Figure 1a schematically depicts the measurement setup. We construct an electrochemical cell for operando XTM, consisting of a polyether ether ketone cell housing tube and two steel current collectors. The system we investigate here consists of two, 250 μm-thick electrodes of platelet-shaped graphite particles spaced with a 250 μm-thick glass fibre separator. To capture both lithiation and delithiation dynamics simultaneously, the top electrode is fully lithiated before the experiment in a standard coin cell in half-cell configuration using a metallic lithium counter electrode. The incident 25 keV monochromatic X-rays penetrate the cell in transmission geometry and are converted to visible light using a scintillator such that the image can be magnified with an optical microscope and recorded by a sCMOS camera.
Figure 1: Measurement setup and parameter selection.(a) Sketch of the electrochemical cell and the measurement setup, including a coordinate system indicating the two IP directions and the TP direction. (b) Comparison of a slice in the bottom electrode, where the phase has been retrieved with different δ/β ratios. Insets show the respective colour-scale histograms. Scale bar length: 100 μm. (c) Microstructure rendering of a part of the bottom electrode using the retrieval parameters from the two extreme cases in (b). Scale bar length: 100 μm. (d) Specific charge, voltage and scanning times during operando electrochemical operation. The inset shows a zoom-in of the voltage profile arising from the applied galvanostatic intermittent titration technique protocol. (e) Vertical cuts through the sample at different states of charge. The blue lines mark the electrode–separator interfaces that shift on electrochemical operation. For better visibility, only a window around the separator is shown. Scale bar length: 50 μm.
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Figure 1b shows a slice through the pristine bottom electrode reconstructed using the Paganin algorithm with different coefficient ratios δ/β and the respective grey value histograms. The applied δ/β ratios provide a trade-off: higher ratios improve the grey value contrast between particles and background but also decrease the effective spatial resolution, which results in a loss of small features. 3D renderings of the bottom electrode for the two extreme cases δ/β=0 (pure attenuation contrast) and δ/β=3333 (strong PPC) in Fig. 1c confirm this observed trade-off. For this paper, we choose δ/β=13.3 to achieve reliable data binarization and preserve the microstructure details.
During the operando experiment, 29 tomographic, 15 min scans are continuously recorded (Fig. 1d), while the lithium ions are electrochemically moved from the top to the bottom electrode at an effective C/7 rate until the cut-off potential at −1.5 V is reached. We use a galvanostatic intermittent titration technique protocol33, where 57 s long current pulses alternate with 3 s long open circuit relaxation times. A potentiostatic step at the cut-off potential is added to ensure that all lithium ions migrate between the electrodes (Fig. 1d). Figure 1e shows corresponding subsections of vertical cuts through the tomograms at different states of charge (SOC). The SOC is computed by dividing the measured charge by the active mass of graphite multiplied with the theoretical capacity of LiC6 (372 mAh/g refs 34 and 35). On lithiation, the bottom electrode has slightly expanded in the through-plane (TP) direction, while the top electrode has contracted in the same direction on delithiation. This is in agreement with our understanding from literature that graphite reversibly expands by approximately 10.5% on full lithium intercalation1,18,19.
To analyse the dynamics of the electrode, we apply DVC directly to the reconstructed data before any post-processing steps. DVC calculates a vector displacement field that maps two volumetric images locally on one another by maximizing the cross correlations between iteratively refined sub-volumes in the respective data sets. From the calculated vector fields, spatially resolved quantities like strain or relative volume expansion can be deduced.
