In Operando Small-Angle Neutron Scattering (SANS) on Li-Ion Batteries

First, the active material powders were characterized with a particle sizer (LA950, Retsch-Horiba) to measure the particle size distribution by laser scattering.

For the cathode, an NMP-based (N-methyl-2-pyrrolidone) slurry was prepared with commercially available NMC, LiNi_0.33Mn_0.33Co_0.33O₂ cathode material, PVDF-binder (Polyvinylidene fluoride, Kynar) and carbon black (C65, Timcal) as a conductive additive with solid weight fractions of 96:2:2, respectively. This slurry was coated with a doctor blade on a thin Al-foil (18 μm). The anode slurry consisted of standard artificial graphite (SGL Carbon GmbH) and PVDF with solid weight fractions of 95:5, coated onto a thin Cu-current collector foil (∼12 μm). Electrodes were dried under vacuum in a Büchi-oven prior to cell assembly in an Argon filled glove box (water content <2 ppm). The cell was assembled as a pouch bag cell with single layer cathode and anode electrodes separated by two layers of Celgard C2325 separator. Before sealing the pouch cell (consisting of a multilayer of Nylon, aluminum and polypropylene), 300 μL of 1M LiPF₆ dissolved in EC:EMC (3:7) were added as electrolyte. Sealing pressure in the vacuum chamber sealing device was 50 mbar.

The anode was overbalanced in terms of loading per area and also geometrically (anode size 3.5 × 3.5 cm², areal capacity 3.07 mAh/cm² calculated with a specific capacity of 372 mAh/g_graphite, thickness 98 μm) vs. cathode (cathode size 3 × 3 cm², areal capacity 2.53 mAh/cm², assuming a specific capacity of 150 mAh/g_(NMC), thickness 97 μm). From the total amount of 152 mg cathode active material in the cell, the maximum cell capacity equates to 23 mAh at a rate of 1 C for a potential window of 3 to 4.2 V. The assembled cell type is shown in Figure 1.

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Cell formation was done by two initial charge/discharge cycles (shown in Figure 2) at a constant current (CC) rate of C/10 to 4.2 V with a constant voltage (CV) hold until the current drops to C/20, followed by a CC discharge at C/10 down to 3 V. The irreversible capacity loss in the first cycle was 3.9 mAh. Thus, the discharge capacity at C/10 reached 21.7 mAh or 142 mAh/g_(NMC) in the second cycle, which was then set as the nominal 100% capacity in the subsequent experiments (i.e., a rate of 0.1 C corresponding to 2.17 mA). The coulombic efficiency of 98% and the rather small charge/discharge overvoltage of 40 to 50 mV at C/10 indicate overall good initial cell performance.

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All experiments were carried out at room temperature. The prepared pouch bag cell was checked with impedance spectroscopy, showing a high frequency resistance of ≈1 Ω and, after formation, a Nyquist-diagram with two semi-circles results, which is typical for this type of cell chemistry after SEI formation.¹⁰

The ex situ samples, the static in situ cell and the dynamically operated in operando cell were mounted at the SANS-1 instrument of the FRM II neutron source at the Heinz Maier-Leibnitz Zentrum (MLZ) in Garching^11–13 (see Figure 3).

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The instrument allows the selection of a wavelength λ within the range of 4.5 Å–20 Å with a wavelength spread of Δλ/λ = 10% through a mechanical velocity selector. For our measurements we used a mean wavelength of 6 Å. The final aperture before the sample reduced the neutron beam to a radial diameter of 8 mm before impinging on the sample. The instrument schematics are displayed in Figure 4.

