In Situ Neutron Diffraction Study of Lithiation Gradients in Graphite Anodes during Discharge and Relaxation

A commercial lithium-ion battery (C₁ = 540 mAh at 300 K, 3.7 V) with a graphite anode and LiCoO₂ cathode was studied in the experiments. The electrolyte contains lithium hexafluorophosphate (LiPF₆), ethylene carbonate (EC), and dimethyl carbonate (DMC). The battery is designed for high power use and allows 1C continuous charging and 12C continuous discharging in a temperature window of 0°C to 60°C. The specified storage temperature window is given as −10°C to 45°C. The battery dimensions are 5.0 cm × 3.1 cm × 0.54 cm (length × width × height) with 18 anode and 17 cathode sheets. The battery properties are summarized in Table I.

A BaSyTec GSM cell tester was used for determination of temperature dependent capacity and rated capacity. Rated capacity was determined for constant current (CC) discharging at 0.1C, 0.2C, 0.5C, 1C, 2C, 3C and 5C (3.0 V, 300 K; constant current constant voltage (CCCV) charging (I_CC up to 1C, I_CV<0.1C, 4.2 V)). Temperature dependent capacity was determined with CCCV (I<0.1C, 4.2 V, 300 K) charging and CCCV (I<0.1C, 3.0 V) discharging at 40°C, 25°C, 10°C, 0°C, −5°C, −10°C, −15°C and −20°C. Temperature dependent impedance was determined with a sample that was discharged ΔQ = 420 mAh from 100% SoC to a target SoC of 22%. At that SoC AC impedance was measured with constant potential with a Biologic VMP3 in the frequency range of 10 mHz to 10 kHz. All tests were performed in a Binder KT170 climate chamber.

During the neutron diffraction measurements, cycling was performed with a BioLogic VSP potentiostat equipped with a 100 A booster unit. Prior to each discharge and relaxation experiment, the battery was charged to 100% SoC using a constant current constant voltage (CCCV) procedure (4.2 V, 1C, I<0.05C). To prevent lithium-plating, all charging was performed at 300 K. For the diffraction experiment, the battery was placed onto a sample stick (Figure 1) and inserted into a cryostat. Helium was used as contact gas for thermal coupling.

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In situ neutron diffraction data were collected at the material science diffractometer STRESS-SPEC at Heinz Maier-Leibnitz Zentrum.^52,53 The neutron wavelength was determined with NIST SRM 640d Si standard powder to λ = 2.0964(2) Å at room temperature. We observed a 0.227902 Å at room temperature. All data presented in this publication is corrected with this zero-shift. The scattering gauge volume V_g≈ 0.5 cm³ was set by a 5 × 20 mm² entrance slit and a 5 mm radial collimator in front of the detector (Figure 1). Since our experiment focuses on lithiated graphite phases during discharge, we collected diffraction data in a limited 2θ range of 28° < 2θ < 42°. The limited fixed 2θ range allows for fast continuous data collection in 3 min intervals with sufficient signal quality. For measurements showing slow graphite phase changes during relaxation, data were combined to 6–30 min intervals to improve signal to noise ratio. The raw data correction and reduction were carried out with StressTextureCalculator.⁵⁴ Pawley analysis of the integral intensity of Li_1-xC₆ reflections was performed using Highscore⁵⁵ and Matlab to fit the data. Integral intensities were determined using pseudo Voigt profiles. For strongly overlapping peaks the FWHM (full width at half maximum) was constrained between reflections.

A fully discharged cell was disassembled in a glove box with argon atmosphere (MBRAUN; < 1 ppm H₂O & < 1 ppm O₂) to extract the graphite anode. Top view and cross view scanning electrode images (SEM, Instrument: JEOL JSM 6000) were taken from a washed (20 min in DMC) and vacuum dried anode. Particle size and shape distribution were determined using BruggemanEstimator.²⁵ Li-metal/electrode half-cells were built for DVA analysis using 14 mm diameter electrode material and 16 mm diameter metallic lithium in 2032 coin cells with 160 μl electrolyte (1M LiPF₆ in EC:EMC (3:7) + 2% VC).

