Indirect state-of-charge determination of all-solid-state battery cells by X-ray diffraction

Determining the state-of-charge of all-solid-state batteries via both ex situ and operando X-ray diffraction, rather than by electrochemical testing (may be strongly affected by electrically isolated/inactive material, irreversible side reactions, etc.), is reported. Specifically, we focus on bulk-type cells and use X-ray diffraction data obtained on a liquid electrolyte-based Li-ion cell as the reference standard for changes in lattice parameters with (de)lithiation.

Electrode preparation. Cathode composite was prepared by mixing a total of 1 g of NCM622 (coated or uncoated) and β-Li 3 PS 4 in a 7/3 weight ratio using 10 zirconia balls (Ø 10 mm) for 30 min at 140 rpm in a planetary ball mill (Fritsch) under Ar atmosphere. Anode composite was prepared via the same milling protocol, but using a mixture of carbon-coated Li 4 Ti 5 O 12 (LTO, BASF SE), Super C65 carbon black (Timcal) and β-Li 3 PS 4 in a 3/1/6 weight ratio.
Cell assembly and electrochemical measurements. For bulk-type SSB cells (round pellets, Ø 10 mm) used for ex situ XRD experiments, a custom cell setup comprising two stainless steel dies and a plastic sleeve (PEEK) was utilized. Specifically, 60 mg of β-Li 3 PS 4 was compressed at a pressure of 125 MPa (≈700 µm thickness). Then, about 13 mg of cathode composite (≈120 µm thickness, 2.1 mAh/cm 2 loading) was pressed onto the solid electrolyte pellet at 375 MPa. Finally, a 100 µm-thick In foil (Alfa Aesar) of 8 mm diameter was attached to the other side. During electrochemical testing, a pressure of 55 MPa was maintained using a Specac Mini-Pellet Press. Galvanostatic charge/discharge measurements were performed at 25 °C and at a rate of C/10 (1C = 180 mA/g) in the voltage range between 2.3 and 3.8 V vs. In/InLi (≈2.9-4.4 V vs. Li + /Li) using a BioLogic VMP3 multi-channel potentiostat. Prior to charging, the cells were held at open-circuit voltage (OCV) for 1 h. After the first charge, first discharge or second charge cycle, the cells were disassembled without breaking the pellet apart.
For galvanostatic intermittent titration technique (GITT), the SSB cells were charged and discharged at C/10 rate with current pulses of 10 min, followed by 2.5 h relaxation periods (OCV), in the voltage range between 2.3 and 3.8 V vs. In/InLi using a BioLogic VMP3 multichannel potentiostat.
For long-term cycling of SSB cells, a setup described elsewhere was utilized. [2,3] Instead of In foil, about 50 mg of LTO anode composite (2.9 mAh/cm 2 loading) were pressed at 250 MPa onto the pellet (note that LTO was chosen to block/prevent severe side reactions at the anode side). All of the other steps were done as described above, but using a MACCOR battery cycler and applying a voltage range of 1.35-2.85 V vs. Li 4 Ti 5 O 12 /Li 7 Ti 5 O 12 (≈2.9-4.4 V vs. Li + /Li).
Ex situ XRD on SSB cells. Disassembled cells were placed with the cathode side up in an airtight, Ar-filled dome cell having a knife-edge to reduce Ar scattering (Bruker AXS, A100B138-B141). XRD patterns were collected on a D8 ADVANCE diffractometer (Bruker AXS) with a Cu-K radiation source ( 1 = 1.54056 Å,  2 = 1.54439 Å) at 40 kV and 40 mA, focusing Bragg-Brentano geometry (goniometer radius of 280 mm) and LynxEye 1D detector. Variable divergence slits, axial Soller slits (2.5°) and a Ni-Kβ filter were used. The irradiated area covered virtually the complete cathode surface of the SSB pellet. The pellet height was carefully adjusted to the customised sample holder. Patterns were collected in the range of 10-90° 2 with a step size of 0.01° and an exposure time of 2.3 s per step.
Data analysis to determine lattice parameters and phase fractions was performed by the Rietveld method using the FullProf software package (version July-2017). The respective Rietveld plots are shown in Fig. S6. The instrumental function (zero point of detector and profile parameters) was determined empirically using NIST material LaB 6 (SRM 660b, a = 4.15691(8) Å).
Stepwise refinement of one (pristine and discharged state) or two (charged state) NCM622 phase fractions (R−3m) was done via (1) scale factor, (2) lattice parameters, specimen displacement and background coefficients (Chebyshev function with 24 parameters), (3) z(O) and overall isotropic atomic displacement and (4) peak shape (modelled using the Thomson-Cox-Hastings pseudo-Voigt function). The site occupancies of atoms were fixed to the nominal content. A retrospective correction by incorporating fixed Li site occupancies for the delithiated (charged) NCM622 [x(Li) taken from operando XRD (Tab. 1): 0.38/0.40 and 0.33 for uncoated and coated material, respectively] in repeated refinements resulted in small errors when calculating the phase fraction (2%). Note that the latter is in the range of the methodical standard deviation. The error in estimating x(Li) by comparison of operando and ex situ XRD data and the difference in using c-or a-lattice parameter as reference point (≈0.04, see Fig. S2) is around 0.02%. Additionally, it should be noted that irreversible capacities from side reactions such as solid electrolyte degradation are not taken into account in the XRD data analysis.
Operando XRD on liquid electrolyte-based LIB pouch cell. Operando XRD was performed on a pouch half-cell comprising pristine NCM622 (see above) and using a high-intensity laboratory diffractometer, equipped with a microfocus rotating Mo-K source ( 1 = 0.70930 Å,  2 = 0.71357 Å) and Pilatus 300K-W area detector. Details of both the setup and calibration procedures can be found elsewhere. [4] Patterns were collected in the range of 5-37° 2 every 75 s with cycling at C/10 in the voltage range between 2.9 and 4.4 V vs. Li + /Li. Rietveld refinement was done using TOPAS Academic (version 5).
Specific charge capacity calculation. For calculating specific capacities of the initial charge (q ch ) of SSB test cells on the basis of x(Li) estimated by ex situ XRD on the NCM622 cathodes, the following equation was used:

Operando synchrotron-based XRD on SSB test cells at PETRA III (DESY, Hamburg).
Operando XRD on SSB test cells was performed at beamline P24 (EH2) of PETRA III at DESY (Hamburg, Germany). The pelletized cells (Ø 13 mm) comprised NCM622, Li 6 PS 5 Cl and In foil (Ø 10 mm, with 6 mm hole in the middle) as cathode, solid electrolyte and anode, respectively. The composite cathode was prepared as described above, but using a 7/2.9/0.1 weight ratio of NCM622, Li 6 PS 5 Cl and Super C65 carbon black. Li 6 PS 5 Cl was synthesised by high-energy milling of stoichiometric amounts of Li 2 S (99.9%, Sigma Aldrich), P 2 S 5 (99%, Sigma Aldrich) and LiCl (>99%, Alfa Aesar, dried at 300 °C in vacuum prior to use). The asmilled powder was treated in vacuum at 300 °C for 5 h to obtain crystalline material with an ionic conductivity of 1.8 mS/cm. A free-standing SSB pellet was prepared by pressing Al mesh (Ø 12 mm), 25 mg of cathode composite (4.0 mAh/cm 2 loading) and 120 mg of Li 6 PS 5 Cl at around 370 MPa. Then, ring-like In foil was attached to the pellet, which was subsequently sandwiched between two stainless steel spacers (Ø 16 mm, with 5 mm hole in the middle) and crimped in a CR2032 coin cell with polyimide windows (Ø 5 mm), eventually allowing for XRD in transmission geometry. Finally, the coin cell was implemented in a setup described elsewhere, [4] suited for operando XRD at beamline P24 (EH2). The energy was set at 28 keV ( = 0.442799 Å), thus ensuring a high-flux beam (up to 10 12 photons per second) with a spot size of 400×400 µm 2 . Patterns were collected in the range of 3-17° 2 every 30 s with cycling at C/20 in the voltage range between 2.3 and 3.8 V vs. In/InLi using a BioLogic VMP3 multichannel potentiostat. A representative contour plot of XRD patterns taken is shown in Fig. S7.       Tab. S1 Summary of quality parameters (figure of merits) from Rietveld analysis of ex situ XRD data obtained on SSB cells using uncoated and LiNbO 3 -coated NCM622 (R−3m).