Three-dimensional operando optical imaging of particle and electrolyte heterogeneities inside Li-ion batteries

Understanding (de)lithiation heterogeneities in battery materials is key to ensure optimal electrochemical performance. However, this remains challenging due to the three-dimensional morphology of electrode particles, the involvement of both solid- and liquid-phase reactants and a range of relevant timescales (seconds to hours). Here we overcome this problem and demonstrate the use of confocal microscopy for the simultaneous three-dimensional operando measurement of lithium-ion dynamics in individual agglomerate particles, and the electrolyte in batteries. We examine two technologically important cathode materials: LixCoO2 and LixNi0.8Mn0.1Co0.1O2. The surface-to-core transport velocity of Li-phase fronts and volume changes are captured as a function of cycling rate. Additionally, we visualize heterogeneities in the bulk and at agglomerate surfaces during cycling, and image microscopic liquid electrolyte concentration gradients. We discover that surface-limited reactions and intra-agglomerate competing rates control (de)lithiation and structural heterogeneities in agglomerate-based electrodes. Importantly, the conditions under which optical imaging can be performed inside the complex environments of battery electrodes are outlined. Confocal optical microscopy is used to visualize—at high speed—solid (particle volume changes and phase-front velocities) and liquid electrolyte (concentration polarization gradients) dynamics inside operating batteries.

Understanding (de)lithiation heterogeneities in battery materials is key to ensure optimal electrochemical performance.However, this remains challenging due to the three-dimensional morphology of electrode particles, the involvement of both solid-and liquid-phase reactants and a range of relevant timescales (seconds to hours).Here we overcome this problem and demonstrate the use of confocal microscopy for the simultaneous three-dimensional operando measurement of lithium-ion dynamics in individual agglomerate particles, and the electrolyte in batteries.We examine two technologically important cathode materials: Li x CoO 2 and Li x Ni 0.8 Mn 0.1 C o 0.1 O 2 .The surface-to-core transport velocity of Li-phase fronts and volume changes are captured as a function of cycling rate.Additionally, we visualize heterogeneities in the bulk and at agglomerate surfaces during cycling, and image microscopic liquid electrolyte concentration gradients.We discover that surface-limited reactions and intra-agglomerate competing rates control (de)lithiation and structural heterogeneities in agglomerate-based electrodes.Importantly, the conditions under which optical imaging can be performed inside the complex environments of battery electrodes are outlined.
A key factor in enhancing the performance of lithium (Li)-ion batteries is the development of high-energy-density cathode materials such as Ni-rich lithium nickel manganese cobalt (NMC) oxides.A long debate still remains into the nature of ion (de)intercalation in such materials [1][2][3] with heterogeneities and irreversibilities in intercalation driving degradation and capacity fade 4 .One of the difficulties in probing ion (de)intercalation in battery electrodes is the complex three-dimensional (3D) morphology of the constituent particles, with the particles microscopic surface, bulk and electrolyte environments playing a role in the (de)intercalation rates over seconds to hours [5][6][7][8] .