Multiple scenarios were monitored to study the impact of discharge rate and battery temperature on the homogeneity of the graphite anode during discharge and relaxation. From a fully charged state, discharge at a rate of 0.9C (1.25 mA/cm²) was performed for controlled temperatures of −10°C, 0°C and 25°C. At 0°C, additional higher rate discharges at 1.8C (2.5 mA/cm²), 3.5C (5.0 mA/cm²) and 5.3C (7.5 mA/cm²) were conducted. For the sub-ambient temperature discharge experiments, the battery was cooled down to the target temperature for a cooling period of 45 minutes. In order to achieve the same state of lithiation in the graphite anode independent from temperature-induced polarization or a reduced capacity due to limited rate capability, an Ah-based discharge limit was used instead of a voltage cutoff. The battery was discharged to a target SoC of 22% which corresponds to a fixed discharged amount of ΔQ = 420 mAh. The subsequent relaxation was monitored up to 6 hours.

The particular target SoC of 22% was chosen as a result of the following examination. As the full cell is discharged, the carbon in the anode is delithiated and undergoes a well-known structural change from LiC₆ over LiC₁₂ and several lower lithiated phases Li_1-xC₆ to graphite. Figure 2 shows the two-phase regime of LiC₆ (0 0 1 reflection, 33.28° 2θ) and LiC₁₂ (0 0 2 reflection, 34.66° 2θ) at 100% - 70% SoC. As the intensity of LiC₆ decreases, the intensity of LiC₁₂ increases until only a single reflection is observed (70% - 40% SoC). At about 40% SoC, the LiC₁₂ reflection broadens and a continuous peak shift to higher 2θ values is observed. At 0% SoC (3.0 V cut off voltage) we attribute the reflection to graphite at 36.28° in 2θ. The corresponding c-axis (d = 6.729 Å) is in agreement with Dolotko et al. (d = 6.722 Å)⁵⁶ but higher than what is observed by Trucano et al. (d = 6.711 Å),⁵⁷ which indicates some residual lithitation in our measurement.

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Figure 2 shows the full cell open circuit voltage (OCV) (C/100) and OCV reconstruction as well as differential voltage profiles of anode and cathode half-cell data (graphite vs. Li/ Li⁺, LiCoO₂ vs. Li/Li⁺). Good agreement between half-cell reconstruction and full cell OCV was achieved through scaling and shifting of the individual contributions of anode and cathode half-cell data. In agreement with the diffraction data, E(x) reconstruction shows the graphite voltage plateaus during phase transition regimes at 100–70% SoC (80 mV) and 60–40% (110 mV) full cell SoC. The dE/dQ data shows changes in slope and additional maxima at 25% SoC (155 mV) and 20% SoC (200 mV) where the ND data shows a shift to lower 2θ angle values toward graphite.

If a temperature or rate induced inhomogeneity in the electrode matrix or graphite particles is present during discharge, a fraction of the active material will deviate from the average state of lithiation of the electrode. With the target SoC set at 22% SoC, the diffraction measurement is sensitive to phase coexistence as more delithiated states are shifted toward higher °2θ values. Graphite phases not yet affected by the discharge remain at 34.66° 2θ (LiC₁₂). In contrast, inhomogeneity at 70–40% full cell SoC cannot be tracked as graphite does not show a change in intensity and angular position. A drawback of this approach is, that while the intensity and the existence of additional phases can be tracked, the degree of lithiation of each phase at low degree of lithiation cannot be directly determined as it is done for the LiC₆/LiC₁₂ fraction, since the description for intermediate states between LiC₁₂ and graphite is subject of debate.

