Anand N. P.
Radhakrishnan
a,
Mark
Buckwell
ab,
Martin
Pham
ab,
Donal P.
Finegan
c,
Alexander
Rack
d,
Gareth
Hinds
e,
Dan J. L.
Brett
ab and
Paul R.
Shearing
*ab
aElectrochemical Innovation Lab, Department of Chemical Engineering, University College London, London, WC1E 7JE, UK. E-mail: p.shearing@ucl.ac.uk
bThe Faraday Institution, Harwell Science and Innovation Campus, Didcot, OX11 0RA, UK
cNational Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, CO 80401, USA
dThe European Synchrotron (ESRF), 71 Avenue des Martyrs, 38000, Grenoble, France
eElectrochemistry Group, National Physical Laboratory Teddington, Middlesex TW11 0LW, UK
First published on 6th July 2022
Abuse testing of lithium-ion batteries is widely performed in order to develop new safety standards and strategies. However, testing methodologies are not standardised across the research community, especially with failure mechanisms being inherently difficult to reproduce. High-speed X-ray radiography is proven to be a valuable tool to capture events occurring during cell failure, but the observations made remain largely qualitative. We have therefore developed a robust image processing toolbox that can quantify, for the first time, the rate of propagation of battery failure mechanisms revealed by high-speed X-ray radiography. Using Gabor filter, the toolbox selectively tracks the electrode structure at the onset of failure. This facilitated the estimation of the displacement of electrodes undergoing abuse via nail penetration, and also the tracking of objects, such as the nail, as it propagates through a cell. Further, by cross-correlating the Gabor signals, we have produced practical, illustrative spatiotemporal maps of the failure events. From these, we can quantify the propagation rates of electrode displacement prior to the onset of thermal runaway. The highest recorded acceleration (≈514 mm s−2) was when a nail penetrated a cell radially (perpendicular to the electrodes) as opposed to axially (parallel to the electrodes). The initiation of thermal runaway was also resolved in combination with electrode displacement, which occurred at a lower acceleration (≈108 mm s−2). Our assistive toolbox can also be used to study other types of failure mechanisms, extracting otherwise unattainable kinetic data. Ultimately, this tool can be used to not only validate existing theoretical mechanical models, but also standardise battery failure testing procedures.
X-ray radiography is a powerful tool for capturing the degradation of individual lithium-ion cells operando, under both standard operation and abuse testing conditions.4,5,10–12 Real-time and high-speed (i.e., slow-motion) imaging offer a valuable insight into the mechanisms of failure, through directly observable changes to the cell structure. X-ray radiography can track three-dimensional structural information at high speeds (i.e., 2000 Hz) offering unparalleled insights into battery failure. Additionally, the efficacy of hazard mitigation strategies, such as safety vents, separator shutdown and current interruption, and positive temperature coefficient devices, may also be investigated.4 However, most failure/safety testing methods do not have accompanying high-speed X-ray radiography data, and the analysis and interpretation of any such available data has remained largely qualitative. This is due to the presence of multiple complex events, involving both gradual and sudden shifts of the electrodes, and their decomposition, as well as, in some cases, the movement of a large object such as a nail. This poses a significant image-processing challenge, for which there is currently no robust, quantitative analytical approach. Typically, videos are examined by eye, with frames of interest selected to produce a timeline of visible events. Although informative, this is a very slow method, owing to the large amounts of information present in a single video, and mechanisms are typically postulated from qualitative observations. By extension, a broad, statistically significant analysis of multiple videos using the same approach is not only extremely time-consuming, but also supremely challenging. Subtle yet key events may also not be apparent to the eye, and such manual observations are likely to be inconsistent between measurements (due to the stochastic nature of these failure events) and between researchers undertaking the data analysis.13 A robust analytical toolbox for quantifying the kinetics of cell failure is therefore required in order to fully exploit the information contained with existing and future X-ray radiography data that are now being collated in open-access databases (e.g., the Battery Failure Databank hosted by the National Renewable Energy Laboratory14).
The internal structure of a lithium-ion cell is typically an assembly of periodic electrode layers, current collectors and separators. In X-ray radiography, this produces a distinct image ‘texture’, composed of bands of compositional contrast resulting from the different X-ray attenuation coefficients of each material. While a variety of feature-detection and object-classification algorithms are available, X-ray radiography of lithium-ion cell failure poses a unique combination of challenges that hinder their applicability:
(i) Although the electrode texture is well-defined, it degrades unevenly across the field of view, disappearing as failure occurs. Frequency-domain analyses, such as fast Fourier transforms, that can identify the initial texture based on spatial or temporal frequencies,15 are unable to track the changes in phase and orientation in the spatial domain as failure progresses.
(ii) High frequency noise is typically present, making the identification of periodic or aperiodic features challenging. Pixel-based region-labelling algorithms fail in accurately deconvoluting the noise from the features of interest.
