Multi-scale quantification and modeling of aged nanostructured silicon-based composite anodes

Advanced anode material designs utilizing dual phase alloy systems like Si/FeSi2 nano-composites show great potential to decrease the capacity degrading and improve the cycling capability for Lithium (Li)-ion batteries. Here, we present a multi-scale characterization approach to understand the (de-)lithiation and irreversible volumetric changes of the amorphous silicon (a-Si)/crystalline iron-silicide (c-FeSi2) nanoscale phase and its evolution due to cycling, as well as their impact on the proximate pore network. Scattering and 2D/3D imaging techniques are applied to probe the anode structural ageing from nm to μm length scales, after up to 300 charge-discharge cycles, and combined with modeling using the collected image data as an input. We obtain a quantified insight into the inhomogeneous lithiation of the active material induced by the morphology changes due to cycling. The electrochemical performance of Li-ion batteries does not only depend on the active material used, but also on the architecture of its proximity.

This plot shows the high capacity retention at C-rates lower and equal to C/2 of the a-Si/c-FeSi 2 /graphite electrode. After 100 cycles, the cell capacity has yet to pass below 70 % of the initial capacity measured at C/2. However, when the cell is cycled at 2C the capacity drops fast due to polarization of the electrode. According to the results in this figure, it is estimated that the cell capacity at C/2 should reach 70 % of its initial value after completing at least 200 cycles following the same procedure. This is in agreement with the results obtained for a 30 mAh fullcell prepared with a 1/1/1 Nickel-Manganese-Cobalt-Oxide (NMC) electrode as cathode (see 3 Supplementary Note 1). The discharge capacity fading of the NMC//a-Si/FeSi 2 /graphite pouchcell is close to 30 % after 321 cycles at C/2. anode with 3 cycles (c) 100 cycles, and (d) 300 cycles, respectively. Red indicates close distance of pore to the next a-Si/c-FeSi 2 compound particles while blue shows far distance. The minimum, maximum and mean norm distance changes from 0.49 µm, 12.73 µm, and 3.62 µm to 0.67 µm, 17.53 µm, and 5.37 µm for the pristine anode and anode with 300 cycles, respectively. Scale bar indicated in a) is also valid for c) -d).

Supplementary Note 1: Electrode preparation
For an optimized and homogenous paste it is necessary to disperse the conducting agent into the binder solution (hereinafter referred to as "C-paste").
Preparation of the C-paste: The conducting agent and the binder (predissolved, 8.0wt% in water) are mixed in a dissolver mixer at 1200rpm for 30min.
Mixing Procedure: (i) 2/3 of the graphite and the whole amount of the silicon based active material are put in a Hivis Mix Modell 2P-03/1 and is mixed with half of the C-paste for 30min at 50rpm.
(ii) In the next step the rest of the graphite and C-Paste are added and mixed for 60min at 60rpm.
(iii) Finally water is added to optimize the viscosity of the electrode paste for further processing and the electrode paste is mixed for 30min at 30rpm.

Supplementary Note 2: FIB-SEM data processing and Segmentation
We use Avizo® to remove curtaining artefacts with the help of FFT and an in-house developed Python script to perform the segmentation. After the pre-processing of the image data, the 3D image are converted to float and normalized between 0 and 1. Next, we use Felzenszwalb 1 algorithm to separate the slice images into regions. This graph-based algorithm tries to find the borders of objects by looking at local differences as well as global (for each slice) differences to decide where to draw a boundary line. For each region, we calculate different features (i.e. mean grey value, standard deviation, number of pixels above/below a certain threshold, etc.) and sequentially narrow down the criteria for each feature to fit our system (e.g. a region is considered graphite if mean grey value is between 0.4 and 0.6 and the std is below a threshold and so on). When we found good conditions for a specific phase (background, graphite, (SEI/C/B), a-Si/c-FeSi 2 ) we assign the corresponding region a label (0,1,2 or 3). After each assignment we iterate over the remaining regions to further narrow down the conditions. We choose to use this iterative approach to avoid mislabeling of shine-through artefacts as best as possible. At the end, we obtain a mask image for the different phases (pores, graphite, SEI and Si/FeSi 2 compound).

Supplementary Note 3: Image Analysis and Segmentation of µ-Synchrotron Data
The measured synchrotron data was performed with an effective voxel size of 0.65 x 0.65 x 0.65 m³ and shows scattering artefacts in the vicinity of the copper current collector; to avoid those artefact affected areas in the segmentation, we mask the Cu substrate as follows: Firstly, we apply the median filter to the data. Then a threshold for the copper current collector is applied using the filtered data. Next, the morphological operation dilation, is utilized to get a mask from the binarized substrate. Finally, the original data is masked by replacing the intensity values of the obtained subtracted mask with the background value.
where is the Li-ion diffusion coefficient and ε is the porosity value of the domain to reflect the influence of the porosity (area fraction) acting on the Li-ion diffusion.

Supplementary Note 5: elaboration on diminishing behavior for the SEI growth
The SEI growth is bound to the available surface area and the "open" Si/C. At the beginning, there is a lot of open surface area and Si/C. Therefore, the initial evolution of the SEI is quite large, but after each cycle, the amount of surface area and Si/C available for new SEI formation decreases until it reaches a limit, which will lead to the growth becoming zero. By that time, the