A fast alternative to the galvanostatic intermittent titration technique

The galvanostatic intermittent titration technique (GITT) has been regarded as the go-to method for determining the diffusion coefficients of Li-ions in insertion electrode materials at various states of charge (SoC). However, the method is time-consuming. In this work, the intermittent current interruption (ICI) method is demonstrated to provide comparably accurate measurements of diffusion coefficients with a drastically reduced experimental time. Theoretically, it is derived from Fick’s laws that the ICI method renders essentially the same information as GITT. Experimentally, both GITT and ICI are then compared side-by-side in a three-electrode half-cell of LiNi0.8Mn0.1Co0.1O2 (NMC811). It is shown that the results from both methods match where the assumption of semi-infinite diffusion applies. Moreover, the benefit of the non-disruptive ICI method to operando characterization methods is demonstrated via correlation of changes in the continuously monitored diffusion coefficient of Li+ in NMC811 to structural changes in the material by operando X-ray diffraction (XRD).

It can be observed that when x < 0.0032, equation S3 can be reduced to which is the same as Equation 5 in the manuscript.
With Equation S5, the impact of the choice of data selection interval for the GITT analyses can be examined. With r = 2 µm (average particle radius) and D = 10 -11 cm 2 s -1 , the maximum t is 12.8 s. However, if only potential measurements within 12.8 s are selected, the linear regression renders very large standard deviations due to the limited number of data points. Therefore, the upper limit of the interval is set at 40 s after confirming that the E-√ plots remain linear. The lower limit is set at 5 s since there is a transition region before the linear region on some of the E-√ plots, as reported in previous GITT works on LiNi0.5Mn0.3Co0.2O2 (NMC523). 5 This transition region is prolonged below 3.7 V, as shown in Figure S1(a). The phenomenon is also observed in EIS measurements in this work and in the literature (for LiNi0.33Mn0.33Co0.33O2, NMC111), 7,8 where the Warburg element shifts to lower frequencies. Thus, as the cell is discharged below 3.7 V, the linear region on the E-√ plots shifts to 50-150 s. The semi-infinite diffusion assumption still holds here because D is significantly lower here. The situation is more complicated when the cell is charged in the same SoC because the transition region is still long, but D derived from 50-150 s is around 5·10 -11 cm 2 s -1 , which makes 150 s considerably long for the semi-infinite diffusion assumption. Therefore, fitting the data to the full solution in S3 is necessary to derive the diffusion coefficient at SoC below 3.7 V upon charging. Figure S1. Examples of GITT measurements below 3.7 V (a) and above 3.7 V (b) analyzed by selecting the datapoints in 5-40 s (red) and 50-150 s (orange) intervals. (c) is an example of an ICI measurement following the GITT measurement in (b).

Limit of the current interruption time (Δt) of an ICI measurement
As demonstrated in section 2.2 in the manuscript, the ICI method is derived on the assumption that F(τ1+Δt) ≈ F(τ1) in Equation 12. Suppose a relative error of δ is allowed, the two terms should satisfy the following; where, the function and parameters are explained previously. The error can be discussed in terms of both asymptotes of ƒ in Equation S5 since the values are bounded by the asymptotes, which can be found out by plotting the function.
Since the τ1 > 1.27rp 2 /D is more likely and Equation S12 is stricter than Equation S10, considering only Equation S12 is sufficient in most cases. Nonetheless, in either case, the Δt = 5 s in the ICI analysis of this work should be considerably below the limit.
It is worth noting that in the standard ICI protocol, the current is only stopped for a few seconds at a time, in contrast to GITT. Therefore, the limit of Δt increases over the number of measurements in the same course of charge or discharge since, τ1 can be effectively accumulated due to the transient current pauses. The limit of Δt discussed above is thus a conservative estimation for the standard ICI protocol.