(iii) In some cases, for example during nail penetration testing, large objects are present in the field of view. These obscure objects introduce variations in the texture, leading to analytical artefacts.
In this work, we apply Gabor filter banks and subsequent post-processing algorithms to high-speed X-ray radiography data of lithium-ion cells undergoing abuse via nail penetration and ball compression testing. Gabor filter banks are commonly used in visual processing, owing to their sensitivity to the orientation (angle) and spacing (frequency) of edge features.16,17 They have been effective in the automated recognition of textures,18,19 structural variations in electron microscopy images,20–23 anatomical structures in X-ray computed tomograms,24,25 as well as human faces26 and fingerprints.27 Texture may be detected and quantified as a function of component feature size, orientation and distribution. The ability to control the frequency and orientation of the Gabor filters enables the user to selectively pick out the electrode texture and omit other objects. Furthermore, the filters can track changes in the spatial domain (directional sensitivity) as failure progresses within a cell. Ultimately, this approach produces frequency-sensitive spatial information, while at the same time being noise-insensitive. Thus, it addresses the challenges outlined above and is a powerful and an appropriate technique for analysis of X-ray radiography data.
We have developed an image processing toolbox outlined in the following manner:
(i) We firstly objectively identify the internal cell structure and nail as separate textures, representing them as Gabor-filtered frames with features defined by distinct functions of angle and frequency. While failure may be induced in any direction, the electrodes present a highly ordered structure that can be resolved based on its particular orientation.
(ii) The Gabor-filtered frames are then cross-correlated over time, facilitating the tracking of the degradation and failure of cells with a high spatiotemporal resolution and allowing us to estimate the displacement of electrode layers before failure.
(iii) Finally, from the conversion to spatiotemporal information we produce a single practical, and illustrative map of the failure events occurring in an entire video, from which we quantify the rate of propagation of failure both axially (parallel to the electrodes) and radially (perpendicular to the electrodes).
Battery failure involves multiple complex events occurring in all three dimensions. Using our technique, we have, for the first time, tracked how the structure of electrodes changes over time, as a direct result of the forces acting on it. Not only does our approach introduce a means of quantifying failure processes, but it may also facilitate the validation of existing mechanistic models. Our spatiotemporal maps reveal that the rate of electrode displacement (before the onset of failure) is higher when a nail propagates radially rather than axially. We also identify and track the onset of failure, which occurs at slower velocities than the electrode displacement and exhibits varied third-order kinetic behaviour. With the spatiotemporal maps, we may accurately describe not only ‘where and when’ failure originates, but also ‘how’ it propagates over time. In the long term, we are confident that this toolbox can further the understanding of battery degradation mechanisms by coupling mechanical failure models28–30 with electrochemical thermal-runaway models.31 Furthermore, our approach provides an open-source analytical toolbox developed on Python that may be readily implemented on video data from any instrumental setup, including legacy data from archives (toolbox available upon request). Furthermore, the toolbox has a user-friendly interface to guide appropriate parameter selection. Not limited to visual assessments, any user may thus gain new perspectives on their data, from which they may readily distinguish interesting behaviours for further characterisation. Analysing a variety of datasets, each of which were clearly distinct from one another in both input and output, we have evidenced that our technique is an extremely robust, efficient, informative and transferable means of analysing such dense datasets. Our technique is therefore extremely promising in advancing and strengthening the understanding of failure mechanisms of lithium-ion cells.
Dataset name | Test type | Cell type | Incidence angle of object (with respect to the central axis of the electrode structure) | Location of test (along the length of the cell) |
---|---|---|---|---|
SI_Video_1.mp4 | Nail penetration | LG ICR18650S3 | Perpendicular | Middle |
SI_Video_2.mp4 | Nail penetration | LG ICR18650S3 | Perpendicular | Middle |
SI_Video_3.mp4 | Nail penetration | LG ICR18650S3 | Parallel | Bottom |
SI_Video_4.mp4 | Ball compression | LG ICR18650B4 | Perpendicular | Middle |
For a set of frames loaded, we define t = 0 s as the first frame selected for analysis, unless otherwise stated, for which the electrode structure is assumed to be pristine and unaffected by any abuse process. ti is defined as the time of the ith frame, where i frames are included in the analysis. All spatial information has been presented in the Cartesian coordinate system, where x represents the position in the axial direction, along the X axis (parallel to the electrodes), and y represents the position in the radial direction, along the Y axis (perpendicular to the electrodes). Unless otherwise stated, the origin, x = 0 mm, y = 0 mm, is the top-left corner of the rectangular ROI selected by the user.