According to the stage formation model, the transition from LiC₁₂ to graphite is described by a periodic array of unoccupied layer gaps at low concentrations of intercalated lithium-ions.^16,17,58 While the staging model is well accepted for LiC₆ (Stage I) and LiC₁₂ (Stage II), varying accounts of higher order stages (s>II) are given. Some recent diffraction experiments find a continuous change in d-spacing at lower lithiated states (x<0.33).^35,59 Senyshyn et al. observe a quasi-solid-solution structural behavior with seven higher order phases (IIL, IV, V, VIII, XIV, XXVIIIp, XXVIIIpp) during discharge and propose an alternative transition mechanism, which they call twisted bilayer formation.³⁵

Since only medium resolution diffraction data of a limited angular range were collected, we cannot comment on the details of the phase transition during graphite deintercalation at lower lithiation states. We aim at providing a qualitative picture of the temperature and rate dependent phase inhomogeneity during discharge and the timescale until homogeneity is achieved. In accordance with Dolotko et al.³⁵ and our previous investigations of charging^4,38 and discharging⁴¹ processes, we refer to lower lithitated phases as Li_1-xC₁₈ and Li_1-xC₅₄ to indicate a certain level of lithiation but without discussing structural features.

At room temperature and CCCV discharge with 1C (I<0.1C), the battery capacity is 540 mAh. The battery maintains its capacity at high rates with 530 mAh at 5C (see supplementary Figure S1). With lowering temperature down to −5°C the available capacity decreases only slightly, but an increasingly larger share of capacity is discharged through the CV phase. At −15°C more capacity is discharged in the CV phase (273 mAh) than in the CC phase (233 mAh).

The decrease in capacity at low temperatures is accompanied by an increase in cell impedance. Figure 3 shows the real part of the cell impedance for 0.01 Hz to 10 kHz. The corresponding Nyquist plots are given in Figure S2 in the supplement. From 40°C to −10°C, the impedance increases moderately for high frequencies and more strongly at mid to low frequencies. The EIS mid to low frequency arcs are commonly attributed to the Li⁺ diffusion across the SEI and charge transfer process at the electrode/electrolyte interface. The full cell EIS contains anode and cathode contributions. We attribute the full cell impedance at low temperatures predominantly to the anode, based on LiCoO₂/graphite three-electrode experiments that observed higher activation energy and higher charge transfer resistance for the anode below 25°C.⁶⁰ The extended constant voltage phase and increase in charge transfer resistance show a limitation of charge transfer kinetics at the graphite surface in addition to the observation of multiple coexistent graphite phases at low temperatures.

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Rather abruptly, at −20°C, very little capacity can be discharged in the CV phase and cell impedance overall increases sharply. We attribute this to electrolyte freezing. EC/DMC/LiPF₆ electrolyte has a well-known, poor low temperature performance due to the high melting points of EC (36°C) and DMC (0.5°C).³¹ Smart et al. observe a similar sharp drop to 15% remaining dischargeable capacity at −20°C for LP30 (1.0M LiPF₆ in EC:DMC (3:7)).⁶¹ Senyshyn et al. see reflections emerging below −15°C in a diffraction measurement of LP30 indicating an additional long range ordered phase not present at higher temperatures.⁶² We conclude that electrolyte freezing did not occur during our diffraction experiment, since no electrolyte features were observed in the ND data and the cell temperature (−10°C) was kept above the threshold of sharp overall impedance increase at −15°C (Figure 3b).

To study the impact of cell temperature on graphite phase inhomogeneity during discharge and relaxation, a fully charged cell was discharged (ΔQ = 420 mAh) to the target SoC at a moderate C-rate of 0.9C and varying temperature; 25°C, 0°C and −10°C. At 0°C cell temperature additional discharges at higher rate of 1.8C, 3.5C and 5.3C were performed.

