particle density variations to detect sub-resolution defects in NMC811 cathode particles. It achieves an order-of-magnitude higher throughput than conventional nano-CT, enabling strong statistics and clear correlations between intra-particle integrity (especially core normalized intensity and radial decay) and capacity fade. Key findings include: a consistent sub-surface layer due to partial volume effects; robust detection of micro-crack signatures before full fracture; strong degradation under high voltage (4.4–4.5 V) and long cycling (100 cycles); and enhanced resilience of smaller particles. The methodology can generalize to other particle morphologies and materials. Future directions include: integrating machine learning for improved, automated segmentation and post-processing trend discovery; in situ/operando 4D imaging to link defect evolution to knee-point failures; and extended cycling studies in half-cells to decouple anode contributions and refine degradation mechanisms. GREAT thus offers a practical, scalable path to early defect detection and informed lifetime management of Li-ion cathodes.

• Segmentation sensitivity is the largest uncertainty: over-/under-segmentation shifts surface intensity and biases normalized profiles (over-segmentation causing larger deviations). Although ±5% tests are beyond typical user error, careful segmentation is critical, with a slight under-segmentation preferable.
• Increased noise near particle cores due to fewer voxels per shell limits precision; averaging across bounds mitigates but variability remains highest at final 0.5–1.0 µm of profiles.
• Binning by particle size mixes different particle radii within a bound, complicating center interpretations and elevating variability near centers.
• Resolution constraints prevent direct visualization of micro-cracks below the voxel size; GREAT infers defects via intensity, relying on partial volume effects rather than explicit crack imaging.
• The method correlates intensity changes with capacity fade but cannot fully deconvolve cathode-induced losses from anode-side phenomena (e.g., SEI growth, Li plating), especially at high voltage.
• Code is not publicly available (under active development), and full automation of segmentation was not implemented; ML approaches are proposed but not yet integrated.