Upon converting the frames to an 8-bit greyscale format, the contrast range of each selected frame was normalised (lowest pixel value set to 0 and highest pixel value set to 255) and a morphological reconstruction step applied to smoothen noise.42 Gabor filter banks were then applied as discrete sinusoidal waves modulated by a Gaussian function. This implementation consisted of a [9 × 9] pixel kernel, which scans across a frame (Fig. 1). The user can choose the most appropriate Gabor filter parameters (angle and frequency), which are then applied on all the selected frames of a dataset.
Following the Gabor filtering step as shown in Fig. 1, post-processing analyses were performed on the filtered frames (Fig. 1c), to estimate electrode displacements and build temporal and spatiotemporal maps, enabling the extraction of cell failure kinetics.
Once we had chosen optimal Gabor filter parameters for a single frame of ‘SI_Video_1’ (ESI†), we applied the same process to each frame in the dataset and extracted the resulting cross-sections for comparison. This allowed us to monitor the condition of the cell over time. Fig. 2a, d and g show raw video frames of a nail gradually penetrating a cell and disrupting the electrodes. To the eye, there is a clear distinction between the nail and the electrodes, but to precisely define their relative arrangement is not trivial, particularly as the nail moves further into the cell and the electrodes deform. However, by filtering the images at θ = 0° (radially) and θ = 90° (axially), we were able to selectively identify the electrodes independently and filter out the nail. Fig. 2b, e, and h show the output frames filtered parallel to the nail. The signal is initially just noisy throughout the cell, i.e., the electrode texture is not picked out by the filter. When the nail enters, we observe the appearance of a corresponding texture perpendicular to the electrodes. Conversely, when the filter is aligned with the electrodes, as in Fig. 2c, f, and i, the signal is initially very pronounced. Its magnitude then decreases in accordance with the texture changing as the nail enters and causes a region of deformation to spread from its entry point (see ‘SI_Video_5.avi’ (ESI†) for an animated comparison of the Gabor filter ranging from θ = 0° to 180°). The outcomes of these contrasting outputs of the filters are highlighted in the bottom row of Fig. 2, which shows single-pixel-wide Y cross-sections from the centres of the filtered images. So, the Gabor signal cross-sections allow us to compare distinct features by tracking, over time, the textures that best describe them. As the texture changes, such as the electrodes losing structural integrity, the corresponding signal changes.
Fig. 2 Selective Gabor kernel filtering of electrode ‘texture’ from the dataset ‘SI_Video_1’ (ESI†). The top row shows video frames at different times during nail penetration. The second row shows the results of applying the Gabor filter at θ = 0° to the video frames. The inner core of the smart nail is detected, while the electrodes are not. The third row shows the results of applying the filter at θ = 90° to the video frames. Here, the electrode texture is captured. However, as the nail penetrates the electrodes, it is filtered out because the texture is no longer aligned with the filter. Plots in the bottom row show the normalised Gabor signals of the electrode structure at θ = 90° (black lines) and θ = 0° (orange lines). As electrodes deform due to the nail (time = 0.437 s), the Gabor signal decreases accordingly due to reducing alignment of image features with the applied filter. The electrode signal in the central region of frame, at time = 0.51 s, has disappeared as the electrodes have been entirely displaced by the nail. A Gabor map of the nail and the electrode layers in frame, at time = 0.437 s, filtered from θ = 0° to 180° has been shown in the Video ‘SI_Video_5.avi’ (ESI†). The scale bar indicates 4 mm. |
Fig. 3 Tracking the velocity of a nail puncturing a cell. (a) A video frame was cropped around the nail (i) and a filter at θ = 140° and f = 0.04 pixels−1 applied (ii), to select one-half of the conical tip of the nail in the dataset ‘SI_Video_1’ (ESI†). (b) Y cross-section of the normalised Gabor signal from (a) (ii), where the peak represents the position of the edge of the nail. The blue circle marker denotes the peak at the current frame, whereas the small black circle markers denote the peak positions in the preceding frames (i.e., the path taken by the nail edge from t = 0.2075 s). (c) Displacement profile of the nail determined from the relative positions of the tip-edge peak. The vertical dotted line denotes the timestamp of the frame shown in (a and b). A temporal map of the nail and its displacement determination are available in the Video ‘SI_Video_6.avi’ (ESI†). A peak nail velocity of 113 mm s−1 was estimated at t = 0.4645 s, i.e., the point when the electrodes fractured and the nail accelerated, leading to the steepest change in displacement. The scale bar indicates 4 mm. |