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Scattered neutrons were recorded with a ³He position-sensitive proportional counter detector with 128 single tubes arranged to a 1000 × 1020 mm² total area and 8 mm pixel resolution (128 × 128 pixel area) with a counting rate of up to ∼1 MHz. Measured intensities were corrected for sample transmission, background intensity, and detector efficiency. In SANS the intensity is recorded as a function of the scattering vector Q which describes the directional change and momentum transfer of a neutron during scattering. The absolute value of Q is given by the scattering angle 2θ (angle between the incoming and the scattered neutron beam) and the wavelength λ according to equation:

2θ is the scattering angle, λ is the wavelength of the neutron beam. Generally, the Q-vector can also be regarded as the yardstick at which length scale the sample is looked at. In a simple consideration with a few assumptions the absolute value of the scattering vector Q can be correlated to the size d of a particle with an estimation of particle diameter of:

The scattering cross section dΣ/dΩ, as a measure of the scattering intensity normalized by the sample volume, is then calculated according to:

I(Q) is the measured intensity within a detector pixel, ΔΩ is the solid angle element, I₀ the intensity of the primary beam, t the sample thickness, T the sample transmission. Absolute intensities are then calculated by scaling with the incoherent scattering of a standard sample such as water with a defined thickness of 1 mm.

Three types of SANS experiments using different resolution settings were used. For the ex situ measurements of single cell components the neutron scattering data were collected and merged from setting three different resolution ranges. Similarly the static in situ measurements comparing the fully charged and discharged states were performed with the same settings. Only for the dynamic in operando measurements we restricted the resolution to the medium Q-range to increase our time resolution and focus on a certain length scale region. The following three configurations were used throughout all experiments.

• (I)  
  high resolution

• sample-detector distance (SDD) = 20 m
• beam collimation length (CL) = 20 m
• Q-range = 0.027 – 0.35 nm⁻¹

• (I)  
  medium resolution

• SDD = 8 m, CL = 8 m
• Q-range = 0.11–0.85 nm⁻¹

• (I)  
  low resolution

• SDD = 1.6 m, CL = 4 m
• Q-range = 0.35–4.11 nm⁻¹

For the in operando charging experiment, the SANS-1 instrument was set to the medium resolution configuration (CL = 8m, SDD = 8m and λ = 6 Å). This setting allows to access a Q-vector region in which particle scattering from 10 to 50 nm can be resolved. The wavelength of 6 Å was selected because SANS-1 has the flux maximum close to this value with a reasonable resolution, thus allowing fastest possible measurements with good statistics. Scattering data were then collected constantly during the charging in 10 min time intervals. For the charging/discharging procedures, a standard Biologic VSP-type potentiostat was connected to the cell.

After finishing the cell formation cycles, the cell was measured for one 1^st cycle in operando on the SANS-1 instrument and afterwards stored under ambient conditions. The cell was also measured statically in situ in discharged and charged state before and after this cycle. After three months the cell was checked, cycled once and then measured again in the 2^nd SANS cycle.

During the 1^st in operando SANS measurement, the cell was charged with constant current of C/3 up to 4.2 V with a CV hold until a current cutoff of C/25. After 150 minutes under OCV conditions (open circuit voltage) the cell was discharged with a constant current of C/3 down to 3 V. After three months the cell was cycled a 2^nd time at C/3 to confirm the stability prior to the repetition of the in operando SANS measurement. In the 2^nd in operando SANS experiment the cell was first charged and then discharged in the same way with C/3. The SANS data were only collected during the discharge for comparison with our 1^st SANS measurement. The discharge capacities of 1^st and 2^nd SANS cycle show aging of less than 4% over the three month storage indicating a sufficient electrochemical stability of the cell.