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https://doi.org/10.1038/s41565-023-01466-4 of charge.However, between 400 and 680 nm for LCO and between 400 and 800 nm for NMC811, the changes in reflectivity with x are non-monotonic, with spectral shifts consistent with the bulk reflectivity measurements of other materials 16,21,22 (Supplementary Note 1).This region should consequently be avoided for microscopic measurements where reflectivity is used to track the lithiation state of particles in an electrode.Fitting the reflection spectra shown in Fig. 1a with the Kramers-Kronig relations 23 (Extended Data Fig. 1 and Supplementary Note 2) allows the extraction of the state-of-charge-dependent RI.The real parts of n for LCO and NMC811 are found to be between 2.0 and 2.5.This is larger than the RI (1.5-1.6)designed for high-NA microscope objective lenses; hence, aberration corrections should be applied to account for the index mismatch (see the discussion below).
In Fig. 1b, we perform operando reflection (confocal) microscopy measurements on an individual polycrystalline LCO particle between 380 and 800 nm.Here, at 800 nm (red curve), when light is focused on/collected from the surface (S) of the agglomerate, the reflectivity decreases linearly as x increases.However, between 380 and 600 nm, a non-monotonic 'W'-shaped curve is observed (green, light blue and purple curves), in line with Fig. 1a.Interestingly, when focusing/collecting light from inside (I) the agglomerate-an advantage offered by confocal sectioning-the reflectivity at 800 nm decreases linearly with x (Fig. 1b, blue dashed line).The difference between the 'S' and 'I' response at 800 nm can be reconciled by noting that the reflectivity at the interface of the two media of RI n 1 and n 2 will be proportional to the difference (n 1 - n 2 ) 2 under normal incidence 24 .At the surface of the agglomerates, n 1 is equal to that of the electrolyte (~1.4-1.6)(refs.25,26)  and n 2 is equal to that of the agglomerate (1.8-2.5)(ref.27).However, inside the agglomerate, n 1 and n 2 will both vary between 1.8 and 2.5.Consequently, depending on the focus, different interfacial RIs, that is, electrolyte/particle versus particle/particle (intraparticle), will be resolved (Supplementary Note 2 discusses changes in the absorptive part of RI (k), which are small).More generally, our results indicate that inter-agglomerate heterogeneities cannot be established from the measurements at a single focal plane (WF).Indeed, as shown in Extended Data Fig. 2 and Supplementary Video 1, even in the absence of any cycling, different intensity patterns-closely resembling patterns that might be ascribed to the motion of phase fronts or arise from morphology inhomogeneities 17,18,28,29 -can be observed across the surface of agglomerates simply by small (20 nm) adjustments in the focus 30 .
The RI (n) also plays a role in the imaged size of an object via the optical path length, OPL = n × s, where s is the geometric path length.The uncertainty in sizing can be estimated by comparing the maximum intensity projection (MIP) (where variations in optical path length are accounted) and single-focus-position (F1) images (Methods).For x = 1 (in LCO), L F1 and L MIP (L is the agglomerate particle length; Fig. 1c, dashed red and blue lines) deviate by 0.12%.This deviation increases monotonically with decreasing x, reaching 0.43% at x = 0.48.Propagating the uncertainty in L to one in volume (Supplementary Notes 3 and 4) suggests that changes in the particle volume below ~1.0-1.5% are challenging to unambiguously detect with optical microscopy.
Having demonstrated the experimental conditions under which optical microscopy measurements can be carried out for battery materials, LSCRM (Fig. 2a shows the schematic) is performed on polycrystalline LCO and NMC811.A laser beam between 820 and 1,100 nm (depending on the exact experiment), where changes in reflectivity with the lithiation state are monotonic for LCO and NMC811, is scanned across the sample.Adjusting the focus of the beam in the sample, whilst using a pinhole to gate the out-of-focus light, allows the probing of different 2D planes up to the optical penetration length (Supplementary Note 5).Stacking the 2D images and correcting for laser attenuation and defocus aberration (Supplementary Note 5) allows for sub-micrometre 3D information to be obtained on individual agglomerates of the particles (Fig. 2b,c).A customized battery half-cell with optical access (Fig. 2a, right) allows for galvanostatic cycling during the recording Optical reflection microscopies are a ubiquitous tool for the low-cost, non-invasive, microscale characterization of evolving systems 9,10 .Typically, microscopic reflection is performed at visible wavelengths (400-800 nm) either in the wide field (WF)-where the entire sample is illuminated-or with line scanning confocal reflectance microscopy (LSCRM), where a focused laser beam is rapidly scanned across a given sample plane and the reflected light is used to build an image.A key difference between WF and LSCRM is that in the latter, specified depths of a material can be individually probed (sectioning).Over the last decade, WF optical reflection microscopies, particularly using high-numerical-aperture (NA) microscope objectives, have emerged as an inexpensive tool for tracking phase 11 and structural 12 changes within operating batteries.This is because the reflectivity of many micrometre-sized features on the electrode surface can dramatically increase, decrease or spectrally shift on (de)lithiation 13,14 .Despite this, little framework still exists for physically understanding the reflectivity signals from such (WF) experiments, with conflicting results emerging 11,15 .Understanding how to apply the technique is particularly pertinent as the (real) refractive index (RI; n) of many battery electrode materials (n = 2.0-3.0)(ref.16) is strongly mismatched from that which high-NA optical microscopes are designed for (n ≈ 1.4-1.6).Furthermore, microscopy studies of battery electrodes have, thus far, been primarily limited to study surface topography changes 17,18 or lithiation in 'flat' single-crystalline particles in two dimensions 11,12,19 using two-dimensional (2D) WF measurements, which limit their applications and skews our understanding of inherently 3D processes.Most importantly, as is the case with other operando methods, optical reflection methods have been unable to directly visualize the liquid electrolyte and its interaction with particles or agglomerates, making it challenging to completely resolve the origins of (de)intercalation heterogeneities.
Here we overcome these limitations by first understanding, howand under what conditions-optical imaging can be performed in batteries whilst avoiding false conclusions from optical artifacts.In contrast to previous studies, we focus on (near-infrared) LSCRM, where sectioning allows individual agglomerates of particles (that is, secondary particles comprising many primary smaller particles) in three dimensions to be studied.We apply LSCRM to examine Li intercalation in Ni-rich Li x Ni 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) and Li x CoO 2 (LCO), both known to experience heterogeneities in Li occupancy during cycling 6,20 .To benchmark the methods, agglomerate particle volume changes and surface-to-core phase-front velocities during cycling are measured, with the interparticle heterogeneity quantified and compared with the results of ensemble studies.We further push the LSCRM technique to distinguish intercalation heterogeneities that occur in the bulk of agglomerates from those limited to the surface, as well as visualize the formation of concentration gradients in the surrounding electrolyte, which we show can be simultaneously tracked from its intrinsic fluorescence.Our results highlight LSCRM as one of the only ways of microscopically imaging both solid and liquid phases of batteries in three dimensions and in operando.

High-resolution optical imaging of battery particles
For many metal oxides, including LCO and NMC811, their reflectivity (and thus the RI) 14 at visible wavelengths changes during the injection of a charge.To investigate the relationship between charge state and reflectivity, the ex situ microscopic reflection spectra of individual LCO and NMC811 agglomerate particles are shown (Fig. 1a) as a function of lithiation (x = 0 corresponds to fully delithiated particles).In both LCO and NMC811, the (surface) reflectivity increases with decreasing x in the near-infrared regime between 680 and 900 nm for LCO and between 800 and 900 nm for NMC811, with changes of up to 20% between x ≈ 0 (0.5 for LCO) and x ≈ 1.0.Hence, in this wavelength range, the magnitude of particle reflectivity can be used as a proxy of the state Article https://doi.org/10.1038/s41565-023-01466-4 of the confocal image stacks of electrodes (~120 s per stack).All the data presented here are taken from the first 2-9 cycles of self-standing electrodes with a low loading of 20 wt% of LCO or NMC811.However, as shown in Supplementary Note 5, our method can be readily applied to electrodes with higher active material loadings (up to 92 wt% with ~40% porosity).