Fig. 4 Temporal cross-correlation of the electrode texture from the dataset ‘SI_Video_1’ (ESI†). (a) Top plot – 2D map showing the temporal evolution of the normalised Gabor signal at a fixed X position, and bottom plot – corresponding normalised temporal cross-correlation, where the Gabor signals at time ti is cross-correlated with that of time t0 (undisturbed electrode structure). (b) Comparison of Gabor signals at different times, ti (orange lines), with that of t0 (black lines). When the electrode texture has a high similarity with the undisturbed texture (t0), the correlation value is large and positive (normalised to +1), e.g., at t1 where t1 − t0 = 5 ms. When the electrode is displaced and so appears inverted compared with the initial texture at t0, the correlation is large and negative (normalised to −1), e.g., at t3 where t3 − t0 = 126 ms. When there is little or no similarity between the textures at ti and t0, the correlation value is close or equal to zero. This happens in two scenarios – when the electrode texture is displaced slightly but not inverted (e.g., at t2 where t2 − t0 = 43.5 ms) or when the electrodes are completely delaminated or expelled from the field-of-view (e.g., at t4 where t4 − t0 = 620 ms). |
Instead, we estimated the electrode displacement using the temporal cross-correlation. This methodology was developed using ‘SI_Video_4’ (ESI†) as an ideal test case, involving compression of the electrodes by a ball (see Table 1), without subsequent mechanical failure or thermal runaway. Fig. 5a shows the raw video frames at t0 and ti = 0.5 s, where the electrodes demonstrate a clear, symmetric shifting and bending under the incident ball. Fig. 5b shows three temporal cross-correlations at different X positions. At x2, corresponding to the centre of the ball, more electrode shifts (full oscillations in the cross-correlation) are present in comparison to x1 and x3, at the edges of the ball. We estimated the electrode displacement by multiplying the number of shifts by the distance between electrodes, 66 ± 17 μm, which we calculated from the average distance between adjacent Gabor peaks in the ‘pristine’ structure, i.e., at t0.
Fig. 5 Estimation of electrode displacement. (a) X-ray frames of a ball compressing the cell at t = 0 s (top) and 0.5 s (bottom) from dataset ‘SI_Video_4’ (ESI†). (b) The normalised temporal cross-correlation signals of the electrode structure at three positions, x1, x2, and x3 (vertical dotted lines in (a)), where each positive peak indicates one complete shift of the electrodes into alignment with the initial position of their neighbouring electrode layer. At t = 0.5 s, the electrodes at x2 have traversed 6.73 ‘electrode shifts’ from their original position. From the Gabor signal profiles at t = 0 s, the distance between electrode layers was estimated to be 66 ± 17 μm, so at t = 0.5 s, the electrode structure at x2 is displaced by an estimated 444 ± 115 μm from its original position. (c) Electrode displacement at various X positions for the dataset ‘SI_Video_4’ (ESI†). (d) Electrode displacement at various X positions for the nail penetration dataset ‘SI_Video_1’ (ESI†), where the distance between electrode layers was estimated to be 111 ± 10 μm. Analysis was cropped at t = 0.6 s, when the electrode layers fractured. At x = 6.7 mm (near the surface of the nail), the electrode displacement is estimated to be 221 ± 21 μm, above which the Gabor signals were lost. Error bars denote ±1 standard deviation in the distance between electrode layers. |
Fig. 5c, shows the resulting electrode displacement across the video frame at six time-points between t0 and ti = 0.5 s. Directly below the centre of the ball, the displacement was the greatest, around 0.44 mm at 0.5 s. This drops off symmetrically in both x directions, to a minimum of around 0.08 mm at a distance of around 3.5 mm from the centre of the ball. We also note, from the broader colour bands in the centre of the plot (around x = 3.5 mm), that the displacement had a larger acceleration directly below the ball. We applied a similar approach to the nail penetration dataset ‘SI_Video_1’ (ESI†). Fig. 5d shows the displacement of the electrodes, wherein the nail (radius = 2 mm) is incident at the right side of the ROI (x = 6.7 mm). Here, the entire structure shifts homogeneously by around 0.1 mm over 0.36 s, before the displacement at the nail location becomes much more pronounced, and then stops at around 0.22 mm, when the Gabor signals were lost. This is an interesting contrast with the ball compression, which instead produced a continuous bending. The initial homogenous shifting of the electrodes in the nail penetration dataset resulted from the overall displacement of the cell as the nail made contact, followed by displacement of the electrodes as the nail pierced through. We note that this is in the plastic flow regime, where the volumetric stress withstood by the electrodes is a property of their tensile strength and Poisson ratio, as discussed by Wierzbicki and Sahraei, 2013.43 Subsequently, as discussed above, the mechanical resistance of the electrodes suddenly yields as their structure fractures, leading to an abrupt acceleration of the nail (to a maximum of 113 mm s−1 as shown in Fig. 3c).