The cell voltage during discharge and relaxation at varying temperature is presented in Figure 4a. The average voltage during the partial discharge is 3.84 V at 25°C but drops considerably by ∼ 200 mV (0°C) and ∼ 400 mV (−10°C) at lower temperature. Consequently, the cell voltage at the end of discharge differs for 25°C (3.65 V), 0°C (3.36 V) and −10°C (3.01 V). The discharge ends and relaxation begins at 0.88 hours. Relaxation was monitored for ∼ 2 hours at 25°C and 6 hours at −10°C where the highest degree of inhomogeneity was expected. The voltage relaxation is slower at lower temperatures. Voltage differences of 50–100 mV remain between −10°C and 25°C for ∼ 1 hour during the rest period.

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The cell voltage during discharge and relaxation at higher rates is presented in Figure 4b. With a higher rate, the polarization increases and the average discharge voltage decreases to 3.55 V (1.8C), 3.41 V (3.5C) and 3.36 V (5.3C). A minimum and a subsequent maximum in the cell voltage is observed for the rates 3.5C and 5.3C shortly after the beginning of discharge. This is due to an improvement of transport properties and a resulting reduction in overpotentials as the battery heats up. The cell voltage at the end of discharge is 3.25 V for 1.8C and 3.22 V for 3.5C and 5.3C, higher than for 0.9C at −10°C. With the last recorded voltage 3.737 V at 0°C taken as reference, voltage relaxation is quickest at 5.3C (0.51 h) but only slightly slower at 3.5C (0.66 h) and 1.8C (0.72 h). In all cases, relaxation is faster than for the reference slow discharge (1.40 h).

The cell temperature change is presented in Figures 4c and 4d. During discharge, the sample heats up, reaches maximum temperature at the end of discharge and cools down during the relaxation period. With respect to the final resting temperature, the cell temperature increases by 1.8°C (T_rest = 25°C), 3.8°C (T_rest = −0.2°C) and 6.5°C (T_rest = −11.8°C) for the varying temperature discharges (Figure 4c) and by 9°C (1.8C), 16°C (3.5C) and 21°C (5.3C) for the higher rate discharge. The cell heats up strongly at higher rates due to the absence of forced convection cooling inside the cryostat chamber. During relaxation, the cell cools down and T-T_rest decreases below 0.5°C within 0.6 h (−10°C), 0.4 h (0°C) and 0.17 h (25°C). Despite the significant temperature increase at higher rates, the time needed to cool down below 0.5°C is similar for all cells; 0.52 h (1.8C), 0.63 h (3.5C), and 0.71 h (5.3C).

During relaxation at 0°C, the voltage shows a qualitatively different behavior compared to 25°C with a dE/dt plateau at 1.2 to 2 hours after discharge (Figure 4a inlet). The periods of constant voltage increase can be explained through graphite multi-phase formation. Due to transport limitations, a fraction of the graphite remains at LiC₁₂ while some of the graphite is delithiated to lower lithiated stages LiC₁₈ and Li_1-xC₅₄. As the anode potential vs. Li/Li⁺ is constant at 150 mV at stage II/IIL, it increases strongly at lower lithiated phases (Figure 2b). During relaxation, the cell establishes thermodynamic equilibrium and the anode relaxes into single or two Li_1-xC_y phases close to the mean lithium content of the discharge target SoC. The lithiation of overshooting (Bauer et al.)⁶³ graphite phases causing a voltage drop in the half cell potential is visible as maximum or plateau in the full cell dE/dt plot. Our observations are consistent with Bauer et al. who find such behavior at low (0 < SoC < 0.25) and medium SoC (0.3 < SoC < 0.6) in the voltage and dilation relaxation after charging. They find that intercalation of plated lithium and temperature gradients can cause a similar and overlapping effects on the battery voltage during relaxation. We can exclude lithium plating as cause for the voltage relaxation features in our experiment, since we measure relaxation after discharge and the samples were charged at a moderate rate at 25°C where no plating is expected for a high power battery.³⁸ We can also exclude that the voltage response is caused by the temperature change of the battery, considering that the shoulder in the dE/dt plateau is observed for up to 2.5 hours at 0°C and the temperature gradients for only 0.4 hours (T-T_rest < 0.5°C). In agreement with Bauer et al., the effect is not observed at higher temperatures (25°C). In contrast to Bauer et al., the multi-phase voltage feature diminishes with higher rate (1.8C, 3.5C) and is not present at 5.3C. This can be explained by the up to 20°C temperature increase at higher rates compensating a potential increase in polarization due to higher currents.