To obtain a qualitative picture of electrode dynamics, we look at cuts C1, C2 and C3 through the electrodes, as indicated by the magenta planes in the sketch in Fig. 2a. Figure 2b shows the horizontal slice C2 through the middle of the top electrode with the superimposed vector field correlating the first with the last scan. Vector arrows point towards an anchor point close to the middle of the electrode, indicating that the electrode contracts within the plane parallel to the current collector (in-plane directions, IP1 & IP2, Fig. 2a) on delithiation. In contrast, for a slice C3 through the bottom electrode (Fig. 2c), the arrows point outwards, indicating that the electrode expands in the IP directions during lithiation. Supplementary Movie 1 shows the displacement field throughout the whole stack. Figure 2d shows magnifications of the image data and the displacement field in the full computationally available spatial resolution (one vector arrow in 32 × 32 × 32 voxels3). The domain taken from the electrode edge (orange box) reveals that the cell housing blocks expansion of the electrode in the IP direction and the domain from the centre of the electrode (blue box) shows a weak random displacement field at the particle scale superimposed on the radial fields describing the overall volumetric changes of the electrode. This indicates that particles and pores of the microstructure slightly deform and reorder with respect to one another during the course of (de)lithiation. The dipole shaped vector field superimposed on the vertical cut C1 through both electrodes and the separator (Fig. 2e) complements the observations from Fig. 2b,c in the TP direction: the glass fibre separator moves upwards, the top electrode contracts, and the bottom electrode expands. The overall volume of the sample remains almost unaffected on a full (de)lithiation, which is expected because of the symmetric cell design and the conservation of charge and mass within the sample.
Figure 2: Digital volume correlation.(a) Schematic of the two electrodes, the separator (black) and the cuts C1, C2, and C3 (purple). The coordinate system indicates the two IP directions and the TP direction. (b) Top electrode with superimposed vector field indicating the IP electrode contraction from the first to the last time step (vectors are scaled by a factor 60). Scale bar length, 300 μm. (c) Analogue graphic for the bottom electrode. Vectors point outwards, indicating an expansion. Scale bar length, 300 μm. (d) Zoom-ins showing the full vector field resolution within the boundary regime (orange box, vectors rescaled by a factor 8) and within a central part in the electrode (blue box, vectors rescaled by a factor 80). Scale bar length, 100 μm. (e) Vertical cut through both electrodes and the separator with superimposed vector field (vectors scaled by a factor 8). Scale bar length, 300 μm.
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We further determine that within the graphite electrodes, microstructural changes occur predominantly along the TP direction. The IP vector field components (Fig. 2b,c) are on the order of only 1–2 μm (arrows are scaled by a factor 60), while the TP vector field components (Fig. 2d) represent an average displacement of 10–20 μm (scaling factor 8). The origin of this is twofold: first graphite expands predominantly along its c-axis, which corresponds to the shortest dimension of the active particles. As most particles align with their flat side parallel to the current collector (Fig. 1c)6, the electrode will favour expansion along the TP direction. Second, from Fig. 2d (vector arrows scaled by a factor of 8), the cell housing constrains further expansion in the IP directions.
To summarize, a qualitative inspection of the vector fields reveals the motion of the electrode and the graphite particles during (de)lithation. In the following sections, we explain how to analyse these vector fields to quantify the electrochemical activity within the electrodes and the corresponding microstructural changes.
Because graphite expands on lithiation, we propose to quantify the electrochemical activity in the electrodes as a function of 3D space and time by calculating the volumetric strain profiles in the electrodes. The relative volumetric change is defined as the divergence of the displacement field, 36:
In Supplementary Note 1 and Supplementary Fig. 1 we explain the relations between different types of strain and the displacement field. For example, the dynamic shear strain distribution within the electrodes can be used to detect crack formation at the electrode level.
In Fig. 3a, we map out the volumetric strain distributions within the electrodes as a function of the SOC by correlating the scans at the different SOCs with the 0% SOC scan. The maps indicate that the top electrode (top row) is gradually contracting while the bottom electrode (row in the middle) is expanding. From the vertical cuts (bottom row), it is evident that, up to 48% SOC, volumetric strains occur rather homogeneously in all parts of the lithiating bottom electrode, while at >50% SOC, ‘strain fronts’ progress from the electrode-separator interfaces towards the bottom current collector. On the contrary, the delithiating top electrode shows inhomogeneous contraction behaviour, where multiple ‘strain fronts’ subsequently progress from the separator–electrode interface towards the top current collector. Supplementary Movies 2–4 show the volumetric strain in all 29 time steps.