Fig. 6 Various events captured by the spatiotemporal cross-correlation map in the dataset ‘SI_Video_1’ (ESI†). (a) Normalised cross-correlation plots at four X cross-sections, x1–4 (vertical dotted lines in (b) showing varying effects experienced by the electrodes due to the nail. (b) The 2D spatiotemporal map plotted by calculating the normalised cross-correlation values at every X position (shown in Fig. 7a). (c) Timeline of frames capturing various events picked out from the spatiotemporal map, namely: (1) nail pierces cell casing and starts pushing the electrodes; (2) the top 3–4 electrode layers are mechanically sheared with the onset of failure propagation, while the rest of the electrode structure continue to be displaced. The apparent non-linearity is potentially due to the combination of the mechanical force from the nail and the failure propagation of the top 3–4 electrode layers from the nail (right edge) towards the left edge of the frames; (3) nail fully pierces the electrode layers, which completely fracture, leading to the localised delamination (4) of the bottom 4–5 electrode layers, captured between x = 0 and 4 mm, and t = 0.45 and 0.62 s. |
(i) Inspect the map for distinct features, such as continuous regions of a consistent colour (e.g., Event (1) in Fig. 6b), or abrupt axial discontinuities (e.g., Event (4) in Fig. 6b).
(ii) Continuous regions of colour characterise the behaviour of the electrodes across the length of the cell. Linear or non-linear changes to such regions of a colour indicate changes to the electrode structure propagating across the X cross-section over time. For example, the dark blue region near the bottom of Fig. 6b suggests that the electrodes are becoming misaligned with their initial structure, and that it propagates in the negative X direction, where the origin is the top left of the frames (x = 0, y = 0) and the nail enters at the right-edge of the ROI. On the other hand, areas of a constant colour indicate that the electrode structure is not changing. For example, the green region at the top right of Fig. 6b suggests the electrode structure has disappeared and no further change takes place (this corresponds to the presence of the nail in the cell once it has stopped moving).
(iii) Axial discontinuities characterise events that take place simultaneously across the distance corresponding to the width of the feature in X; at a single point in time, the colour changes homogeneously. For example, if the electrodes in a region delaminate altogether, the map would show an abrupt transition to green, as we observe at around 0.42 s in Fig. 6b.
Using the map in Fig. 6b, we have identified four different events occurring in the electrode structure. These events overlap one another in time; a timeline of raw frames is shown in Fig. 6c. Firstly, the map highlights the point of entry of the nail (right edge of the cropped ROI, x ≈ 6.7 mm) at t ≈ 0.04 s, where the electrodes shift from the right edge to the left edge. Event (1), a region of inverted electrode alignment, represents the rate at which the nail pierces the cell casing and displaces the electrodes, although they have not failed structurally at this point. Event (2) highlights the onset of failure, where the top 3–4 electrode layers are sheared by the nail, with the rest of the electrodes continuing to be displaced. This combination of failure-onset and electrode-displacement propagates non-linearly between t = 0.19 s and t = 0.42 s. This also indicates the onset of Joule heating originating from the sheared top 3–4 electrode layers, marking the increase in the internal cell temperature as reported by Finegan et al. (2017).6 The region of inverted cross-correlation marked as Event (3) represents the point at which the electrodes fail structurally by fracturing, leading to localised delamination, shown as Event (4). This occurs very rapidly; the colour transition in the mapping appears horizontal, indicating that the delamination occurred almost homogeneously over 4 mm along the X cross-section. This indicates the need to analyse the Gabor signals in the radial direction (as discussed in the sections below).
Fig. 6 demonstrates the strength of spatiotemporal mapping of X-ray radiography data. We can now assess an entire dataset of thousands of video frames, and thus an entire failure experiment with multiple sub-events, in a single picture. From this, we can observe, directly, how each process propagates along the cell, without needing to scroll through the video manually, further validating our analytical technique. The mapping also reveals and resolves processes that may be missed by manual interrogation, such as the distinction between the electrodes shifting, as in Event (1), and the onset of failure, as in Event (2) in Fig. 6b.
We produced spatiotemporal maps using multiple datasets of nail penetration, as well as the ball compression test, to unravel the events occurring in each experiment (Fig. 7). The maps are interpreted as follows:
Fig. 7 2D spatiotemporal cross-correlation mapping as a quantitative technique to track failure propagation. (a) Spatiotemporal map for the same dataset as in Fig. 6b, that of ‘SI_Video_1’ (ESI†). The map shows the nail entering at the right edge (x = 6.7 mm), causing a more pronounced displacement of the electrodes (Fig. 5d). The map also shows multiple events that are distinct from the electrode displacement, such as failure propagation and localised delamination. (b) Spatiotemporal map of dataset ‘SI_Video_2’ (ESI†), where the nail enters the left edge of the analysed X-ray frames (x = 0 mm) at t ≈ 0.1 s. (c) Spatiotemporal map of dataset ‘SI_Video_3’ (ESI†), where the nail traverses in the axial direction, piercing the bottom of the cell. The electrode structure is located between x = 0 and ≈2 mm. At t = 0.34 s, the core (mandrel) detaches from the bottom of the cell as the nail pierces through the cell, displacing the electrodes. (d) Spatiotemporal map of the dataset ‘SI_Video_4’ (ESI†), where a ball compresses the electrode structure. The map indicates that the centre of the ball, x ≈ 3.45 mm, starts displacing the electrodes from t ≈ 0.04 s, where the extent of displacement reduces radially due to the circular profile of the ball. |
At around 0.34 s, the decrease in cross-correlation speeds up, with a transition from green to blue as the nail begins pushing the electrodes. A sudden shift (seen from the horizontal dark blue line) indicates the mandrel detaching from the bottom of the cell, though thermal runaway has still not initiated. This is followed by another region of decreasing cross-correlation close to 0.39 s, where the onset of thermal runaway has been captured with the mandrel starting to disintegrate.