Operando tracking of agglomerate particle volume changes
To first benchmark our LSCRM methodology, we monitor the volume changes in individual agglomerates during a cycle.By calculating the number of voxels occupied by agglomerate-containing regions within the reconstructed volumes, volumes at the individual agglomerate level can be obtained.In Fig. 3a-c, the normalized change in single agglomerate particle volumes (ΔV/V) of LCO and NMC811 are shown as a function of time/charge state and cycling (C) rate.The volume of the LCO agglomerates in all the cases increases during charging and decreases during discharging (standard deviation in the maximum volume change (σ ΔV/V ) is 0.42), with the maximum volume change of ~3% (±1%) (Supplementary Note 5 provides the error bar estimation).For NMC811, σ ΔV/V is 0.63 with the volume decreasing during the charging (|ΔV/V max | ≈ 12% (±2%)) (Fig. 3c).In NMC811, we observe major changes in volume only between Li fractions of 0.3 ≤ x ≤ 0.7 and as for LCO, there are also inactive agglomerates that show ΔV/V ≈ 0 throughout the cycle.x in Li x CoO 2 0.97 S@380 nm S@430 nm 0.52 S@600 nm S@800 nm I@800 nm Time (min) 20  25   Fig.Interestingly, the changes in volume correlate well with the degree of reflectivity change at the agglomerate particle centre (Supplementary Note 5), that is, change in the state of charge and reaction extent, suggesting that this latter quantity is responsible for the interparticle heterogeneity in volume changes.The correlation between reaction extent and ΔV/V is independent of the agglomerate size and the average ΔV/V changes we observe are similar at different electrode loadings (Extended Data Fig. 3 and Supplementary Note 5), suggesting that intra-agglomerate properties dominate the structural heterogeneities.
The results shown in Fig. 3b,c are consistent with previous ensemble X-ray diffraction measurements and corroborate well with our own correlated ex situ scanning electron microscopy (SEM) (Extended Data Fig. 4) and X-ray nanocomputed tomography measurements (Supplementary Note 6).

Surface-to-core transport
To further understand how structural inhomogeneities might be related to (de)lithiation asymmetries, we examine the transport velocities of Li-ion-containing phase fronts from the exterior to the centre of the agglomerate particles.To track the motion of phase fronts through polycrystalline NMC811 or LCO during the cycle, the normalized time-varying reflectivity-a proxy for the state of charge-is extracted for each z plane across the central area of an agglomerate particle.
From this, the depth dependence of the time-varying reflectivity can be extracted (Fig. 4a,b) as a function of the C rate.For each z plane, the point at which the reflectivity crosses zero is then determined (Fig. 4a,b, dashed line); from the variation in this reference point with depth, a transport velocity for ion-containing fronts can be estimated (Extended Data Fig. 5 and Supplementary Note 7).
For NMC811 (Fig. 4a), both delithiation and lithiation occur from the surface to the core, in an approximately symmetric manner across the agglomerate particle z span, with qualitatively similar behaviours from C/2 to 2C.In LCO, delithiation occurs from the surface to the core, as for NMC811.However, lithiation occurs approximately uniformly across the agglomerate volume, with all the depths simultaneously changing reflectivity (Fig. 4b, flat dashed line).The agglomerate nature of the NMC811 and LCO studied here means it is not appropriate to ascribe a single overall mechanism to (de)lithiation.As shown in Extended Data Fig. 6 and Supplementary Note 7, for large (>5 μm) agglomerates, where subparticles can be resolved, the onset of reflectivity change and surface-to-core transport velocity is slightly different for each subparticle within an agglomerate.In addition, there is significant compositional heterogeneity on the surface of the agglomerates, particularly during fast delithiation (see the discussion below and Fig. 5).Combined, these observations suggest that-as initially highlighted by another work 6 for multiply separated particles-surface kinetics and the multiparticle nature control the precise (de)lithiation patterns and timescales in agglomerates.However, by the end of charge-discharge, there will be a drive to have similar composition profiles in agglomerate subparticles 6,20 , as evidenced by the qualitatively similar shape for the reflection profiles of subparticles (Extended Data Fig. 6).We note, particularly for LCO, several studies 1,31,32 have reported drastically different intercalation behaviours between charging and discharging, which may explain the uniform surface-to-core lithiation profile for our LCO.
The through-agglomerate phase-front velocities (v p ) we obtain here are averaged across all the particles that make up an agglomerate and increase with the C rate for delithiation and lithiation, but remain on the same order of magnitude of 1-5 nm s -1 across C rates.The linear scaling of v p with the C rate in both NMC811 and LCO suggests that the motion of phase fronts is kinetically, rather than thermodynamically, limited for both layered oxides 6,20 .Furthermore, the fact that v p remains relatively independent of electrode loading (Supplementary Note 5) suggests that intra-agglomerate as opposed to inter-agglomerate effects control the (de)lithiation rates.

