Probing three-dimensional sodiation–desodiation equilibrium in sodium-ion batteries by in situ hard X-ray nanotomography

Materials degradation—the main limiting factor for widespread application of alloy anodes in battery systems—was assumed to be worse in sodium alloys than in lithium analogues due to the larger sodium-ion radius. Efforts to relieve this problem are reliant on the understanding of electrochemical and structural degradation. Here we track three-dimensional structural and chemical evolution of tin anodes in sodium-ion batteries with in situ synchrotron hard X-ray nanotomography. We find an unusual (de)sodiation equilibrium during multi-electrochemical cycles. The superior structural reversibility during 10 electrochemical cycles and the significantly different morphological change features from comparable lithium-ion systems suggest untapped potential in sodium-ion batteries. These findings differ from the conventional thought that sodium ions always lead to more severe fractures in the electrode than lithium ions, which could have impact in advancing development of sodium-ion batteries.

The electrochemical measurement was performed by cyclic voltammogram between 0.005 and 2.5 V at a scanning rate of 0.04 mV/s. Similar to the in situ 3D TXM experiment with galvanostatic cycle, large volume expansion and shrinkage occur after the first sodiation and desodiation process, respectively. In spite of this significant volume change, no obvious microstructural pulverization was found at the Na ion extraction process (desodiation). As a result, the first sodiation process plays a predominant role in Sn microstructural failure. This conclusion is consistent with the in situ 3D TXM result.  Na/Na + ) Capacity (mAh/g)

Supplementary Tables
Supplementary Table 1. Quantitative 3D morphological analysis of Sn anodes at the first cycle. *specific area is defined as the surface area in per unit volume. While specific area is generally inversely proportional to the size, its reciprocal (1/specific area, S v -1 ) is then a suitable parameter used to indicate the representative size in a structure. Note that the precise relationship between the S v -1 and the feature size in a system depends on sample's geometry. For instance, if the sample geometry can be represented by a sphere with a radius r, then the S v -1 is: Note that there is a geometric factor of 1/3, which is due to the spherical geometry.

Supplementary Note 1. Challenges for in situ 3D electrochemical cells.
Developing such a working cell is very challenging because this cell must i) allow a 180-degree rotation without blocking x-ray beam; ii) fit micron scale studying electrode within the x-ray beam to fit within the x-ray field of view (40×40 µm); iii) function normally as a working battery; and iv) allow electrochemical measurement for correlating the microstructural changes with the electrochemical reaction stages. The widely used coin cell is insufficient because it blocks beam when it is rotated, leading to a very limited angle of rotation and producing an unusable 3D reconstruction. The supporting materials of the cell along the x-ray beam path must be highly transparent to allow sufficient transmission of the xray beam through the studied electrode. In addition, properly sealing such a cell is critical to ensure that the cell can work normally and be stable enough for repeated cycling. The complexity of developing the cell has hindered the investigation of in situ 3D microstructural evolution using TXM.

Supplementary Note 2. Electrochemical measurements.
Considering that Sn is difficult to maintain as fully sodiated to Na 15 Sn 4 at high rates, particularly for the larger Sn particle size, we used an ultra-low current density of 5 mA/g to maximize the sodium ion insertion. The first galvanostatic cycle is between 0.005 to 1.0 V 1-3 . The initial high current pulse (done by pushing the cell voltage to be below 0.8 V) and the low cutoff voltage (1.0 V) strategies were applied to minimize the decomposition of electrolyte on Sn particles. In spite of this strategy, the electrolyte decomposition cannot be completely avoided. Therefore, to obtain the true capacity of Sn materials, a pure carbon paper (CP) electrode without Sn particles was tested with the same condition and the discharge profile was shown in Supplementary Figure 16. The discharge capacity is determined to be ~90 mAh/g (discharge to 0.005 V), which can be attributed to the carbon paper capacity and electrolyte decomposition. From the discharge-charge profile of Sn electrode, the overall discharge and charge capacity were determined to be 685 mAh/g and 405 mAh/g, respectively, with a coulombic efficiency of 59.1%, which is remarkably lower than most literature related to Sn in lithium-ion batteries 4,5 , particularly considering the "minimization strategy" and the small capacity contribution (~90 mAh/g) from carbon paper and electrolyte decomposition. Therefore, this high irreversible capacity (~280 mAh/g) can be mainly attributed to the irreversibility in Na ions insertion/extraction due to the partial trapping of sodium ions in Sn electrodes, which can be further confirmed by the irreversibility at the above attenuation coefficient change and 3D microstructural evolution.
The discharge capacity of Sn at the second dataset point (~0.25 V) is determined to be 302 mAh/g, in which ~310 mAh/g (the entire Sn/CP electrode discharge capacity at ~0.25 V) substrates ~8 mAh/g (the CP electrode discharge capacity includes electrolyte decomposition at ~0.25 V). Therefore, the 302 mAh/g corresponds to a Na x Sn phase (x=~1.3).
The comparative study of Sn anodes in LIB was performed with the similar battery design and electrochemical methods. The only difference is using Li foil and 1M LiPF 6 in ethylene carbonate/diethyl carbonate (1:1) as counter electrode and electrolyte, respectively.

