Fig. 1. Multi-scale hierarchical electrode structure in lithium ion battery.锂离子电池中的多层电极结构

Fig. 2. Fitting results and experimental results of open-circuit potential of silicon electrode proposed by Sethuraman et al.^[19]. The red data point is the lithium data measured in the experiment, and the blue data point is the dilithiated data measured in the experiment. The solid line was obtained under a C/8 constant current charge-discharge operation, and the dashed line is the fitting function Sethuraman等^[19]硅电极开路电势的拟合结果和实验结果, 其中红色的数据点是实验测得的锂化数据, 蓝色数据点是实验测得的去锂化数据, 实线是在C/8恒流充放电条件下的实验曲线, 虚线是依据实验数据拟合的结果

Fig. 3. Effect of diffusion induced stress on voltage hysteresis: (a) Distribution of concentration of lithium ions in a electrode particle during lithiation and delithiation; (b) diffusion-induced stress evolution diagrams of particles with different sizes in primary charge-discharge cycle扩散诱导应力对电压迟滞的影响　(a)电极颗粒在锂化和去锂化过程中锂离子的浓度分布; (b)一次充放电循环中, 不同尺寸的颗粒扩散诱导应力演化

Fig. 4. (a)−(d) Overpotential evolution charts of each part with particle size of 10, 100, 400, 700 nm, respectively(a)−(d)分别是颗粒尺寸为10, 100, 400, 700 nm的各部分过电势演化图

Fig. 5. Dependence of overpotential gap consumed by stress, total overpotential gap and the corresponding percentage on different particle sizes. The gap refers to the difference between the maximum value and the minimum value in the overpotential loop应力分担过电势的差值、总过电势差值及其所占百分比在不同颗粒尺寸下的变化, 其中差值是指过电势回线中最大值与最小值之差

Fig. 6. Evolution curve of surface tension due to surface effect and the corresponding overpotential. The dark line represents the mean stress in a cycle and the bar defines the range. The three subplots are evolutions of surface stress due to surface effects in a cycle由表面效应引起的表面张力及其分担过电势的演化曲线, 其中黑色曲线的应力值为一次充放电循环中的平均应力值, 竖直曲线为各自的变化范围; 3张子图为对应的表面张力演化曲线

Fig. 7. (a) Evolution of surface hydrostatic stresses in consideration of both diffusion induced stress and surface effects under different particle sizes; (b), (c), (d), (e) evolutions of all parts of overpotential in the particles of 4, 10, 100 and 400 nm radius, respectively(a)不同颗粒尺寸下, 表面张力和扩散诱导应力共同作用下的表面静水应力演化图; (b), (c), (d), (e)分别是颗粒尺寸为4, 10, 100和400 nm时的各部分过电势演化图

Fig. 8. Absolute values of the hydrostatic stress due to surface effects and the surface stress due to diffusion induced stress under different particle sizes.不同颗粒尺寸下扩散诱导应力和表面效应引起的静水应力的绝对值对比

Fig. 9. Evolution diagram of the sum of diffusion induced stress and surface effect under different particle sizes不同颗粒尺寸下扩散诱导应力与表面效应之和的演化

Fig. 10. Impacts of interparticle compression on the voltage hysteresis: (a) Stress hysteresis for electrodes with different porosity ratios; (b)−(e) loop diagram of all parts of overpotential in the electrode with different porosity ratios.p is the porosity of the electrode structure. 颗粒间挤压对电压迟滞的影响　(a) 不同孔隙下电极的应力迟滞回线图; (b)−(e) 不同孔隙率下电极各部分过电势的回线图; 其中p为电池结构的孔隙率