Imaging phase-front dynamics on different surfaces
Having shown that the velocity of phase fronts from the surface to the core of agglomerates can be tracked using LSCRM, we further push the technique to spatially separate (de)lithiation inhomogeneities between the surface and bulk of individual agglomerates.For that, we compare, using mathematical reconstructions shown in Fig. 5a (Supplementary Notes 8 and 9) at different points during a charge-discharge cycle, the spatial distribution of the reflected intensity (lithiation state) between the agglomerate exterior and core for LCO agglomerates cycled at different C rates (C/2 and 2C).In Fig. 5b,c 52,53 , aberration correction 54 and thresholding (Supplementary Note 5), a 3D reconstruction of the agglomerate particle can be obtained.The z sampling size is predetermined as ~300 nm.
https://doi.org/10.1038/s41565-023-01466-4outermost (exterior) and innermost (core) shells are shown for pristine, charged and discharged states during galvanostatic cycles at C/2 and 2C.At C/2, for the agglomerate exterior, the contrast in reflectivity both within and between domains remains small throughout the cycle, indicating large-area uniform (de)lithiation.Furthermore, for the pristine and discharged states, the distribution of different lithiation domains is almost identical, demonstrating a reversible cycling process.At the agglomerate centre, a spatial rearrangement of Li phases is observed from the pristine to charged states.This rearrangement remains on discharging, but the differences in lithiation degree between the domains, for a given overall state of charge, are small.The observation of changes at both exterior and core, however, indicates that (de)lithiation occurs throughout the agglomerate.
For 2C, at the agglomerate exterior, the pristine and discharged states do not show a similar spatial distribution of lithiation phases.For the core, no rearrangement of Li domains at the end of charge is observed, unlike at C/2.Only minimal changes in both contrast and spatial distribution of Li domains occur between the pristine, charged and discharged states.This observation suggests that (de)lithiation does not occur throughout the agglomerate particle volume, in agreement with the limited cycling capacity measured at 2C compared with C/2 (Fig. 3b shows an example).For the exterior, regions of contrastingly high (dark blue) and low (yellow) Li content appear on going from the pristine to charged state, and persist to the discharged state.This indicates non-uniform lithiation on the surface of LCO agglomerates at high C rates, consistent with several previous observations in layered oxide materials [33][34][35] and Raman imaging at the surface of agglomerates (Supplementary Note 6).For NMC811, a more complex behaviour is observed (Extended Data Fig. 7) and generally further work, for example, using synchrotron methods, is needed to quantitatively link lithiation extents and reflectivity.

Visualization of electrolyte dynamics
Thus far, optical and other operando imaging methods have been limited to visualize particles of active materials.However, we show that LSCRM offers the opportunity to image both Li transport in solids, as demonstrated above, simultaneously with concentration gradients forming in the liquid electrolyte on polarization.Indeed, LiPF 6 , the Li-conducting salt in the electrolyte used, has previously been observed to be a source of fluorescence at visible wavelengths, although the exact origin is debated 36 .Following these past observations, we find that under two-photon excitation (2PEF), the fluorescence of LiPF 6 salt (solid) is significantly more efficient than with one-photon excitation (1PEF; Fig. 6a).In Fig. 6b, we perform ex situ 2PEF experiments on LiPF 6 solutions at different concentrations and find a strong monotonous brightening with concentration.Figure 6c shows the evolution of the electrolyte 2PEF intensity, at different focal planes above a self-standing LCO electrode, during a charge-discharge cycle at 2C.In all the cases, the electrolyte 2PEF increases near linearly on charging to 4.2 V, that is, on the release of Li ions to the electrolyte, with a slight plateauing in the rate of brightening between 4.1 and 4.2 V. Discharging, that is, the depletion of Li from the electrolyte, results in dimming of the electrolyte 2PEF.The response is repeatable and of a similar magnitude over eight cycles (Supplementary Note 10).Together, the ex situ and operando measurements show the electrolyte 2PEF to be highly sensitive to the Li-ion concentration and indicate that the 2PEF must indeed

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https://doi.org/10.1038/s41565-023-01466-4derive from the LiPF 6 salt or a compound bound to it 36 .Furthermore, the measurements indicate that the 2PEF response is unrelated to cycling or light-induced electrolyte degradation 37,38 (Supplementary Note 10).Consequently, it is suggested that the intensity of the 2PEF can be used to qualitatively track the Li-ion concentration in the electrolyte.
Our attention is then turned to examine the spatial distribution of salt concentration on cycling.To do so, LSCRM experiments are repeated with an excitation of 1,020 nm with two separate detectors, one for collecting the particle reflectance and another for 2PEF (Fig. 2a; ~250 s per confocal stack).This allows for the simultaneous volumetric imaging of the electrolyte and LCO agglomerates (Fig. 6d).In Fig. 6e, the 2PEF signal of the electrolyte in the plane ~300 nm above the top surface of the electrodes is plotted at selected time points (labelled A-F, which correspond to points marked in the charge-discharge curves; Fig. 6c) and spatial locations during a C/2 cycle.On charging, the 2PEF intensity increases due to delithiation and an increase in the LiPF 6 concentration .A gradient in the 2PEF intensity also becomes present above potentials of 4.0 V around the LCO agglomerates.This 2PEF/electrolyte concentration gradient originates from the difference between the rate of delithiation at the LCO surface and the rate at which PF 6 − anions diffuse towards the LCO agglomerates 39,40 to balance the released Li + ions and maintain electroneutraility [41][42][43] .Furthermore, at all the potentials, the 2PEF is relatively uniform in regions not containing LCO (Fig. 6c, bottom) and on discharging, the concentration gradient around agglomerates disappears.Altogether, our results indicate a reversible process and the concentration gradient we observe extends as far as ~1.5 μm.We note that on charging the electrode and then allowing it to relax to the open-circuit potential, the polarization gradient rapidly disappears (Extended Data Fig. 8).Switching to a greater C rate, that is, 2C, during the initial charge up to 3.9 V (Fig. 6, panels marked A), the 2PEF of the electrolyte is the brightest around the LCO agglomerates, with the intensity decaying approximately homogeneously away from the agglomerates.Increasing the potential to 4.2 V (Fig. 6, panels marked B, C, D and E) results in a drastic increase in the 2PEF intensity, but the distribution of electrolyte 2PEF also becomes heterogeneous around both agglomerates and in regions of the electrode ~20-50 μm away from the LCO agglomerates (Fig. 6e,f, bottom).The latter observation suggests inhomogeneous electrolyte diffusion within the self-standing electrode as a result of the geometry and distribution of pores within the agglomerate-carbon/binder matrix 44 .This influence of the matrix can be expected at higher C rates where the rate of (de)lithiation at the LCO surface and ionic diffusion rate in the electrolyte are more significantly mismatched 45 .Finally, on discharging to 3.9 V (Fig. 6, panel marked F), the 2PEF distribution returns to its initial state, confirming that our observations do not stem from electrolyte degradation.We note that at higher electrode loadings (Supplementary Note 5), the microscopic electrolyte polarization gradients we observe remain.Calibrating the 2PEF response (Supplementary Note 10) allows us to approximately quantify the locally increased salt concentration, ΔC salt .At C/2, we find a ΔC salt value of approximately +0.25 (±0.01)M and at 2C, a ΔC salt value of approximately +0.30 (±0.01)M on reaching the maximally charged state (Fig. 6, panels marked C, D and E), in line with previous spatially resolved studies 43,[46][47][48][49] and our own Raman measurements (Supplementary Note 10).However, the relatively thick electrodes used here (~300 μm) and the fact that our measurements are made from the far side of the separator may result in slightly exaggerated salt concentration profiles.In NMC811, similar behaviour is observed as for LCO but with polarization gradients that are slightly less pronounced and more anisotropic, requiring further in-depth analysis (Extended Data Fig. 9).