Generally, when analyzing small-angle scattering data, the intensity or magnitude of the sample scattering is fitted with models to obtain the information about particle size, size distribution, volume fraction and shape of particles and other parameters. From the general scattering theory the scattering amplitude of a particle is given as:

ρ(r) is the distribution function of scattering length densities and thus directly related to the chemical composition of the scattering system. The measured intensity of the scattered neutrons on the detector is then the absolute square of the amplitude normalized with the sample volume V:

In summary, for a condensed particle scattering system consisting of homogenous isotropic scattering centers of a defined coherent scattering length density ρ dispersed in a matrix of a medium scattering length density <ρ>, the intensity of the scattering per volume can be generalized by the following expression according to Grillo et al. or Kostorz:^14,15

The measured intensity is thus the product of the total neutron flux Φ, particle volume V_p, contrast factor Δρ², particle form factor P(Q) and structure factor S(Q). The form factor can be regarded as the function of the shape of the scattering particles while the structure factor S(Q) describes the distribution of the particles in space and inter-particle interactions. The contrast factor Δρ² is the scattering contrast resulting between the modelled particles with scattering length densities ρ and the surrounding matrix of the averaged scattering length density <ρ>. Particle volume is essentially constant in the course of our experiment and thus a sample and experiment specific constant K can be defined. Typically, when dealing with the scattering of a simple system the form and/or structure factor is fitted to models yielding information about the discrete particle parameters like particle shape, size, distribution etc.

From eq. 6 we can deduce that the magnitude of the scattered intensity is a function of the so called scattering length density (SLD), respectively the scattering contrast Δρ in the form of the contrast factor Δρ²:

In a typical SANS experiment this contrast is usually between a liquid or a matrix (SLD_A) and the particles (SLD_B) dispersed in this medium. This contrast can also be considered as the scattering from the surface of the particles, or the interface between the two systems. The SLD is a function of the atomic composition and can be calculated from the tabulated specific neutron scattering length of the corresponding nuclei and the respective atomic number density of the particle in view. For a given molecule A_iB_j the SLD hence is:¹⁵

where b_A, b_B are the scattering length of nuclei A, B (usually tabulated in units of fermi = 10^–13 cm), M the molar mass (g/mol) of the molecule A_iB_j, N_A the Avogadro number and ρ the mass density per volume (g/cm⁻³).

Typical SLDs of our sample components are summarized in Table I. The scattering length density for a certain phase can be either positive or negative. Negative values mean that the scattered neutrons are phase shifted by 180°. This phase shift is visible as an additional contribution to the scattering amplitude as the contrast factor Δρ² is the absolute square value (see eq. 7) of the different scattering length density values.

For a sample with complex scattering like a pouch bag cell battery, the problem arises that the obtained data are not just the scattering of a single "sample" with an effective scattering contrast factor, form and structure factor like described in eq. 6. In this case of a large macroscopic sample one has to consider that the scattering observed is a superposition of various microscopic scattering systems, but macroscopically independent scattering contributions. This can effectively be expressed as:

Each part i of the superposition is the description of an independent system of scattering centers which are otherwise largely separated from each other within the sample. In our case, for example the anode particles dispersed in the electrolyte are adequately distinct from the cathode particles dispersed in the electrolyte, so they can be regarded as independent scattering contributors, each of them with its own structure and form factor.

When dealing with the scattering of a complete pouch bag battery, one can still gain information from the calculated SLD and contrast factors. So let us first consider various contrast factors of the sub-scattering systems present in the pouch bag cell (see Table II). For example, it can be checked, which component i should be the major scattering contributor. We can experimentally check these values by measuring the individual components of the pouch cell under the same conditions using the same absolute intensity scaling (i.e., water). The scattering contrast factors Δρ² of the respective component A vs. the electrolyte solution as component B is tabulated in Table II. Additionally, the values for LiC₆ and LiC₁₂ as component A vs. LiC₁₂ respectively graphite as component B are added to this list.

A typical pouch bag envelope consists of a polymer/Al metal foil composite which is normally composed of three major layers, an outer and inner polymer layer coated on both sides of a water and air tight Al-metal foil. A schematic overview of the experimental cell is shown in Figure 5.