The in situ neutron diffraction data of the Li_1-xC₆ reflections during discharge and relaxation at 25°C (a, d) 0°C (b, e) and −10°C (c, f) are shown in Figure 5. For comparison, selected moments in time are marked in the contour plot and the reflection intensity is shown in the subplots a, b, c. The time evolution of the integral intensity (a) and d-spacing (b) of the graphite phases present during relaxation is presented in Figure 6. While all three measurements show at the beginning of discharge equal LiC₆/LiC₁₂ balance and a subsequent decrease in LiC₆ intensity with a corresponding intensity increase of LiC₁₂, pronounced differences arise at the later stages of discharge and relaxation that support the multi-phase interpretation of the voltage relaxation feature.

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At 25°C, a slightly broadened reflection with some remaining LiC₁₂ (34.9°) and a second, lower lithiated phase (35.5°) shifted to higher angle is observed at the end of discharge. The integral intensity of the LiC₁₂ is about 1400 a.u. at the end of discharge and decreases quickly during relaxation while the intensity of the second phase increases. The d-spacing of the lower lithiated phase increases continuously from 3.455 Å to 3.471 Å while the LiC₁₂ reflection intensity reduces. In agreement with previous work^4,41 we identify this phase as Li_1-xC₁₈. After 30 minutes, little change is seen in the ND data (Figures 5a, 5d) and the profile can be fitted well with only a single Li_1-xC₁₈ phase.

In comparison to 25°C, the anode shows greater polarization after discharge at 0°C (Figures 5b, 5e; Figures 6a, 5b). Two distinct phases, LiC₁₂ (34.9°) and a lower lithiated phase (36.2°) are observed with about equal integral intensity ( ∼ 3800 a.u). With a d-spacing of 3.402 Å, this phase is identified as Li_1-xC₅₄ in agreement with previous work.^4,41 Similar to what is observed at 25°C, the reflection intensity and thus the amount of LiC₁₂ decreases during relaxation while the Li_1-xC₅₄ phase is lithiated for both experiments at 0°C and −10°C. Consequently, the reflection intensity increases and the graphite phase is shifted to higher d-spacing values. Compared to 25°C, this process is much slower at 0°C. One hour after the end of discharge LiC₁₂ still maintains 30% of the combined reflection intensity. After 1.8 hours the intensity change and Li_1-xC₅₄ reflection shift slows down markedly. The anode maintains a degree of polarization until the end of measurement at 3.7 hours. The lower lithiated phase, initially identified as Li_1-xC₅₄, reverts back to Li_1-xC₁₈ (d = 3.453 Å) toward the end of the measurement. The slightly lower d-spacing, compared to the final state of LiC₁₂ at 25°C (d = 3.471 Å), is explained by some lithium remaining in the LiC₁₂ state.

At −10°C the diffraction data show an even greater polarization and a slower relaxation process than for 25°C and 0°C. Similar to the situation at 0°C, we observe two phases with about equal integral intensity, LiC₁₂ (4000 a.u.) and Li_1-xC₅₄ (3450 a.u.) at the end of discharge at −10°C. Li_1-xC₅₄ is shifted to d = 3.387 Å, which indicates a slightly lower degree of lithiation compared to corresponding graphite intercalation phase (d = 3.402 Å) at 0°C. Over several hours, phase separation is clearly visible during relaxation (Figure 5). After 5.8 h relaxation, LiC₁₂ (d = 3.510 Å) remains with 28% of the combined integral intensity. The final d-spacing of the Li_1-xC₅₄ reflection (d = 3.435 Å) is lower than observed at 0°C (d = 3.453 Å) which can be attributed to the temperature effect. The broadening of the anode reflection due to multiple phases present causes a lower observed maximum intensity for the last measured reflection data at −10°C (7750 counts/3 min), 0°C (8450 counts/ 3 min) and 25°C (8650 counts/3 min).