Conclusions
This paper demonstrates that high-resolution LSCRM is a powerful tool for the 3D microscopic tracking of particle structural transformations, Li-ion intercalation and electrolyte dynamics in operating batteries (Supplementary Note 11 provides further discussion).Applying LSCRM important functional parameters of LCO and NMC811, such as the velocity of Li-containing phase fronts from the surface to the core of agglomerates and the volume change in an individual agglomerate during a cycle, are obtained.These parameters display a large degree of heterogeneity due to the differing extents of reaction progression for agglomerates, an effect not captured by ensemble techniques.Specifically, we discover that in LCO and NMC811 agglomerates, the competition between surface-limited reactions and the multiparticle

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https://doi.org/10.1038/s41565-023-01466-4 Further work is needed to place some of our material-specific observations, such as the rapid lithiation observed in our LCO and the origin of LiPF 6 fluorescence on firmer footing.More generally, using mid-infrared photothermal techniques 50 or wavefront shaping 51 might help push the depth and chemical sensitivity of optical methods for batteries.Nonetheless, the label-free nature of LSCRM and the outlined application framework imply that beyond batteries, such methods will find use in the study of 3D solid-and liquid-phase dynamics in a range of functional materials and devices. https://doi.org/10.1038/s41565-023-01466-4

Preparation of LCO self-standing electrodes
The 50.0, 112.5 and 145.8 mg polycrystalline LCO (2.5-7.5 μm average diameter), carbon black Super P Conductive and 60 wt% PTFE dispersion in water were carefully mixed and grinded in a mortar with a pestle for 15 min.Ethanol was added from time to time to help the different components bind together and structure the mixture.When the mixture became thick, it was taken out of the mortar and rolled onto a clean surface for 15 min to make a smooth and thick (~300 μm) electrode film with LCO, carbon and PTFE mass ratios of 20, 45 and 35%, respectively.The as-prepared film was dried overnight in an 80 °C oven under a vacuum.For the preparation of electrodes with 60, 80 and 92 wt% of LCO, the same procedure as above was applied using the following masses: 60 wt% LCO: 150 mg; carbon, 50 mg; PTFE dispersion, 83 mg.80 wt% LCO: 200 mg; carbon, 25 mg; PTFE dispersion, 42 mg.92 wt% LCO: 230 mg; carbon: 10 mg; PTFE dispersion: 17 mg.

Preparation of NMC811 self-standing electrodes
The 50.0, 112.5 and 87.5 mg polycrystalline NMC811 (5 μm average diameter), carbon black Super P conductive and dry PTFE were carefully mixed and grinded in a mortar with a pestle for 15 min in an argon-filled glovebox.A few drops of acetonitrile were added from time to time to help the different components bind together and structure the mixture.When the mixture became thick, it was taken out of the mortar and rolled on a clean surface inside the glovebox for 15 min to make a smooth and thick (~300 μm) electrode film with NMC811, carbon and PTFE mass ratios of 20, 45 and 35%, respectively.

Preparation of materials for ex situ studies
LCO, NMC and LFP.LCO, NMC811 and lithium iron phosphate (LFP) powders synthesized or purchased as previously described above were ball milled for 20 min with 10% in weight of carbon black Super P. Swagelok-type cells were assembled in an argon-filled glovebox with approximately 10 mg of powder, using two Whatman separators filled with LP30 electrolyte and with metallic Li as the counter electrode.The cells were cycled with fixed capacity, before the powder was recovered and washed two times with dimethyl carbonate, and then centrifuged and dried for 1 h under a vacuum.This allowed for the preparation of LCO, NMC811 and LFP powders with different states of charge/ Li fractions for ex situ experiments.LiPF 6 solutions in 1:1 vol% EC/DMC.In an argon-filled glovebox, 3.1, 15.2, 30.4,151.9, 303.8, 607.6 and 1,215.2mg of LiPF 6 were dissolved in 2.0 ml of 1:1 vol% EC/DMC mixture to yield 0.01, 0.05, 0.10, 0.50, 1.00, 2.00 and 4.00 mol l -1 LiPF 6 solutions in EC/DMC.