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In our case the outer pouch bag envelope (45 μm thickness each side) has roughly the same thickness as our anode and cathode active material layers, respectively. From Table II we can extrapolate that the casing will scatter only marginally (∼10%) compared to the signal we obtain from the active material layers. Also, the separator with only 2 × 25 μm thickness and a low contrast factor of only 2.49 × 10¹⁰ cm⁻² should not give rise to large amounts of the total scattering intensity. This is directly visible when looking at our ex situ SANS measurements of individual components of the cell. The components of the pouch bag were evaluated by merging data obtained with all three SANS instrument configurations (high, medium and low Q-range, see experimental details). From Figure 6 we can conclude that the major scattering contributions of a graphite|NMC pouch cell can be attributed to the cathode (red circles) and the anode (gray rectangles), while the entire casing pouch bag contributes only a little amount to the total system scattering (green triangles).

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Figure 7 shows a simulation of the full pouch bag cell (red circles), created by adding up the single component data, which is also compared to the obtained scattering signal of a full pouch cell (black rectangles). The prominent curvature of the cathode contribution (Figure 7) is decreased by adding the anode part to the plot in the log-scale. Note the incoherent background (flat straight region at high Q) is increased for the simulated cell because the separator and electrolyte scattering where present in each contribution part (empty cell, single cathode, single anode) while the full cell contains this background only once. The otherwise excellent fit shows that the superposition of the independent scattering subsystems from eq. 9 is a good approximation of the observable experimental pouch battery scattering. We will use this interpretation later in more detail when considering the in situ and especially the in operando experiments. First, however, we used some classical SANS methods to further analyze the data of the single component measurements.

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The empty pouch bag casing data can be fitted with a Porod-like background (eq. 10).

The slope of the empty cell a = 3.70 deviates slightly from an expected Porod-like background (a = 4), see Figure 8. This is probably because the pouch bag envelope itself is not just an isotropic scatterer, but obviously has a rough surface fractal microstructure, which gives rise to a decrease in the expected Porod-like background scattering. The parameter c₀ in eq. 10 describes the incoherent background scattering, while the parameters c₁ and a, represent the coherent scattering contributions. Comparison of the total amount of scattering intensity from the single components shows that the impact of the empty envelope is rather small and has no impact on the scattering of the electrode layers.

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Single NMC cathode data can similarly be fitted with a superposition of a Porod-background and the scattering of the electrode particles using a structure factor for a mass fractal (see eq. 11). The mass fractal approach is suitable for secondary particle agglomerates consisting of smaller primary particles like NMC material (see SEM-picture, Figure 10).

Here the parameter D is the dimensionality of the mass fractal, I₀ is the fitted intensity extrapolation for Q(0) and x_i is the size of the fractal particles. By replacing x_i with eq. 12, the radius of gyration (R_g) of the aggregated primary particles can be calculated:

The obtained mean average radius of gyration R_g ≈ 87 nm can be converted into equivalent radii of spherical or disc like particles according to:¹⁶

This yields a mean particle diameter of 2x R_disc, or ∼250 nm, which compares reasonably well to the primary disc or platelet shaped particles sizes of the NMC-material as observed in SEM images (see. Figure 10). The dimensionality D of the mass fractal is close to 3 which can be expected for a random globular agglomeration of spherical shaped particles.

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The raw data of the single anode measurement are shown in Figure 11. We fitted them with a model of a Porod-like background similar to the equation of the empty cell (eq. 10) with a slope of a = 3.610(5). This can be rationalized as the scattering of a fractal surface for which the following relation holds (see e.g.^17,18):

where I(Q) is the scattered intensity, Q the value of the Q-vector and D_s the surface dimension of the fractal. Any surface fractal system will give rise to a slope of 6-D_s in a small-angle scattering experiment in the region of Q where the single particles are too large in size to be resolved individually. While for a smooth surface interface the special case of Porod's approximation is obtained (when D_s = 2, then a = 4). Since the large graphitic particles of our samples are in the region 10–50 μm size (see SEM in Figure 12) these large particles cannot be resolved in size with our SANS experiment which is shown by the fact that the curve has a constant slope for the single anode as the scattering from the fractal rough surface of these large particles.