Notably, the d-spacing of LiC₁₂ differs at the beginning of the relaxation process between measurements at 25°C (3.517 Å) and at lower temperatures, 0°C and −10°C (3.502 Å) (Figure 6b). The difference of 0.015 Å can be partially explained by thermal contraction. With a thermal expansion coefficient of α_c = 6.5 × 10^{− 5} Å K^{− 1} for lithiated graphite,⁶⁴ we find that the temperature change from 25°C to −10°C corresponds to a shift of −0.008 Å (3.517 Å → 3.509 Å). The remaining difference of 0.007 Å is within the combined d-spacing uncertainty of 0.004 Å for both phases.

In summary, the multiphase interpretation of the voltage relaxation feature is in good agreement with the phase coexistence observed in the anode during discharge and relaxation. At 25°C neither voltage nor diffraction measurements show lasting phase coexistence. At 0°C the intensity change slows and Li_1-xC₅₄ reflection shift decreases for up to 1.8 hours after end of discharge (2.6 hours after start of discharge), which is the same time that the end of the dE/dt plateau is observed.

The observed graphite phase evolution and voltage relaxation can be explained well with phase separation due to transport limitations at low temperatures. This section discusses whether we can localize the phase separation and differentiate between transport limitations on cell, layer, or particle level based on the sample and electrode design. Figure 7 shows potential contributions to graphite inhomogeneity observed in neutron diffraction experiments.

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Potential gradients

Temperature homogeneity

Good thermal homogeneity is given in all test scenarios. The maximum distance between center to surface is 0.27 cm for the sample cell compared to 0.9 cm for an 18650 cell configuration. Assuming identical electrode properties and thus similar heat transfer properties orthogonal to the electrode layers, the heat transfer resistance from surface to center is about three times lower for the pouch cell reducing the temperature gradient in high rate test scenarios. The surface-center temperature gradient can be approximated with the Biot number B.⁶⁶

With a total thickness t_Batt of 5.4 mm and assuming a convective heat transfer coefficient h = 5 Wm⁻²K⁻¹ (no ventilation in cryostat) at the cell surface and a thermal conductivity k_⊥ = 1 Wm⁻¹K⁻¹ and k_|| = 33.9 Wm⁻¹K⁻¹,⁶⁷ we assess B_⊥ < 0.02 in orthogonal direction and B_|| < 0.003 in the in-plane direction. It follows that the temperature at the core of the battery, and thus in the observed volume in the center, deviates by less than 2% from the measured surface temperature.⁶⁸ The temperature deviation is thus less than 0.5°C in the test scenario with the strongest heating (I = 7.5 mA/cm², ΔT = 21°C). We conclude that for all test scenarios the temperature variations in the gauge volume are too small to cause the observed graphite phase differences, given the small influence of less than 1°C temperature change on electrolyte conductivity and diffusion coefficient.⁸

Anode properties

The graphite phase coexistence can be explained well with particle and electrode transport limitations (Figure 7), which can be shown by analyzing the electrode properties. Figure 8 shows top view (a) and cross view (b) SEM images of the anode. The particle size (c) and shape (d) is determined by matching 110 particles with an elliptical shape. The visual impression of spherical particles is confirmed by the ratio of long axis c and short axis a which is c/a < 1.2 for the majority of particles (d). Idealizing the particles as spherically shaped, the diameter distribution can be plotted and fitted well with normal distributions (c). The average diameter is d₅₀ = 16.4 μm (d₁₀ = 10.5 μm, d₉₀ = 22.4 μm).