Ex situ reflection microspectroscopy
Reflection microspectroscopy of individual battery agglomerates was performed on a customized ZEISS Axio microscope.Illumination was provided using a halogen lamp (ZEISS HAL100) focused by a 50×/0.4NA objective (Nikon, T Plan SLWD).Reflected light was spatially filtered (collection spot diameter, <5 μm) using a 100-μm-diameter optical fibre (Avantes FC-UV100-2-SR) mounted in the confocal configuration and connected to a spectrometer (Avantes AvaSpec-HS2048).Agglomerates were pressed onto glass microscope slides before measurement and encapsulated with a second cover glass inside any argon-filled glovebox to avoid aerial oxidation/hydrolysis.A minimum of 20 individual agglomerates (well separated from any carbon) were used to obtain the spectra and Gaussian smoothing applied to remove noise.

Agglomerate size error estimation using time-domain optical coherence tomography
Time-domain optical coherence tomography was used to generate the MIP and F1 images discussed in the main text.F1 was taken from the position in the time-gate position where there was the maximum electric field.For the time-domain optical coherence tomography setup, a beam delivered from a Ti:sapphire laser (Mai Tai HP, Spectra-Physics) was divided into two paths by a polarizing beamsplitter.On one path, the light was focused onto the back focal plane of a 0.8 NA objective (Olympus), which delivers collimated light on the sample.The reflected light from the sample is collected by a beamsplitter and recombined with the second path on another beamsplitter.Light on this second (reference) arm does not pass onto the sample but onto a delay stage (Newport), which controls the temporal overlap between the reference and signal arms.The combined signal and reference light are imaged onto a charge-coupled device camera (Manta G-046B, Allied Vision).A polarizer in front of the camera ensures that only light with a selected polarization is measured.The reference arm is scanned to measure the electric-field amplitude as a function of time delay (focal position) within the sample.From this trace, the MIP and F1 images can be generated.

X-ray computed tomography
High-resolution, X-ray nanocomputed tomography was performed on the triangular tip of the electrode using a ZEISS Xradia 810, 5.4 keV Ultra nanocomputed tomography instrument (Carl Zeiss) in a large field-of-view mode.Sequential tomography sequences using absorption contrast and Zernike phase contrast were collected and later stitched together in the Dual Scan Contrast Visualizer (DSCoVer 16.1.14271)software.A pixel binning of 2 was used for each scan, resulting in a pixel size of ~128 nm.The sample was rotated through 180° with radiographs collected at discrete angular intervals amounting to 1,601 projections for each of the absorption-contrast and phase-contrast scans.Scans were reconstructed using XMReconstructor 10.0.3878 software (Carl Zeiss) and the resulting images had 50% contribution from the phase mode and 50% contribution from the absorption mode.Data were then processed using the Avizo 3D visualization software package (Avizo, version 2020.2FEIO, VSG).The initial image was cropped to 502 × 503 × 286 voxels at a size of 128.0 × 128.0 × 128.0 nm 3 per voxel.Segmentation was carried out via a simple thresholding algorithm.The 'separate objects' module was applied to detect and subtract surfaces that separate the agglomerate particles.The 'opening' module was then used to reduce unnecessary artifacts and excess noise by removing small objects and smoothing object boundaries.Finally, 'label analysis' was applied to collect statistical data of each particle in the sample.

Raman microspectroscopy
Raman spectroscopy of the samples was performed using a home-built 532 nm Raman microscope (along with the analysis methods) previously described elsewhere 56 .A high-NA oil-immersion objective (Nikon 60×/1.4NA oil) was used to ensure high-resolution imaging and increase the collection efficiency.The maximum pump power before the objective was ~20 mW, a power level that ensured no degradation of samples.

SEM
SEM images were acquired on a GeminiSEM 360 microscope from ZEISS, using an acceleration voltage of 5 kV.Supplementary Note 6 https://doi.org/10.1038/s41565-023-01466-4provides details about the 3D reconstruction based on the images acquired at different tilt angles.

Wavelength-resolved reflection imaging
The wavelength-resolved reflection imaging of an LCO electrode was performed on an Axio Observer 7 inverted microscope from ZEISS.The sample was illuminated from the back side by means of an unpolarized white-light source through a ×63 oil-immersion objective with NA of 1.4 (Plan Apochromat, ZEISS).The light reflected by the sample was then collected by a complementary metal-oxide-semiconductor colour camera (Axiocam 705 colour, ZEISS) through the same objective, which allows probing three wavelength regions at once.Cycling was performed using a CHI760E potentiostat (CH Instruments), in the same cell as the one used for the LSCRM experiments.

Ex situ 1PEF and 2PEF spectroscopy
For liquid measurements, 1-mm-path-length glass cuvettes were filled with LiPF 6 solutions in 1:1 vol% with EC/DMC of a predefined concentration.Cuvettes were sealed in an argon-containing glovebox before measurement.For measuring the solid LiPF 6 , the powder was sandwiched between two microscope coverslides.The coverslides were sealed together with epoxy resin inside an argon-filled glovebox before measurement.For 1PEF, excitation light from a 532 nm laser (Laser Quantum Gem, continuous wave, 532 nm, 100 mW) was focused onto the sample with a 50-mm-focal-length lens (Thorlabs).The fluorescence was collected, collimated and focused onto the fibre port of a spectrometer (Ocean Optics, Ventana 532 nm).The exciting laser light was separated from fluorescence using a dichroic mirror (Semrock 532 nm RazorEdge long-pass filter).For 2PEF experiments, the same configuration was used, except the exciting light was the 1,020 nm output of a Ti:sapphire laser (Mai Tai HP, Spectra-Physics) and an additional 1,000 nm short-pass filter (Thorlabs) was placed in front of the spectrometer to remove any of the exciting beam.We note that the 2PEF efficiency dramatically decreased with wavelength and when excited below 900 nm (450 nm for 1PEF), very little emission was observed.For 1PEF, the laser power at the sample was ~10 mW (continuous-wave laser) and for 2PEF, the fluence at the sample was ~15 μJ cm -2 (pulsed laser).