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After characterizing the single cell components, dynamic in operando charge/discharge experiments were performed. Above we used classical fitting of structure/form factor models to the SANS data. In SANS experiments, a change in particle shape or size typically creates shifting peaks in the log-log plots. For the evaluation of the obtained in operando small-angle scattering data, a different approach must be taken. In our case, the direct changes to the intensity vs. Q-vector plot are negligible because the size of the scattering objects is not changing significantly during the in operando study. On the other hand, the scattering contrast factor is changing due to the intercalation of lithium in the active materials, especially in graphite. In Figure 13 we have measured the cell statically in situ just before charging (termed SOC0) and then in the fully charged state (termed SOC100), using all three resolution settings of the SANS-instrument. By the naked eye, the plots are nearly identical, but they differ in detail which is obvious when calculating the difference plot between both. Such a systematic intensity change has been observed earlier (see Wang et al.).⁹ In order to analyze these changes more clearly, we convert the cross sections dΣ/dΩ into integrated intensity A(Q) (independent from the structure and shape of particles) by integrating the intensity over the measured Q-Range with eq. 14:

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The integrated intensity A(Q) is plotted vs. capacity in Figure 14b. On charging one can observe that the neutron scattering intensity drops continuously until a first plateau is reached after a discharge of ∼5 mAh (Figure 14b), which coincides with the onset of the voltage plateau in the charging curve at ∼3.7 V (Figure 14a). The integrated intensity decreases from initially 6.48 × 10¹⁰ nm⁻² to 6.23 × 10¹⁰ nm⁻² at the plateau, corresponding to a ∼ 4% drop of its initial value. The end of the plateau coincides with another step in the cell voltage plot at ∼3.85 V and the integrated intensity decreases further from 6.23 × 10¹⁰ nm⁻² to 5.91 × 10¹⁰ nm⁻² until the end of the charging process, corresponding to another ∼5% decrease referenced to its initial value. Considering the reversible capacity in the first formation cycle (∼21.7 mAh, see Figure 2) and the graphite capacity within the cathode area (∼27.6 mAh, see experimental), the lithiation degree of the graphite anode (i.e., x in Li_xC₆) can roughly be estimated, and is plotted along the top x-axis in Figure 14. Based on this estimated lithiation degree, the two initial steps in the cell voltage plot (Figure 14a) seem to be largely caused by the potential dependence of the graphite anode, i.e., by the two initial lithiation stages of lithium intercalation into graphite, for which two distinct voltage plateaus are observed for Li_xC₆ around x∼0.1 and x∼0.2–0.5.¹⁹ In Figure 17, the potential vs. capacity plot is analyzed further. Half cell measurements of the graphite and NMC electrodes give typical differential plot dV/dQ (Figure 17a), where peaks indicate the step-wise transitions between two-phase plateau regions, which mark the end and beginning of phases in the lithiation process. For graphite and accordingly for the full cell (Figure 17b), we can thus relate the dV/dQ peaks to the onset of formation of Li_xC₆ phases. The three peaks on the left are attributed to the onset of LiC₂₄, LiC₁₈ and LiC₁₂ formation; the single peak to the right can be attributed to the formation of LiC₆. The first three phases cannot be distinguished by SANS, but correlate to the first step in the integrated intensity, whereas the onset of LiC₆ is clearly related to the second step in the integrated intensity. After charging, the cell was kept for 150 min at OCV. When the discharge is being started after the rest at OCV, the initial integrated intensity is ∼2% higher (6.03 × 10¹⁰ nm⁻²) compared to the value directly at the end of the charging, and within another 10 minutes (SANS acquisition time) rises by another ∼2% to 6.16 × 10¹⁰ nm⁻². From there, it gradually increases until it reaches 6.31 × 10¹⁰ nm⁻² at ∼5 mAh (or x∼0.2). In the final part of the discharge, the integrated intensity rises more rapidly until the final value of 6.41 × 10¹⁰ nm⁻² is reached, which is ∼1% below the original value at the beginning of this charge/discharge sequence.