Equivalent circuit model and selected impedance spectra
The impedance spectra above 3.7 V were fitted to the equivalent circuit model (ECM) in Figure S2. The ECM is adopted from a previous work on NMC111 8 but the finite-space Warburg element is substituted here by a semi-infinite Warburg element because the spectra here, with the lowest frequency at 10 mHz, do not show a vertical tail. The spectra below 3.7 V show enlarged second semicircle (R2 and CPE2) and do not possess sufficient data points to fit the Warburg element, as shown in Figure S4. Some spectra between 3.6 and 3.7 V from cell 2 can be fitted to the ECM but majority of the spectra from cell 2 show a depressed Warburg element, which is discussed in the next section.
Complete set of impedance spectra can be found via Zenodo. 9 Figure S2. The equivalent circuit model used to fit the impedance spectra above 3.7 V. Details of the interpretation of the model are stated in the source of the model. 8 Figure S3. Selected impedance spectra above 3.7 V from the first discharge of cell 1. Figure S4. Selected impedance spectra below 3.7 V from the first discharge of cell 1.

Data from both cells in both cycles
The chemical diffusion coefficient of Li-ions (D), diffusion resistance coefficient (k) and internal resistance (R) obtained by the GITT, ICI method and EIS are presented below. The results of the first cycle of cell 1 is also plotted to facilitate the comparison between the data. The comparison between OCP and pseudo-OCP of cell 2 is also shown. The Warburg element in majority of the impedance spectra from cell 2 does not show a 45° phase angle and is substantially depressed (~22.5°). Therefore, the resulting k and R from the EIS fittings of cell 2 should be interpreted with caution.

Details of operando XRD measurement
The XRD experiment was carried out using a conventional Li/NMC811 pouch cell. Uniform stack pressure on the cell was ensured by fixing it between two beryllium discs. Diffraction patterns at the start and end of the operando run, with all the peaks ascribed to the corresponding cell components, are shown in Figure S13(a). The peaks arise from the pouch cell/separators (polyethylene and polypropylene, circles), Li metal (triangles), Al from the tabs and the pouch (square), Be discs (pentagon) and Cu tabs (hexagon). The peaks from these components do not undergo any noticeable change upon cycling. Four peaks from the rhombohedral (R 3 m) NMC811 material (stars) are also visible. However, only the 003 reflection (~18° 2θ) is distinct and free from overlap with peaks from other cell components. Therefore, Rietveld refinements 10,11 of the NMC811 structure were carried out against the 003 reflection. As the objective of the refinements were to track the changes in the c lattice parameter of the R 3 m phase and to distinguish the "active" and the "fatigued" phases, 12 structural refinements using only the 003 reflection is sufficient. As a guide to interpreting the results from the refinements, the evolution of voltage (E) as a function of the XRD pattern no: is shown in Figure S13(b). Rietveld refinements were carried out using the Topas-Academic (V6) software. 13 A second-degree Chebychev polynomial function was used to fit the background. The profile of the 003 reflection was modeled using a Thompson-Cox-Hastings pseudo-Voigt function (TCHZ_Peak_Type) together with a peak asymmetry function (Simple_Axial_Model), to account for the axial divergence imparted by the diffractometer setup. The latter was calibrated using a NIST Si 640c standard reference material and was fixed during the refinements. The NMC811 structure model used was similar to the one used in a previous study. 14 The peak shape functions and the refinement metrics mentioned in the following sections are defined in the Topas-Academic manual.

Single R3 m phase sequential refinement
Results from the sequential Rietveld refinements of the R3 m NMC811 phase are shown in Figure S14(a). In the top panel, the Rwp (R-weighted pattern) and GoF (Goodness of fit) values are shown, where it is seen that these metrics increase substantially between pattern numbers 10-17. The bottom panel shows the evolution of c lattice parameter. Here, the expected trend of shrinking c at high SoC and the recovery upon discharging is seen. Note that, in certain cases, the estimated standard deviation is large due to the poor fit of the model to the data. This is further evidenced in Figure S14(b) where two patterns at the end of charge (scans 13 and 14) are compared to ones before (scan 10) and after (scan 17). It is clearly seen that scans 13 and 14 are composed of more than one phase.

Dual R3 m phase refinement of the 003 reflection
To confirm the presence of the "active" and "fatigued" R3 m phases as reported by Xu et al., 12 Rietveld refinement of two phases against the 003 reflection from patterns 10-17 were carried out. Here, it is seen that an improved fit is obtained.