Operando laser scanning confocal microscopy
Laser scanning confocal microscopy was performed using a custom-built microscope.The output of a Chameleon Ultra II Ti:sapphire laser (Coherent) was directed to a laser (galvo-) scanning microscope body (Scientifica), with x-y-z piezo control.The reflected light from the sample was collected and focused through a 0.7 AU pinhole for spatial filtering.Dichroic mirrors (500-620 nm and >650 nm) spectrally filtered the light, which was focused onto two silicon avalanche photodiodes.Recording was performed using the Abberior Instruments Imspector 16 software.Depending on the exact experiment and signal magnitude, the pixel dwell time was varied between 10 and 20 μs, with regions between 300 × 300 and 600 × 600 pixels scanned again depending on the agglomerates of interest.Pixels ranged between 40 and 80 nm in size.Overall, this resulted in z-stack acquisition times of between 100 and 220 s, although for small agglomerates, acquisition times down to 60 s could be achieved.The coherence length of the laser used here is <2 μm such that reflection interference contrast effects can be minimized.In all the experiments, a laser fluence of <10 μJ cm -2 at the sample was used.For experiments shown in Fig. 1b, light-emitting diodes at the appropriate excitation wavelength were used as the source.
The operando half-cell (ECC-Opto-Std; El-Cell) was modified to accommodate a 1.4 NA objective and 0.15-0.17-μm-thickcoverslips (Supplementary Note 12).To prevent the buildup of artificial regions of higher/lower salt concentrations when preparing our cells, we fill the cell with electrolyte (that is, not just wetting of the separator).All cycling was performed using a Gamry Reference 600 potentiostat, with home-built software to control synchronization between the potentiostat and microscope.Throughout the manuscript, a C rate of 1C corresponds to charging in 1 h.

Image processing
Image processing was performed with custom Python 3.5, MATLAB R2022b and ImageJ 1.53t (ref.57) scripts (Supplementary Notes 2-8 provide further details of the algorithms).Before performing any analysis or image correction, xyz image registration was performed using the ImageJ registration plugin 58 .There is a spread in the onset time of reflectivity changes between sub-particles.The uncertainty on the pixel intensity increases with depth but sits between 3% and 5% for all points.

Extended Data
Extended Data Fig. 7 | Spatial propagation of (de)lithiation heterogeneities at the surface and core of NMC811 agglomerates.Charge-discharge cycle of NMC811 at C/2 and 2 C showing projections from shells at exterior and centre of agglomerate at set points during the cycle (letters A to F).For NMC811 the semi-major axes of the surface ellipsoid are 3.5, 2.8 and 6.5 μm, for the core it is 1.2, 1 and 1.8 μm.As for LCO some movement of intensity from the edges of the projection to the centre on delithiation and a reverse on lithiation can be observed, however the exact nature of the motion is unclear.For NMC811 there are a range of domains with different degrees of lithiation at the start of the charge, further complicating the analysis.Qualitatively it appears the overall difference in degree of lithiation within and between domains decreases on charge and increases once again on discharge.However, further work is required to fully interpret these observations.Data across the two C-rates represent measurements of identical agglomerates.At a rate of C/2: A -3.85 V, B -4.00 V, C -4.17 V, D -3.85 V, E -3.73 V F -3.55 V.At a rate of 2 C: A -3.90 V, B -4.01 V, C -4.17 V, D -3.72 V, E -3.64 V F -3.45 V.
Extended Data Fig. 9 | Two-photon excited fluorescence (2PEF) from LP30 electrolyte during a 2 C top and C/2 cycle of NMC811.In a similar manner to LCO there is brightening of the electrolyte 2PEF on charge and dimming on discharge.Around the agglomerates (solid and dashed black lines are guides to the eye), the 2PEF is initially homogeneously distributed (panels A and B) before a concentration/2PEF gradients build-up at higher voltages above 4.0 V.The 2PEF concentration gradient is somewhat inhomogeneously distributed around agglomerates above 4.0 V (panels C and D).At C/2 the onset of the 2PEF concentration gradient is at higher voltages as compared to 2 C. Scale bar is 4 μm.Data across the two C-rates represent measurements of identical agglomerates.