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The interpretation of these changes is the following. The initial scattering of the sample, and thus the integrated intensity is dominated, as the preliminary experiments show, by the contrast factor of the anode and cathode active materials. The scattering contribution from these components arises from the contrast of the particles in relation to the surrounding electrolyte matrix. Table II shows the contrast factors relative to the electrolyte for these systems, indicating that the anode contrast factor vs. the electrolyte is nearly a magnitude larger than the contrast factor of any of the other phases. Figure 16 shows the evolution of the contrast factors depending on electrode composition. In Table I and II the compositions of LiNMC/Li_0.75NMC and Li_0.5NMC are taken only as example nominal compositions for better showing the trend.

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Now let us consider the electrochemical processes inside the cell. During charging, the intercalation reaction starts with pure graphite particles in which Li-ions are intercalated gradually. Examining the change in contrast factor when going from discharged pristine graphite, C, to the half-charged phase LiC₁₂ (x = 0.5), we see that the contrast factor of the anode drops relative to the initial value (see Table II). On the contrary, the cathode scattering contrast increases relative to the initial value when going from the Li₁NMC (discharged) to Li_0.75NMC (partially charged). Since the measured scattering is a superposition of all scattering systems in our sample, as described in eq. 9, the amplitude of the entire cell system is proportional to the relative scattering contrast factors of all components multiplied by the number of particles in the system. If we consider the relative changes of the contrast factors of cathode/electrolyte and anode/electrolyte, we obtain the values calculated in the last column of Table II. The simple difference when going from discharged to half-charged anode (Δρ² = −19%) and cathode (Δρ² = +11%) sums up to a −8% net decrease of scattering intensity as long as the form and structure factors remain approximately unchanged (i.e., unchanged shape, size, and number of particles in the system). The assumption that form and structure factors are nearly constant in our case seems to be valid, as otherwise we would see directly discrete changes to the scattering in the I(Q) vs. Q plot (see Figure 13). The calculated 8% intensity decrease is the same order of magnitude as the observed decrease of 4% in the integrated intensity vs. capacity plot reached at a charge capacity of ∼5 mAh (see Figure 14b). A further net decrease of 10% (anode Δρ² = −34%, cathode Δρ² = +24%) is calculated when going from half-charged (LiC₁₂) to charged state (LiC₆), while the data show a net decrease of 5%, which is again in the right order of magnitude.

Now we consider the detailed lithiation process during discharge. For NMC it is well established that the phase composition is changing continuously, shown, e.g., in XRD studies by Yabuuchi et al.²⁰ For a continuously changing contrast factor we would thus expect a linearly changing scattering in SANS (again assuming constant form and structure factors) (see with Fig 16.). However, since the SANS data represent a superposition of cathode and anode scattering contributions, we have to consider the changing contrast factors from the graphite as well. For graphite the situation is more complicated because there are multiple phases, like LiC₁₂ and LiC₆ that form gradually and also coexist, as shown for example by neutron diffraction studies.²¹ Despite that if we assume a continuous lithiation of the graphite with no discrete phases we would as well obtain a linearly changing scattering length density and as such a linear dependence in the scattering contrast (see Fig. 16).

To understand our SANS data, we also have to consider the coherence length of our SANS experiment, i.e., the length scale on which SANS is sensitive to contrast differences, which is ∼500 nm in the configuration used for the in operando studies. This means that SANS is sensitive to inhomogeneities in the distribution of phase domains on this scale. For the small cathode primary particles (diameter <<500 nm), the SANS signal derives from the entire particle, corresponding to the contrast factor resulting from the calculated average scattering length density. Therefore, this does not contribute to the step-like features in the SANS curve (Fig 14.), as the SANS intensity should otherwise be dropping monotonously.