It is worth noting that the slope of this region represents the rate of propagation of thermal runaway for this dataset between 0.39 s and 0.8 s. Subsequently, there was a release of gas into the base of the cell, leading to the bulging of the base plate that then escaped through the vent.
(1) |
(2) |
(3) |
(4) |
a(t) = a0 + j0t | (5) |
Fig. 8 Quantification of the kinetics of events in three nail penetration datasets. The 2D spatiotemporal maps have been transposed such that time is on the horizontal axis and X cross-section is on the vertical axis. (a) The regions of low and high cross-correlation values of three events (described in Fig. 6) in the dataset ‘SI_Video_1’ (ESI†), traced using a simple yet robust maxima/minima finding algorithm and their corresponding 3rd order polynomial fits shown in the bottom panel (trends i–iii). (b) Two events relating to electrode shifting and propagation of failure in the dataset ‘SI_Video_2’ (ESI†), identified and traced. The bottom panel shows the 3rd order polynomial fits of these traces (trends iv and v). (c) The rates of electrode shifting in the dataset ‘SI_Video_3’ (ESI†), where the nail traverses along the axial direction of the electrodes, have been quantified as shown in the bottom panel (trends vi and vii). The results of the 3rd order polynomial fitting, corresponding to Newton's equations of motion, are shown in Table 2. Note that (vi) is composed of two smaller sections, due to difficulty in reliable peak-tracing. |
Dataset | SI_Video_1 (ESI) | SI_Video_2 (ESI) | SI_Video_3 (ESI) | ||||
---|---|---|---|---|---|---|---|
Trends | i | ii | iii | iv | v | vi | vii |
Type of eventa | (1) | (2–3) | (2–3) | (1) | (2–3) | (1) | (1) |
a The type of the event refers to the ones described in Fig. 6. Event (1) denotes electrode displacement before onset of failure, Events (2–3) denote the onset of failure propagation and further electrode displacement leading to fracture or delamination | |||||||
Jerk [mm s−3] | 0.0 | 0.0 | 3209.2 ± 102.8 | 2572.43 ± 23.25 | 0.0 | 0.0 | 871.69 ± 4.74 |
Acceleration [mm s−2] | −578.0 ± 29.3 | 108.43 ± 10.01 | −281.48 ± 8.31 | 514.46 ± 1.41 | −34.51 ± 0.71 | 4.91 ± 0.17 | −92.39 ± 0.45 |
Initial velocity [mm s−1] | 91.66 ± 0.53 | 22.72 ± 0.38 | 24.58 ± 0.28 | 0.0 ± 0.04 | 9.46 ± 0.03 | 2.49 ± 0.01 | 7.49 ± 0.02 |
Origin of event along x [mm] | 0.13 ± 0.01 | 0.64 ± 0.01 | 0.64 ± 0.01 | 0.61 ± 0.01 | 0.07 ± 0.01 | 1.75 ± 0.01 | 1.28 ± 0.01 |
R 2 | 0.82 | 0.98 | 0.93 | 0.98 | 0.94 | 0.99 | 0.99 |
A non-linear least-squares fitting method was used to fit eqn (3) to the averaged x data (regression performed using Python 3, with a convergence tolerance = 1 × 10−8). The fitting coefficients were constrained such that v0 is positive, i.e., we define that the events progress in the positive x direction due to the expected unidirectional movement from the nail surface propagating away from the nail. x0 was constrained 0 ± 2 mm, i.e., events begin within the region defined by the diameter of the nail. For each fit, the model uncertainty (±1 standard deviation) was calculated from the square root of the diagonal of the covariance matrix. The corresponding R2 of the fits was also estimated.
Trends (i) and (iv) represent the shifting of the electrodes prior to structural failure for nail penetration in the radial direction. Trend (i) has j0 = 0, i.e., there is no jerk present and the acceleration is constant, whereas trend (iv) has an initial jerk of 2570 mm s−3. Trend (i) has an initial velocity of 91.7 mm s−1 but decelerates at 578 mm s−2. We note that this deceleration term has quite a large error of ±29 mm s−2, which might result from the noise in the data. Conversely, trend (iv) has an initial velocity of zero, but accelerates rapidly at 515 mm s−2 resulting in v(t0.31) ≈ 250 mm s−1 at t = 0.31 s. This highlights the intrinsic variation between the mechanical processes occurring during nail penetration tests carried under the same conditions.
