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The realistic three dimensional (3D) microstructure of lithium ion battery (LIB) electrode plays a key role in studying the effects of inhomogeneous microstructures on the performance of LIBs. However, the complexity of realistic microstructures imposes a significant computational cost on numerical simulation of large size samples. In this work, we used tomographic data obtained for a commercial LIB graphite electrode to evaluate the geometric characteristics of the reconstructed electrode microstructure. Based on the analysis of geometric properties, such as porosity, specific surface area, tortuosity, and pore size distribution, a representative volume element (RVE) that retains the geometric characteristics of the electrode material was obtained for further numerical studies. In this work, X-ray micro-computed tomography (CT) with 0.56 μm resolution was employed to capture the inhomogeneous porous microstructures of LIB anode electrodes. The Sigmoid transform function was employed to convert the initial raw tomographic images to binary images. Moreover, geometric characteristics of an anode electrode after 2400 cycles at the charge/discharge rate of 1 C were compared with those of a new anode electrode to investigate morphological change of the electrode. In general, the cycled electrode shows larger porosity, smaller tortuosity, and similar specific surface area compared to the new electrode.

Rechargeable lithium ion batteries (LIBs) have shown excellent potential as power sources for electric vehicles [

In the past several years, numerical studies have been conducted to investigate the morphological effects on the performance of LIBs. For instance, Wang

Recently, tomographic technologies have been used to obtain the real configuration of LIB electrode microstructures. For instance, focused ion beam SEM (FIB-SEM) has been used to reconstruct the 3D microstructure of LIB electrodes [

However, the complexity of realistic microstructures imposes a significant computational cost on numerical simulation of large size samples. A representative volume element (RVE) that retains the geometric characteristics of an inhomogeneous electrode material allows minimizing the volume of the porous microstructure generated by tomography techniques for further numerical studies. Kehrwald

A commercial LIB with 40 mA·h capacity (SP035518AB, Tianjin Lishen Battery Co., Tianjin, China) was cycled to obtain an aged anode electrode. It was charged/discharged from 2.8 V to 4.2 V at 1 C (40 mA) current rate under galvanostatic condition. The anode of the LIB is mesocarbon microbeads (MCMB) graphite (92 wt% MCMB and 8 wt% polyvinylidene fluoride (PVDF) binder) and the cathode is lithium cobalt oxide (94 wt% LiCoO_{2}, 3 wt% carbon black, and 3 wt% PVDF binder). After 2400 cycles, the capacity of the LIB decreased more than 10% of the initial capacity. In this study, a new anode electrode and the aged anode electrode were scanned to perform the structural analysis. An Xradia microXCT-400 system (xradia, Pleasanton, CA, USA) was employed to obtain the CT images of the electrodes. A total of 729 projection images were captured over 182 degrees scan angle. The spatial resolution of the CT had been set as 0.56 μm. To enhance the brightness and contrast of the whole dataset, X-ray measurement parameters were optimized for different samples. For the new anode electrode, the X-ray source was set at 60 kV and 8 W and each projection exposure time was 30 s. For the cycled anode electrode, the X-ray source was set at 25 kV and 5 W and each projection exposure time was 25 s. Detailed information about sample preparation can be found in our previous publication [

To reconstruct the 3D porous microstructure of the anode electrode, the raw data set generated by micro-CT needs to be converted to binary data, which is completely divided in material and pore phases. The pixel values in the raw images indicate the X-ray absorption rate that depends on the material at the given position. The intensity values of pixels in a 2D sample image are shown as a grayscale image in ^{2} that corresponds to 80 × 70 pixels. To generate a binary matrix from a raw data set, a simple threshold method could be applied on the raw data by a local minimum of the intensity histogram [_{min} and _{max} are the minimum and maximum values of the output image; α is the width of the input intensity range; and β is the centered intensity of the range. This method has been applied as an intensity transformation to enhance low contrast images [

After segmentation, a set of binary images were stacked with a 0.56 μm interval to reconstruct the porous microstructure. ^{3}. The graphite geometry is indicated in gray color and the pore structure is indicated in yellow color. The volume fraction of pores over the bulk domain is 0.27 with 99% of pore connectivity.

Geometric parameters, such as porosity, tortuosity, specific surface area, and pore size distribution are important factors affecting the capacity, reaction kinetics, and lithium ion transport of LIBs. Porosity is a fraction of the pore volume over the total electrode volume and was directly calculated from the binary matrix. Specific surface area is the solid-electrolyte interface area of an electrode per bulk volume and was calculated after reconstructing the microstructure from the binary matrix. Tortuosity quantifies the sinuosity and interconnectedness of the electrolyte phase to predict lithium ion transport in the porous electrode. The approach in [

Three domains with the same size (112 × 112 × 39.2 μm^{3}) were captured from the binary data of a new anode material to determine the optimal size of the RVE. Sub-divisions of each domain were obtained by increasing ^{3}) to investigate the influence of the volume on porosity. The thickness (^{3}.