On the other hand, for the larger graphite particles, this is not the case, since the mean particle diameter is ≈22 μm (volume-averaged diameter, obtained by laser scattering). Thus, the SANS scattering signal from the graphite/electrolyte only derives from interactions in certain parts of the graphite particles.

Based on the above consideration, the SANS data in Figure 14b could be interpreted as deriving from the gradual diffusion of lithium from a first established surface layer at the outside perimeter of the graphite particles into the particle center. Indications of the varying Li concentration along the radial direction of graphite particles during charge and discharge pulses are provided by dynamic battery models.^22–24 In this case, an initial LiC₁₂/C phase boundary (Figure 15b) followed by a LiC₆/LiC₁₂ phase boundary (Figure 15c) will move from the surface to the center of graphite particles. Again since SANS is sensitive only to surface layers of ∼500 nm thickness or to phase boundaries in domains of this size, the relevant scattering contributions will thus only be from electrolyte vs. surface layer and from phase boundaries inside the particle.

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In Table II, the relevant contrast factors are listed. Lithiated graphite against electrolyte gives us the few % relative contrast change as mentioned above. But the contrast factor of the (non-)lithiated graphite interfaces inside particles is rather low (<1% of the value of graphite) and probably not observed in the integrated intensity plot. This implies that at first the integrated intensity drops linearly, and when all surface regions (within the coherence length) have been transformed to LiC₁₂, the integrated intensity should remain rather constant until all particles are lithiated up to the point of LiC₁₂.

We can now compare the active masses of the whole particle to the active mass in a surface layer of a thickness equal to the coherence length. Then a 500 nm surface shell represents approx. 7% of total active mass. The capacity until the first plateau (∼5 mAh) in relation to the total anode capacity (27.6 mAh opposite of cathode area) is ∼18%. The lower value of the calculated active mass in the shell when compared to the observed values of nearly 18% can be rationalized by the diffusion and presence of some lithium deeper into the particle core and thus lithiated phases LiC₁₈ or LiC₂₄ are already present beyond the shell which is determining the scattering contrast. The amount of lithium which already moved deeper into the particles is barely giving contrast and thus is nearly invisible.

When all particles are lithiated to LiC₁₂ one can expect to see another linear drop in scattering intensity due to the beginning transformation of LiC₁₂ to LiC₆ on the particle surface (compare Figure 15b, 15c). Once the particle surfaces are completely transformed the scattering intensity should again remain rather constant until the particles are fully transformed into LiC₆ as the scattering between a shell of LiC₆ and a core of LiC₁₂ also gives only a small contrast factor (see contrast factors from Table II).

This is what is observed in our in operando experiment. The evaluation of the discharge plots of integrated intensity vs. capacity reveals another interesting feature. The integrated intensity rises more quickly back to the intermediate plateau which is much longer lasting than in the charging process. Only, shortly before the end of the discharge a further increase of the integrated intensity is observed.

This we interpret as a result of the fact that Li-release out of the particles into the electrolyte seems to be faster than the Li-diffusion into the particles upon intercalation as previously reported by S. R. Sivakkumar et al.²⁵ This causes a very fast creation of an intermediate LiC₁₂ surface yielding an intermediate scattering contribution reflected in the extended intermediate value of the integrated intensity plateau. The contrast between the shrinking LiC₆ in the core and the LiC₁₂ shell is again very low. In the end a contrast of a (nearly) pristine graphite shell to surrounding electrolyte is observed.

To confirm the results the experiment was repeated with the same cell after 3 months and the results for discharging were approved not only qualitatively but also quantitatively (see Figure 14b).

Each time the small step in the voltage plot nearly coincides with the beginning of the plateau in the integrated intensity.