Trends (ii), (iii) and (v) correspond to the combined effects of failure propagation and electrode shifting. There are also distinct differences in the acceleration and initial velocity of these processes. Trends (ii) and (iii) have accelerations of 108 mm s−2 and −282 mm s−2, and initial velocities of 22.7 mm s−1 and 24.6 mm s−1, respectively. They accelerate to a velocity of v(t0.42) ≈ 62 mm s−1 and v(t0.45) ≈ 135 mm s−1. Trend (v) appears to be much slower, with an initial velocity of 9.5 mm s−1 decelerating at −34.5 mm s−2. This again emphasises the broad range of cell failure kinetics that result from nail penetration tests, although inspection of the videos might lead one to conclude that the processes leading up to full electrode destruction are quite similar.
Trend (iii) has a large initial jerk of 3210 mm s−3, although (ii) and (v) have j0 = 0. Trend (iii) has a high jerk potentially due to the rapid delamination of the bottom 3–4 electrode layers captured in the video, leading to a sudden inflexion in the x data. We note that fitting higher order polynomials is sensitive to input data, which in our case are peak traces from spatiotemporal maps extracted from legacy data. This may be overcome with acquisition of higher resolution images at higher frame rates, improving the quality of the peak traces.
We also observe abrupt transitions at 0.42 s in Fig. 8a and 0.37 s in Fig. 8b as the cells fail across their length, which effectively ends trends (iii) and (v). From the spatiotemporal maps the shape of the trends appears to diverge at these points. This end point corresponds to the nail reaching the middle of the cell as the electrodes fracture, so the spreading in the colour map likely indicates a rapid final shift of the electrodes away from the nail before they are destroyed.
Trends (vi) and (vii) characterise the electrode response for the case in which the nail entered the cell in the axial direction, causing reduced tensile strain on the electrodes in comparison to entering in the radial direction. a0 and j0 are relatively low in comparison to those for the nail entering in the radial direction. Trend (vi) has j0 = 0 mm s−3, while trend (vii) has j0 = 872 mm s−3. They have accelerations of 4.9 mm s−2 and −92.4 mm s−2, and initial velocities of 2.5 mm s−1 and 7.5 mm s−1, respectively. We also do not observe a near-homogeneous electrode shift across the cell. We suspect that this contrast in behaviours is due to the difference in mechanical resistance of the electrode layers in each case. It is interesting to compare this behaviour to the ball compression in ‘SI_Video_4’ (ESI†), wherein the electrodes do not fracture and there is no thermal runaway. Likewise, axial penetration of the nail does not stress the electrodes into fracturing, thus it is likely that when thermal runaway occurs it results from internal shorting caused by the nail.
From our quantification of the failure kinetics, we note that the propagation of structural damage (i.e., at the onset of catastrophic failure or uncontrolled thermal runaway) is slower than previously believed. Ignoring the abrupt and total cell failure, and if a certain specific trend propagation were to travel the entire length of a cell (in our case 65 mm), we may extrapolate the model to estimate the velocities to which the failures would accelerate. In the case of trend (iv), the electrodes would be displaced at a maximum velocity of 396 mm s−1 (v0 = 0 mm s−1) by t = 0.578 s, traversing the entire length of an 18650 cell, whereas, a failure trend involving a delamination event, e.g., trend (iii), would traverse the entire length of an 18650 cell by t = 0.7 s, reaching a maximum velocity of 163 mm s−1 (v0 = 24.6 mm s−1). This reinforces the view previously put forward by the authors that, counter-intuitively, failure due to nail penetration may not be as severe a mode of failure/abuse as has been reported in the literature.
Fig. 9a shows the temporal Gabor signal from the ‘SI_Video_1’ (ESI†) dataset (nail travelling in the radial direction), 3.7 mm from the nail surface (x ≈ 1 mm); similar to that of Fig. 4a which represents the temporal map at the nail surface (x ≈ 4.7 mm). Until around 0.5 s, the electrode structure remains intact with just a gradual shift due to the nail. However, there is then a sudden shift and loss in magnitude in the lower electrode layers, from y = 2.75 mm to 6 mm, which indicates the localised delamination captured in this dataset (Fig. 6b, Event (4)). In order to extract the kinetics of this event, which was very abrupt on the (x, t) spatiotemporal maps, we tracked the net shift of each Gabor peak in the temporal Gabor map (along the y axis).
