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Owing to, Solid-state batteries have gradually become the focus of people's attention and research in recent years due to the advantages of high energy density and high safety factor. Lithium dendrites are a key factor affecting battery safety and service life, and in severe cases, battery short circuits can occur. Compared with liquid batteries, solid-state batteries rely on solid-state electrolytes with higher mechanical strength, which can effectively inhibit the growth of lithium dendrites, but with the increase of the number of charge-discharge cycles, the dead lithium produced by the incomplete dissolution of lithium dendrites gradually accumulates, and the performance of the battery gradually decreases. In this work, the problem of dead lithium in solid-state batteries is studied by using COMSOL Multiphysics 6.2 finite element simulation software. Due to the fact that existing research on dead lithium mainly focuses on phase field models combined with binary physics, there is little research on the influence of electrochemical parameters on dead lithium. Therefore, the phase field method is used to simulate the dissolution of lithium dendrites and the formation of dead lithium under the coupling of force-thermal-electrochemical fields. When the heat transfer model is coupled, the difference in the morphology of dead lithium before and after the coupled heat transfer model is further studied by applying an external pressure to change the stress of lithium dendrites. When the coupled mechanical field changes, the morphology of dead lithium before and after the coupled mechanical field is further studied by changing the temperature magnitude. At the same time, the effects of changes in three electrochemical parameters, namely diffusion coefficient, interfacial mobility and anisotropic strength, on the area of dead lithium are also explored. The research results indicate that when the heat transfer model or mechanical field is coupled into the phase field model, the dendrite dissolution cut-off time and dead lithium area will change. When the base rises at high temperature or when low external pressure or high external pressure is applied, the area of dead lithium decreases. For changing the electrochemical parameters, reducing the diffusion coefficient, increasing the interfacial mobility and reducing the anisotropic strength can effectively reduce the area of dead lithium.
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Keywords:
- solid-state battery /
- phase field method /
- lithium dendrites /
- dead lithium
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图 1 不同相场模型下锂枝晶的生长情况 (a) 未耦合传热模型的锂枝晶形貌; (b) 耦合传热模型的锂枝晶形貌; (c) 未耦合传热模型的von Mises应力(单位: MPa); (d) 耦合传热模型的von Mises应力(单位: MPa)
Figure 1. Growth of lithium dendrites under different phase field models: (a) Lithium dendrite morphology of uncoupled heat transfer model; (b) lithium dendrite morphology of coupled heat transfer model; (c) von Mises stress for uncoupled heat transfer model (in MPa); (d) von Mises stress coupled to the heat transfer model (in MPa).
图 2 未耦合传热模型的锂枝晶溶解情况 (a) 锂枝晶形貌变化; (b) von Mises应力(单位: MPa)
Figure 2. Dissolution of lithium dendrites in uncoupled heat transfer models: (a) Lithium dendrites change in morphology; (b) von Mises stress (in MPa).
图 3 耦合传热模型的锂枝晶溶解情况 (a) 锂枝晶形貌变化; (b) von Mises应力(单位: MPa)
Figure 3. Dissolution of lithium dendrites in coupled heat transfer model: (a) Lithium dendrites change in morphology; (b) von Mises stress(in MPa).
图 4 未耦合传热模型加压5 MPa (a) 锂枝晶形貌; (b) von Mises应力(单位: MPa); (c) 死锂形貌
Figure 4. Uncoupled heat transfer model is pressurized to 5 MPa: (a) Lithium dendrite morphology; (b) von Mises stress (in MPa); (c) dead lithium morphology.
图 5 耦合传热模型加压5 MPa (a) 锂枝晶形貌; (b) von Mises应力(单位: MPa); (c) 死锂形貌
Figure 5. Coupled heat transfer model is pressurized to 5 MPa: (a) Lithium dendrite morphology; (b) von Mises stress (in MPa); (c) dead lithium morphology.
图 6 不同外压下锂枝晶的生长和溶解情况 (a) 锂枝晶形貌; (b) von Mises应力(单位: MPa); (c) 死锂形貌
Figure 6. Growth and dissolution of lithium dendrites under different external pressures: (a) Lithium dendrite morphology; (b) von Mises stress (in MPa); (c) dead lithium morphology.