Figure 3: Divergence and strain.(a) 3D divergence distribution in the electrodes computed from the displacement field correlating the scans at the indicated times with the first scan (that is, cumulative in time). Scale bar length, 1,000 μm. (b) 3D divergence integrated within cylindrical test volumes at various heights in the two electrodes as a function of flowed specific charge. The blue curves represent the average over the whole electrodes. (c) First electrochemical cycle of a graphite electrode cycled versus a metallic lithium electrode. The blue dashed lines indicate regimes in the charge- and discharge curves with different slopes.
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To further quantify these observations, we slice the electrodes along planes at equidistantly spaced positions in the TP direction and spatially integrate the divergences of the displacement fields within each of the resulting cylindrical sub-volumes for all time steps. This provides the relative volumetric changes of the electrode sub-sections as a function of the flowed specific charge:
The resulting plot in Fig. 3b shows the per cent volumetric change versus the SOC for the electrode sub-sections at varying distances from the separator. In agreement with our findings from Fig. 3a, we find that both electrodes expand (contract) by ∼6% on average (blue curves) during the course of lithiation (delithiation). Furthermore, we find that (i) the delithiating top electrode contracts progressively along the TP direction, starting from the section closest to the separator and then towards the current collector, and (ii) the lithiating bottom electrode shows a homogeneous expansion throughout the entire electrode up to about 50% SOC followed by a progressive expansion of portions of the electrode beginning with the section closest to the separator.
We now show how DVC-based analysis of volumetric strain can provide insights into electrochemical behaviour. Our analysis leads to two observations: (i) lithiation starts at the electrode–separator interfaces and progresses towards the current collectors and (ii) SOC gradients build-up immediately in the delithiating electrode, while they develop only during the second half of the experiment in the lithiating electrode. The first observation is consistent with our understanding from literature that lithiation kinetics within graphite electrodes are limited by ionic diffusion and conductivity rather than by electric conductivity11,26,37. The second observation can be understood by plotting the first electrochemical cycle of a lithium metal/graphite half cell that has been slowly operated at a galvanostatic C/10 rate (Fig. 3c). During our operando experiment, the top electrode will behave similarly to the delithiation curve (black line), while the bottom electrode will behave as the lithiation curve (red line). The larger average slope of the lithiation curve implies that overpotentials developing along the TP direction will induce only smaller SOC gradients within the lithiating bottom electrode, while the smaller slope of the delithiation curve suggests that overpotentials can trigger larger SOC variations within the delithiating top electrode. From the galvanostatic intermittent titration technique protocol (Fig. 1d, inset) used during the experiment, we estimate the overpotential to be approximately 20 mV, or equivalently ΔΦ=10 mV per electrode. According to the calculated slopes, this can lead to SOC variations of within the top electrode during the first half of the experiment, while the expected SOC variation within the bottom electrode is below 1 %. Only in the second half of the experiment corresponding to the flat regime of the lithiation curve, can gradients also develop in the bottom electrode. The agreement between the expected behaviour of graphite during (de)lithiation and our observations in tomography indicate that for low attenuation contrast and small volume expansion materials such as graphite, DVC is a robust method for tracking small changes in microstructure that can be correlated to electrochemical activity.
Next we demonstrate that our imaging and analysis approach can be used to determine whether the mechanical deformation of the porous electrodes during the (de)lithiation process impacts the transport of lithium ions in the electrode. Here, we focus our analysis on the lithiating bottom electrode.
Suppression of lithium ion diffusion due to microstructure is summarized by:
where D is the diffusion coefficient of lithium ions in pure electrolyte, Deff is the effective diffusion coefficient3,6, ρ is the porosity, and τ is the tortuosity15,38. In contrast to DVC, which operates directly on the raw data, quantification of microstructural parameters, such as porosity or tortuosity, requires data binarization. Additionally, for a dynamically evolving microstructure, determination of microstructural parameters requires the analysis of sub-volumes containing the same particles and pores for each time step.