Supplementary Note 3. 3D morphological analysis method.
This system has a precision cylinder mounted on a low run-out ball bearing rotation stage and three integrated capacitive sensors as shown in schematic 1 to measure the residual run-out of the rotation axis as a function of rotation angle. These measured sensor readings are calibrated through multiple sets of tomography data from a standard gold ball (3 micron in diameter). Then, a program reads the calibrated measurements with an algorithm to obtain the run-out corrections Δx(θ) and Δy(θ) at each rotation angle as a function of the measured displacements of the capacitive sensors. When taking a tomography data for a sample, these run-out corrections are automatically applied to produce a transparent mode of usage that emulates a perfect system without any rotational run-out. Without any need for user interaction, each collected 2D projection is automatically aligned for 3D reconstruction to fulfill automated 3D tomography (Supplementary Figure 17). 6 A standard Filtered Back-projection Reconstruction algorithm was again used to reconstruct the 3D images. The reconstructed volumes were cylinders with 40 µm in both diameter and height. The volumes from different electrochemical cycle states were then registered using commercial software (Avizo, VSG, version 7). A median filter with a kernel size of 3×3×3 voxels was then applied to the original image for noise reduction. The Sn/Na x Sn and exterior regions (electrolyte and carbon fiber) were labeled via simple threshold segmentation. The histogram of the reconstruction images consist of two distinctive peaks for these two phases and therefore the threshold value can be chosen as the minimum value between the two peaks. A smoothed surface mesh of the Sn/Na x Sn particles was then generated from the segmented images also using Avizo with a constraint that preserves the particle volumes within the surface meshes.
Various 3D parameters were then calculated from the segmented structure and surface meshes: particle feature size distribution, volume change, surface area, specific area, and curvature analysis. The volume change was calculated by voxel counting. The surface area was measured from the surface mesh. Specific area is defined as surface area per unit volume. It was calculated from dividing the surface area of all particles in the entire sample by the volume of all particles in the entire sample. It is a direct indication of the size change of the sample. A smaller particle of the same shape has larger specific area than a larger particle with the same shape. Therefore, the decrease of specific area indicates the morphological change such as fracture, cracking and pulverization which all lead to increase the surface area while the total volume remains constant. The reciprocal of the specific area was then a common parameter used to characterize the average feature size.
The feature size distribution was calculated using software deFveloped in-house (MatLab, R2011b, MathWorks) with the algorithms described elsewhere by Holzer et al. The principal curvature calculations were carried out using commercial package (Avizo, v.7, VSG) 7 . The interfacial shape distribution (ISD) was then plotted using customized written software (MatLab, R2011b, MathWorks) with method developed by Voorhees et al. 8 In the ISD calculation, as the surface meshing in Avizo results in a triangular mesh with tiles of various areas, an area weighting procedure is used when generating the probability map.
Surface curvedness computes the surface scalar field which value are equal to √ Where C1 and C2 are the two principal curvatures.

Supplementary Note 4. Analysis of fracture degree.
The fracture degree (a unit-less parameter, ƞ) is measured by the ratio of R s to R v . Here the R s is the radius calculated from the actual surface area S, and the R v is the radius from the actual volume V So, the fracture degree, ƞ, can be determined below, Here, the S and V are the 3D statistical analysis results based on hundreds of particles in the electrode.