Non-destructive visualization of short circuits in lithium-ion batteries by a magnetic field imaging system

To develop a high-density and long-life lithium-ion battery, a technology is needed that allows non-destructive visualization of the spatial distribution of deteriorated parts after cycle test. In the present study, we measured the distribution of the magnetic field leaking from the lithium-ion battery during its operation. Based on the measurement results, we evaluated the spatial distribution of electric current density that corresponds to the reaction rate of the active material and the ion diffusion rate in the electrolyte solution inside a battery using the electric current reconstruction process. With respect to the changes in the internal state of the lithium-ion battery associated with cycle deterioration, we successfully visualized the part where the electrical conductivity has changed that is the deteriorated part causing the battery capacity to decrease inside the lithium-ion battery.


Introduction
Because of their high energy density and long life, lithiumion batteries are widely used in electric vehicles, hybrid electric vehicles, mobile phones, etc. Lithium-ion batteries, however, are also known for forming dendritic lithium crystals, which deposit on negative electrodes during charging. [1][2][3][4] Dendrites degrade the performance of the negative electrode and cause capacity deterioration. [5][6][7][8] In addition, it has been reported that some overgrown dendrites penetrate separators, which causes short circuits that results in serious accidents such as ignition and burning of the organic solvent. [9][10][11][12] Observation of the negative electrode crosssection using synchrotron hard X-ray microtomography 1) and microscopic observation of specially shaped cells [13][14][15] demonstrated that the dendrites form due to the heterogeneous reactivity of the negative electrode. Accordingly, for a purpose of developing high-quality lithium-ion batteries, it is indispensable to establish a method for directly observing the phenomena occurring inside lithium-ion batteries to visualize the spatial non-uniformity of the reaction kinetics. [16][17][18][19] The methods for observing the non-uniformity of reactions include three-dimensional structural analysis using X-ray tomography, 20,21) visualization of the lithium ions distribution using X-ray Absorption Spectroscopy, [22][23][24] energy dispersive X-ray spectroscopy for element mapping, 25,26) and the Raman spectroscopy to visualize the crystal structure distribution of active materials in lithium-ion batteries. 27,28) Also, in this study, in contrast to the mentioned methods, by using a magnetic sensor we measured the distribution of magnetic field generated by the currents during operation of a lithium-ion battery. Then, based on these results, we developed a method to visualize the conductivity distribution inside a lithium-ion battery using the analytical relation between the solution of the current in a battery and the magnetic field it induces. Therefore, this paper deals with a non-destructive visualization of changes in conductivity inside the lithium-ion battery associated with its cycle deterioration.

Experimental methods
Assigning the boundary conditions as the two-dimensional Fourier transform f x (k x , k y ,) and f y (k x , k y ,) of the measured magnetic field distribution in Eqs. (1) and (2), the analytical solution of the basic equation of the static magnetic field in free space without a magnetic source can be derived by Eqs. (3) and (4). 29) As shown in Fig. 1, the x-axis and y-axis are in the electrode plane direction. With the magnetic field reconstruction method using this solution, the magnetic field distribution on the surface of the lithium-ion battery can be obtained based on the measurements.
Further, the relationship between the magnetic field distribution on the battery surface ( Fig. 1) and conductivity inside the battery can be derived in the following manner. In the Eq. (5), as shown in Fig. 1, h T is the distance between the electrodes, h is the thickness of the electrode and σ (x, y) is the conductivity distribution between the electrodes of a lithium-ion battery, j (x, y) is the two-dimensional potential distribution on the electrode surface, z 0 is the electrode coordinate and σ 0 is the electrode conductivity. Q x (k x , k y , z 0 ) and Q y (k x , k y , z 0 ) are two-dimensional Fourier transforms of the x and y components of the magnetic field on the battery surface according to Eqs. (6) and (7).
Using Eqs. (6) and (7), j (x, y) can be derived from Eq. (5) as shown in Eq. (8). 30) Furthermore, the analytical solution σ (x, y) of the two-dimensional conductivity distribution in the battery can be obtained from Eq. (9). This distribution represents the electric current between the electrodes, and corresponds to the reaction rate of the active material and the ion diffusion rate in the electrolyte solution. From the magnetic field distribution on the surface determined by this method, the conductivity distribution inside the battery can be reconstructed  Figure 2 shows a schematic diagram of the magnetic imaging system. We used a magnetic sensor (Detectability: 30 pT/Hz 0.5 at 1 Hz) that was developed based on the magneto-impedance effect. 31) The magnetic field distribution was measured by controlling the X and Y stepping motors and performing two-dimensional scanning. Further, the angle of the magnetic sensor was adjusted by the θ stepping motor to measure the x component H x and the y component H y of the magnetic field. When applying the alternating current with the 1 Hz frequency source to the battery, the generated magnetic field was detected by the magnetic sensor. After digitalization of the magnetic sensor signals by a 16 bit A/D converter, magnetic field phase delay was determined compared to the reference signal of the current source. Then, the conductivity distribution in the lithium-ion battery was reconstructed following Eqs. (4) and (9).

Results and discussion
In the cycle test, we used a laminated single-layer lithium-ion battery having an electrode size of 80 mm × 240 mm. The  ( ) The magnetic field was measured by applying to the battery the AC (1 Hz, 240 mAp-p) superimposed with the DC voltage of 3.4 V. Using the non-destructive magnetic imaging system illustrated in Fig. 2, measuring magnetic field was performed over the area of 260 mm × 120 mm divided into 32 × 16 pixels, and one measurement time was 3.6 h per frame. By processing the difference between the magnetic field distributions before and after the cycles following Eq. (9), we visualized the changes in the conductivity distribution during the cycle test. This procedure makes it possible to visualize only the changes in conductivity inside the battery associated with cycle deterioration, and to neglect the initial current density distribution bias. Figures 3(a) and 3(b) show the results of the spatial distribution of H x and H y components of the magnetic field leaking from the lithium-ion battery before the cycle test. , it is clear that the changes associated with the cycle test were most significant in the center of the battery, and the region of abnormal conductivity expands during the cycle tests. The spatial resolution of this system is determined by the size of the magnetic sensor and is 5 mm. The detection limit of the leakage current of a short circuit is determined by the detectability of the magnetic sensor, which is 27 μA in the case of a point short circuit with a sensor-sample distance of 2 mm.

Conclusions
In this study, we visualized the spatial changes in the conductivity distribution inside a Li-ion battery due to cycle deterioration by measuring the magnetic field generated by the current flowing during its operation. In addition, we successfully identified the deteriorated part causing the battery capacity to decrease during the charging-discharging cycles. Furthermore, as this system provides a non-destructive analysis, the defective part size and shape can be tracked during the cycle tests. Thus, it was demonstrated that the developed system was efficient for visualizing the short circuits that occurred in lithium-ion batteries.