To create dynamic sub-volumes, we use the information readily available from DVC to warp an initial volumetric observation window according to the corresponding computed displacement fields in each time step. This concept is illustrated in Fig. 4a using a small part of the bottom electrode, shown before lithation on the left. During lithiation, the particles in this sub-volume expand, distorting the sub-volume shape. The sub-volume containing the same set of particles is shown in the very last time step (right). For better visibility, the computed displacement field (middle) and the warping effect (right) have been rescaled by a factor 40 in the IP directions and by a factor 6 in the TP direction. Supplementary Movie 5 visualizes this dynamically deforming subvolume.
Figure 4: Microstructure analysis on dynamic volumes.(a) Left: sketch of a cylindrically-shaped observation volume within the bottom electrode in the initial time step. Middle: vector field representing the displacements within this volume between the first and the last time steps. The IP and TP vector field components have been rescaled for better visibility. Right: dynamic volume in the last time step resulting from warping the initial red volume with the displacement field. (b) Electrode volume, particle volume and porosity as a function of charge as determined from the dynamic volumes. (c) Tortuosities along the two IP and the TP direction as a function of specific charge. The right axis refers to their change relative to the initial value.
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The chosen δ/β ratio in the PPC tomography reconstruction provides the appropriate trade-off between resolution and contrast such that each data set can be binarized into a particle phase and an electrolyte/binder/carbon black background phase using Huang’s method39 (Supplementary Fig. 2 and Supplementary Note 2). In each time step, the threshold that partitions the volumetric grey scale image is calculated by minimizing the Shannon entropy function. As described, a different thresholding method yields similar results, indicating that the binarization is robust (Supplementary Fig. 3 and Supplementary Note 2).
In Fig. 4b, we plot the relative volumetric changes of the dynamic observation window and of the active graphite particles as a function of the flowed specific charge. The overall electrode expands by almost 7% (blue curve), consistent with our findings in Fig. 3b, and the particles (black curve in Fig. 4b) expand by more than 10%, in excellent agreement with literature where it is reported that the crystal lattice of graphite expands predominantly along its c-axis direction by approximately 10.5% on a full lithiation1,18,19. The porosity (red curve) first slightly decreases from 48 to 46%, but then remains at 46% for the second half of the lithiation because the particles expand more than the overall electrode only during the first half of lithiation.
Figure 4c shows the absolute and relative values of the tortuosity along the two IP and the TP direction as a function of time. These values have been calculated on a smaller dynamic volume (initial size: 350 × 350 × 250 voxels3=227.5 × 227.5 × 162.5 μm3), which is sufficiently large for variations due to spatial inhomogeneities in the microstructure to not influence the result (Supplementary Fig. 4 and Supplementary Note 3). The large anisotropy (factor of two) between the IP tortuosities and the TP tortuosity arises from the fact that the graphite particles are platelet shaped and tend to align with their flat-side parallel to the current collector, which results in significantly longer diffusion paths along the TP direction6. However, while the TP tortuosity is constant over time, the IP tortuosities increase by ∼2% during the course of lithiation. This effect could arise from the graphite platelets expanding predominately along their c-axis direction, thereby narrowing the diffusion paths along the IP directions. Again, as the rate of electrode expansion overtakes the rate of particle expansion (above 50% SOC), the IP tortuosities no longer increase.
As described in Supplementary Fig. 5 and Supplementary Note 4, use of dynamical volumes enables further types of microstructural analysis techniques.
In summary, for the relatively porous electrode in this cell (designed to keep pressure in order to maintain good electrochemistry, but still accomodating volumetric changes of the sample in the TP direction) lithium transport will not be significantly affected by the reduction in porosity and the narrowing of the pore space (increasing τ). The temporal changes in microstructure that occur during lithiation are on the same order of magnitude as the spatial microstructure inhomogeneities across the electrode (Supplementary Fig. 4). However, we emphasize that these finding are electrode and cell specific. Different electrode preparation (for example, lower porosity) or cell configurations (for example, wound versus stacked) could result in sections of the electrode that experience significant changes in the microstructure.