Adapting the size, we collected 16 sample candidates from Domain 1, which have porosities within 2% deviation from the porosity of Domain 1. 3D surfaces of the 16 samples were reconstructed to obtain specific surface area. As shown in ^{−1} and the specific surface area of Domain 1 is 0.25. The maximum deviation from the specific surface area of Domain 1 is 6.26%. 10 samples have the specific surface areas within 2% deviation from the specific surface area of Domain 1.

The average absolute deviations from the pore size distribution of Domain 1 are shown in

With the quantified geometric characteristics shown in ^{3}, because the porosity fluctuation of the sub-divisions converged to within 2% of the porosity of the domain. Second, 16 samples were collected from Domain 1. The size of samples is 44.8 × 44.8 × 39.2 μm^{3}, and the porosity of the samples is within 2% deviation of the porosity of the domain. Third, the RVE candidates were filtered by selecting samples within 2% deviation of the domain's specific surface area and tortuosity. Three RVE candidates (samples number are 4, 12, and 14) were selected. Finally, the three RVE candidates were filtered by the pore size distribution. Since the pore size distribution has much larger deviation from the domain value, we chose 2% difference from the domain value as the threshold. After filtering, Sample 4 maintained the geometric characteristics such as porosity, pore size distribution, specific surface, and tortuosity of Domain 1 and it can be selected as the RVE for further numerical studies.

In order to investigate the geometric change of the LIB anode electrode after a large number of discharge and charge cycles, a commercial LIB was discharged/charged at 1 C current rate under galvanostatic conditions for 2400 cycles. As shown in ^{3}) were selected to decide the size of the RVE from the binary data. As shown in ^{3} same as the new electrode. For the cycled electrode, 15 samples were collected as RVE candidates with 2% porosity deviation from Domain 2 (ε = 0.31). ^{−1} and the specific surface area of Domain 2 is 0.26, which is similar to the new electrode. The maximum deviation from the specific area of Domain 2 is 8.46%. Five samples have specific surface areas within the 2% deviation from the specific surface area of Domain 2.

In this study, the geometric characteristics of the cycled anode microstructure were investigated and a RVE was determined based on the structural analysis. The geometric properties of the new and cycled anode material are summarized in

In this work, realistic microstructures were generated to characterize the geometric properties of the anode electrode material by employing X-ray micro-CT technology on a commercial LIB. The binary data which represents graphite and pore phases were obtained from the grayscale CT images by applying the Sigmoid transform function in an open-source, cross-platform system—ITK. Geometric properties of the anode microstructures, such as porosity, pore size distribution, specific surface area, and tortuosity are inhomogeneous. Based on the quantified geometric properties, a RVE retaining the geometric characteristics of the original geometry was determined for further numerical studies. Also, the geometric properties between a new electrode and a cycled electrode were compared. The cycled anode electrode shows larger porosity, smaller tortuosity, and similar specific surface area. The cycled electrode includes more large pores compared to the new electrode.

The authors would like to thank Tianjin Lishen Battery Joint-Stock Co. for providing lithium ion batteries. Acknowledgment is made to the donors of The American Chemical Society Petroleum Research Fund for support of this research.

The authors declare no conflict of interest.

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_{0.2}cathodes investigated by

_{2}-based rocking-chair rechargeable batteries

_{2}positive electrode

_{2}Li-ion battery cathode

_{2}-Li(Ni

_{1/3}Mn

_{1/3}Co

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_{2}Li-ion battery positive electrode using X-ray nano-tomography

_{2}cathode based on X-ray nano-CT images

_{2}cathode during galvanostatic discharge

_{2}-based non-aqueous rechargeable batteries

Image processing to generate a binary matrix: (

Reconstruction of an anode electrode: (

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Pore size distributions of the sample microstructures of Domain 1 for the new anode electrode are shown as relative volume fraction of the pore phase. The red lines are the values for Domain 1 and the gray regions indicate the 2% difference from the domain values for each pore size.

Discharge capacity of the commercial lithium ion battery (LIB) by the number of discharge and charge cycles.

Porosity profiles of the domains for the cycled anode electrode by increasing

(

Pore size distributions of the sample microstructures of Domain 2. The gray regions indicate the 2% difference from the domain values (red lines).

Pore size distributions of the new anode material and the cycled anode material.

Average absolute deviations of the pore size distribution of sub-samples from the domain value for the new and cycled anode electrode.

Average absolute deviation | New | 4.56% | 3.26% | 5.57% | 7.59% | 36.69% | 131.33% | - | - |

| |||||||||

Cycled | 8.54% | 5.56% | 5.56% | 9.35% | 17.84% | 29.67% | 89.84% | 184.06% |

Quantitative geometric parameters of the new anode material and the cycled anode material.

New anode | 0.27 | 0.25 | 2.11 |

Cycled anode | 0.31 | 0.26 | 1.86 |