Fig. 2 |
Fig. 2 | Three-dimensional imaging in polycrystalline battery electrodes.a, Schematic of the LSCRM setup (left) and operando battery cell (right).A tunable laser source is directed to the microscope body via a beamsplitter (BS), with the reflection signal and fluorescence passed through pinholes (PHs) before being collected onto two separate avalanche photodiodes (APDs).Long-pass dichromic mirrors (DMs) and band-pass filters (BPFs) control the spectral selectivity: APD1, 700-1,100 nm; APD2, 550-680 nm.The z sampling is performed by the movement of an objective piezo.Self-standing LCO and NMC811 electrodes are placed in an optical microscopy half-cell (WE, working electrode; CE, counter electrode).A Li metal counter is used along with a glass fibre separator with the cell filled with a carbonate liquid electrolyte (LP30 (Methods); blue shading); depth resolution (red arrow) is limited to ~10 μm.b,c, Confocal z stacks of LCO and NMC811.Scale bars, 5 μm.Following attenuation correction52,53 , aberration correction54 and thresholding (Supplementary Note 5), a 3D reconstruction of the agglomerate particle can be obtained.The z sampling size is predetermined as ~300 nm.

xFig. 3 |
Fig. 3 | Tracking agglomerate particle volume changes during cycling.a,b, Tomographic reconstruction of LCO (a) and NMC811 (b) throughout a 2C charge-discharge with specific capacities and times above and below.Rows are different agglomerates.Scale bars, 5 μm.c, Percentage change in agglomerate volume compared with that at the open-circuit potential (black for LCO and red for NMC811) as a function of time during a 2C, C and C/2 charge-discharge

Fig. 4 |
Fig. 4 | Measurement of phase-front velocities through agglomerate particles.a,b, Reflectivity as a function of z plane and charge state/time through a NMC811 (a) and LCO (b) agglomerate.The top of the agglomerate (0 μm) is taken as the first plane inside the agglomerate.Galvanostatic charge-discharge is performed at C rates from 2C to C/2 (top); all the data are taken after the first cycle.The dashed line is a guide to the eye at which the normalized ([-1, 1]) reflected intensity changes sign.From the time/depth dependence of this point, a phase-front velocity through the agglomerate can be estimated (Supplementary Note 7).c-e, Phase-front velocity for delithiation and lithiation (only NMC811) as a function of C rate.The points represent the mean velocity obtained across measurements of more than ten NMC811 and LCO agglomerates.The error bars show the standard deviation and take account for the measurement and fitting uncertainty on each point, which is ~7%.Data across different C rates represent the measurements of identical agglomerates.At slower cycling rates greater axial sampling can be performed.

Fig. 5 |Fig. 6 |
Fig. 5 | Unwrapping of particle surfaces.a, Schematic demonstrating the enclosing of agglomerate particle 'shells' onto the surface of an ellipsoid followed by projection onto the 2D plane.b,c, The 2D projections from shells at the exterior and the centre of an LCO agglomerate in pristine (x = 0.96 at C/2 and x = 0.95 at 2C in LCO), charged (x = 0.44 at C/2 and x = 0.52 at 2C) and discharged (x = 0.95 at C/2 and x = 0.94 at 2C) states for C/2 (b) and 2C (c) charge-discharge

Fig. 1 |Extended Data Fig. 3 |
Refractive indices of battery electrodes.a-b.Real (n) and imaginary (k) parts of the refractive index of LCO and NMC extracted from fitting model as detailed in supplementary information 2. Agglomerate volume changes as a function of electrode loading.a-c.Extracted volume changes of individual LCO agglomerates as a function of electrode loading (60 wt%, 80 wt% and 92 wt%).The volume of agglomerates increases to a maximum of ~4% on charging before shrinking once again, in-line with previous studies as discussed in the main text.There is a large degree of heterogeneity in the absolute expansion.Some agglomerates in the electrode are inactive and hence remain at a constant volume throughout.The standard deviations of volume changes are as follows: σ 60wt% = 0.44 σ 80wt% = 0.58 σ 92wt% = 0.48.The regions 1 and 2 correspond to different areas (20 μm × 20 μm) of the electrode which were imaged.All data is extracted from volume changes in the third or fourth cycling of the electrode.Data is shown for 40 agglomerates in a, 55 agglomerates in b and 75 agglomerates in c.The cycling rate was 2 C. The uncertainty on each ΔV/V value is ~10% as derived from measurement errors.Error bars are not shown on the plot to avoid obscuring of the data.Extended Data Fig. 4 | Correlation between LSCRM and SEM.a-d.LSCRM (top) and SEM images (bottom) of same LCO agglomerates of four different regions of the electrode before and after charging to 4.25 V. Scale bars: a -left panel 4 μm, right panel 5 μm; b -left panel 4 μm, right panel 5 μm; c -left panel 5 μm, right panel 4 μm; d -left panel 4 μm, right panel 4 μm.Colour scale is arbitrary in images.Extended Data Fig. 5 | Cartoon explaining extraction of planes from agglomerates for velocity estimation.The agglomerate is first orientated and slices through the core of the agglomerate extracted.For each slice the mean reflection intensity is calculated (after appropriate attenuation correction).This is then repeated over time (during the cycling) such that a depth and time varying reflectivity profile can be obtained.Extended Data Fig. 6 | Extraction of reflectivity profiles through subparticles of an agglomerate.a. 2D bright-field image of NMC811 agglomerate.Scale bar is 5 μm.b. 3D reconstruction of NMC811 agglomerate and re-orientation along long axis (z) to show agglomerate sub-structure (faded red lines) labelled P1 -P4.Scale bar is 5 μm.c.Normalised change in reflectivity for P1 -P4 regions in agglomerate shown in (a) as a function of time at top, centre and bottom of agglomerate.d-e.Normalised change in reflectivity for two other agglomerate with 3 and 5 identifiable sub-particles labelled P1 -P3(5).Reflectivity change shown as a function of time and depth in agglomerate.

1 | Tracking charge state with optical reflection microscopy. a, Reflectivity spectra
the two linecuts.Absolute percentage difference in the estimated agglomerate volume between the MIP and F1 as a function of the state of charge (x) in LCO (right).The measurement uncertainty on each data point in the right panel (derived from the signal-to-noise ratio on the images) is ~1%.