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Solid diffusion limitations

Layer contribution

The neutron diffraction data of the graphite reflections (32° to 38° 2θ) during discharge and relaxation at 0°C under variation of discharge rate is shown in Figure 9. The fully charged cell is discharged at 1.8C (a,d), 3.5C (b,e) and 5.3C (c,f) while diffraction data were continuously recorded over 3 min intervals. The time evolution of the integral intensity (a) and d-spacing (b) during relaxation is shown in Figure 10. Despite a rate increase by a factor of two to six, the anode shows a lower degree of polarization and faster relaxation compared to 0.9C measurements at 0°C and −10°C.

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Polarization of the anode with some remaining LiC₁₂ and at least one additional phase with lower degree of lithiation (Li_1-xC₅₄) is observed for all rates. At 1.8C, the phases are well separated with more LiC₁₂ integral intensity (3800 a.u.) than Li_1-xC₅₄ (3200 a.u.). In comparison, the contribution of the lower lithiated phase has approximately equal share in intensity at 1.8C. Similar to the low rate discharge at 0°C the d-spacing of the Li_1-xC₅₄ phase shifts to 3.406 Å (at 1.8C), 3.412 Å (at 3.5C), and 3.406 Å (at 5.3C) respectively. At one hour after discharge, relaxation is well advanced for all higher rates. The remaining LiC₁₂ contribution of appoximately 25% is seen in the asymmetry of the reflection in Figure 9 (blue). The Li_1-xC₅₄ phase after 5.3C discharge is lithiated slightly faster during relaxation than at lower rates, which causes an earlier shift to higher d-spacing values (Figure 10) and a less broadened reflection with a higher maximum intensity (8000 counts/3 min) compared to (7800 counts/3 min) at 1.8C and 0.9C.

In summary, the cell shows a similar degree of polarization and slightly faster relaxation process at higher rates compared to the slow discharge at 0°C. This can be explained by the increased heating of the cell at higher rates that causes a temperature increase of 9°C (1.8C) to 21°C (5.3C) compared to only 4°C at 0.9C. The self-heating of the cell reduces charge transfer resistances (Figure 3) and increases diffusion rates in solid and liquid phases^8,11 and thus compensates the effect of higher rate. After one hour, when the cell has the same temperature for all discharge scenarios, intensity change and Li_1-xC₅₄ reflection shift continue at similar speed. In addition to the effect of cell heating, the lack of polarization increase at higher rates is consistent with the high power layout of the sample in contrast to our previous results with a high energy cylindrical cell where we observe a more pronounced inhomogeneity at higher rates.⁴¹ The anode layer thickness of 51 ± 2 μm corresponds to the sum of three average particle diameters. With the close to spherical particle shape the electrode has a low tortuosity of τ_z = 1.6 and a McMullin Number of N_M = 4, as determined from SEM 2D reconstruction, finding a Bruggeman exponent of α_z = 0.51. This is close to the often used Bruggeman approximation α = 0.5 for ideal spheres.⁷⁹ While limitations of the 2D reconstruction compared to 3D tomography²⁵ and other methods²⁴ have to be considered, tortuosity and McMullin Numbers are low compared to flake graphite.²⁴ We conclude that the neutron diffraction data do not show a contribution of additional layer inhomogeneity at higher rates since we do not observe a qualitative change in polarization or relaxation time. The low temperature and medium rate discharge scenario is most critical in terms of anode polarization since self-heating improves transport parameters and reduces polarization as well as relaxation time at higher rates.

It is less clear to which extent particles differ in lithiation due to differences in size and surface area. Phase inhomogeneity and equalization between particles if present, would be visible in the anode diffraction data in similar manner as solid diffusion limitations. Equalization between particles through lithium exchange with the electrolyte slows considerably at low temperatures due to lower lithium diffusivity in the electrolyte and higher charge transfer resistance at the electrolyte particle interface. With graphite particle radii ranging from 4 μm to 16 μm (Figure 8) in the sample cell, a contribution to the observed phase coexistence cannot be excluded.