图 7 锂枝晶的溶解以及相场温度变化情况 (a) 未耦合力学场锂枝晶溶解情况; (b) 未耦合力学场温度变化; (c) 耦合力学场温度变化
Figure 7. Dissolution of lithium dendrites and changes in phase field temperature: (a) Dissolution of lithium dendrites in the uncoupled mechanical field; (b) temperature changes in the uncoupled mechanical field; (c) temperature changes in the coupled mechanical field.
图 8 未耦合力学场、环境温度353 K下锂枝晶的溶解形貌
Figure 8. Dissolution morphology of lithium dendrites at ambient temperature of 353 K in the uncoupled mechanical field.
图 9 耦合力学场、环境温度353 K下锂枝晶的溶解情况 (a) 锂枝晶形貌; (b) von Mises应力(单位: MPa)
Figure 9. Dissolution of lithium dendrites at ambient temperature 353 K: (a) Lithium dendrite morphology; (b) von Mises stress (in MPa).
图 10 耦合力学场、环境温度273 K下锂枝晶溶解情况 (a) 锂枝晶形貌; (b) von Mises应力(单位: MPa)
Figure 10. Dissolution of lithium dendrites at ambient temperature 273 K: (a) Lithium dendrite morphology; (b) von Mises stress (in MPa).
图 11 不同扩散系数下锂枝晶的生长与溶解情况 (a) 增大扩散系数锂枝晶形貌; (b) 减小扩散系数锂枝晶形貌; (c) 增大扩散系数死锂形貌; (d) 减小扩散系数死锂形貌
Figure 11. Growth and dissolution of lithium dendrites under different diffusion coefficients: (a) Lithium dendrite morphology when the diffusion coefficient is increased; (b) lithium dendrite morphology when the diffusion coefficient is decreased; (c) dead lithium morphology when the diffusion coefficient is increased; (d) dead lithium morphology when the diffusion coefficient is decreased.
图 12 不同界面迁移率下锂枝晶的生长与溶解情况 (a) 锂枝晶形貌; (b) 死锂形貌
Figure 12. Growth and dissolution of lithium dendrites under different interfacial mobility: (a) Lithium dendrite morphology; (b) dead lithium morphology.
图 13 不同各向异性强度下的锂枝晶生长情况
Figure 13. Lithium dendrite growth under different anisotropic strengths.
图 14 不同各向异性强度下的死锂形貌
Figure 14. Dead lithium morphology under different anisotropic strengths.
表 1 相场参数
Table 1. Phase field parameters.
参数名 符号 数值 文献 梯度能量系数/(10–10 J·m–1) $ {\kappa }_{0} $ 1 [15] 各向异性强度 $ \delta $ 0.1 [15] 各向异性模数 $ \omega $ 4 [22] 势垒高度/(105 J·m–3) $ W $ 3.75 [22] 标准体积浓度/(103 mol·m–3) $ {c}_{0} $ 1 [22] 环境温度/K $ {T}_{0} $ 293 [14] 电极杨氏模量/GPa $ {E}^{\mathrm{e}} $ 7.8 [14] 电解质杨氏模量/GPa $ {E}^{\mathrm{s}} $ 1 [14] 电极泊松比 $ {v}^{\mathrm{e}} $ 0.42 [15] 电解质泊松比 $ {v}^{\mathrm{s}} $ 0.3 [15] –0.866×10–3 Vegard应变系数 $ {\lambda }_{i} $ –0.773×10–3 [14] –0.529×10–3 界面迁移率/(10–6 m3·J–1·s–1) $ {L}_{\sigma } $ 1 [22] 反应常数/s–1 $ {L}_{\eta } $ 0.5 [22] 对称因子 $ \alpha $ 0.5 [22] 固相锂浓度/(104 mol·m–3) $ {C}_{\mathrm{s}} $ 7.64 [22] 电极电导率/(107 S·m–1) $ {\sigma }^{\mathrm{e}} $ 1 [14] 电解质电导率/(S·m–1) $ {\sigma }^{\mathrm{s}} $ 0.1 [14] 电极比热容/(J·kg–1·K–1) $ {c}^{\mathrm{p}\mathrm{e}} $ 1200 [14] 电解质比热容/(J·kg–1·K–1) $ {c}^{\mathrm{p}\mathrm{s}} $ 133 [14] 电极导热系数/(W·m–1·K–1) $ {\lambda }^{\mathrm{e}} $ 1.04 [14] 电解质导热系数/(W·m–1·K–1) $ {\lambda }^{\mathrm{s}} $ 0.45 [14] 对流换热系数/(W·m–2·K–1) $ \mathrm{h} $ 10 [17] 
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