Fig. 9 Estimation of rate of failure/delamination in the radial direction from the dataset ‘SI_Video_1’ (ESI†). (a) 2D temporal Gabor map showing the evolution of the electrode structure over time (normalised) ≈3.7 mm away from the nail surface (x ≈ 1 mm), similar to that of Fig. 4a (at the nail surface). The point of delamination has been shown in the inset box, which was cropped to extract radial propagation velocities, as shown in (b). (b) The radial shift in electrodes over time was extracted by tracing the Gabor signals over a range of Gabor angles 100°–165° (see ‘SI_Video_7.avi’, ESI†). The most prominent Gabor traces were skeletonised to single-pixel wide lines that denote the rate of delamination. (c) The delamination velocity of each electrode layer was calculated by performing linear regression on the skeletonised lines at every Gabor angle and the distribution plotted. |
Fig. 9b shows data manually cropped from Fig. 9a, corresponding to the delamination. This region appears disordered, with electrodes shifting in the positive y direction at different rates. In order to characterise how this failure propagates, we studied the distribution of electrode-shift velocities by capitalising on the power of Gabor filter banks again. We applied a further Gabor filter bank (θ = 100° to 160°) on the temporal Gabor signal data, with a fixed frequency equivalent to the electrode width. For each orientation we obtained an output image highlighting the most prominent trajectory taken by each electrode over time (see ‘SI_Video_7.avi’, ESI†). Fig. 9b shows the segments picked out at three angles, where we can observe a range of trajectories taken by each electrode layer. However, the filter produced some signal even for features that are slightly misaligned with the orientation. The output signals were therefore binarized in order to convert the trajectories into single-pixel-wide skeletal lines, on which a linear regression was performed to extract the velocities. By summing all the pixels of the Gabor-filtered trajectory images for every angle, we also obtain a signal intensity (Fig. 9c, top panel), wherein a higher signal indicates a greater presence of structure aligned with the filter. For a range of velocities of the electrodes per orientation, as shown in Fig. 9c bottom panel, we may use the signal intensity to guide the user to obtain the velocity distribution for angles that produce high signal intensities. Fig. 9c shows the signal intensity plot and associated velocity distribution.
Interestingly, there were two distinct peaks in the intensity, at θ = 110° and 155°. At θ = 100° we captured the top electrode layers at the onset of delamination with a velocity of around 4 mm s−1, while at θ = 162.5° we captured the bottom-most electrodes that delaminated the fastest, at a velocity of 140 mm s−1 leading on to delamination. Above θ = 162.5°, the extracted Gabor lines were that of the noise from the filter and not representative of the temporal electrode shifts. The orientation at θ = 130° was representative of the delamination velocities of most of the electrodes in the cropped ROI, with an average velocity of 13 mm s−1. We suggest that this delamination velocity acts as a point of transition between the electrode shifting due to the force from the nail, and a fully uncontrolled thermal runaway process.
The true novelty of this analytical technique is the amount of kinetic information that may now be extracted, relating to the events propagating axially and radially in these datasets. Through proof-of-concept validation of our method via the analysis of distinct battery failure datasets, we observed that the nail penetration event occurs more slowly than previously supposed, indicating that the slower onset of electrode failure might render them less dangerous than instantaneous short-circuiting events or thermally induced degradation events.
With an automated, user-friendly toolbox that helps to reduce human-induced error, several X-ray radiography datasets are currently being processed to elucidate the mechanisms and rates of failure induced by a range of thermal, electrical and mechanical sources. It is worth noting that unique events such as mechanical delamination, gas generation and gas-induced electrode shifting can now be robustly identified and their propagation rates quantified. The toolbox can be applied to existing data available from databanks, such as the one hosted by the National Renewable Energy Laboratory, which can help standardise abuse testing procedures. As a first step, the toolbox directly outputs empirical data describing the mechanics of failure, presenting an opportunity for these data to be applied to mechanical as well as thermal runaway multi-physics models of Li-ion batteries. Our toolbox also has the potential to analyse high-resolution, low frame rate images captured using X-ray CT instruments, highlighting that our technique may not be limited to synchrotron radiography data.
Furthermore, this toolbox will be powerful in helping to couple mechanical models with electrochemical thermal runaway models, when used in conjunction with other electrochemical techniques, such as fractional thermal runaway calorimetry (FTRC).49 Despite the lower sampling resolution of FTRC compared to high-speed imaging, with advances in calorimetry measurements, it may be possible for high-resolution FTRC data to be used in conjunction with our toolbox to advance understanding of battery degradation.
In the future, the many advantages of this technique can be further exploited by incorporating the ability to analyse data presented radially, i.e., investigating the failure mechanisms across the ‘jelly-roll’. One possible feature addition to our toolbox would be to apply ‘virtual unrolling’ of the jelly-roll before performing Gabor filtering,50 thereby facilitating the analysis of batteries with any form-factor, interrogated in any direction, to truly capture the complex nature of thermal runaway.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d1ee03430h |
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