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Solid-state lithium batteries possess numerous advantages, such as high energy density, excellent cycle stability, superior mechanical strength, non-flammability, enhanced safety, and extended service life. These characteristics make them highly suitable for applications in aerospace, new energy vehicles, and portable electronic devices. However, the growth of lithium dendrite at the electrode/electrolyte interface remains a critical challenge, limiting both performance and safety. The growth of lithium dendrites in the electrolyte not only reduces the Coulombic efficiency of the battery but also poses a risk of puncturing the electrolyte, leading to internal short circuits between the anode and cathode. This study is to solve the problem of lithium dendrite growth in solid-state lithium batteries by employing phase-field theory for numerical simulations. A phase-field model is developed by coupling the mechanical stress field, thermal field, and electrochemical field, to investigate the morphology and evolution of lithium dendrites under the condition of different ambient temperatures, external pressures, and their combined effects. The results indicate that higher temperature and greater external pressure significantly suppress lithium dendrite growth, leading to fewer side branches, smoother surfaces, and more uniform electrochemical deposition. Increased external pressure inhibits longitudinal dendrite growth, resulting in a compressed morphology with higher specific surface area and compactness, but at the cost of increased mechanical instability. Similarly, elevated ambient temperature enhances lithium-ion diffusion and reaction rate, which further suppress dendrite growth rate and size. The combined effect of temperature and pressure exhibits a pronounced inhibitory influence on dendrite growth, with stress concentrating at the dendrite roots. This stress distribution promotes lateral growth, facilitating the formation of flatter and denser lithium deposits.
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Keywords:
- solid-state lithium batteries /
- phase-field model /
- lithium dendrites /
- mechaincal-thermo-electrochemical coupling
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图 1 二维锂枝晶生长的有限元模型示意图
Figure 1. Schematic diagram of the finite element model of two-dimensional lithium dendrite growth.
图 2 有限元结果验证 (a) 有限元网格与初始形核点位置设置; (b) 当t = 40 s时当前模型的锂离子浓度; (c) 当t = 40 s时Yang等[31]得到的锂离子浓度
Figure 2. Verification of finite element results: (a) Setting of finite element mesh and initial nucleation point; (b) lithium-ion concentration (mol/m3) of current model when t = 40 s; (c) lithium-ion concentration (mol/m3) morphology obtained by Yang et al. [31] when t = 40 s.
图 3 锂枝晶生长演化结果 (a) 锂枝晶生长形貌; (b) 锂离子浓度(mol/m3); (c) 电势分布(V); (d) von Mises 应力分布(MPa)
Figure 3. Evolution results of lithium dendrite growth: (a) Growth morphology of lithium dendrites; (b) lithium-ion concentration (mol/m3); (c) electric potential (V); (d) von Mises stress distribution (MPa).
图 4 施加不同外压力时的锂枝晶生长演化结果 (a) 锂枝晶生长形貌; (b) von Mises应力分布 (MPa)
Figure 4. Evolution results of lithium dendrite growth under different external pressures: (a) Growth morphology of lithium dendrites; (b) von Mises stress distribution (MPa).
图 5 不同外压力下锂枝晶生长趋势结果 (a) 锂枝晶高度与宽度的比值(b/a)随时间的变化; (b) 锂枝晶宽度与高度的比值(a/b)随压力的变化
Figure 5. Results of lithium dendrite growth trend under different external pressures: (a) The ratio of height to width (b/a) of lithium dendrite changes with time; (b) the ratio of width to height (a/b) of lithium dendrite changes with pressure.
图 6 不同环境温度下的锂枝晶生长演化结果 (a) 锂枝晶生长形貌; (b) 锂离子浓度(mol/m3)
Figure 6. Evolution results of lithium dendrite growth at different ambient temperatures: (a) Growth morphology of lithium dendrites; (b) lithium-ion concentration (mol/m3).
图 7 不同环境温度下锂枝晶高度与宽度的比值(b/a)随时间的变化
Figure 7. Ratio of height to width (b/a) of lithium dendrites changes with time at different ambient temperatures.
图 8 不同环境温度和外压力耦合作用下锂枝晶生长演化结果 (a) 锂枝晶生长形貌; (b) von Mises应力分布(MPa); (c) 锂离子浓度(mol/m3)
Figure 8. Evolution results of lithium dendrite growth under coupling of external pressure and ambient temperature: (a) Growth morphology of lithium dendrites; (b) von Mises stress (MPa); (c) lithium-ion concentration (mol/m3).
图 9 在外压、环境温度以及这两种条件耦合作用下锂枝晶生长高度对比
Figure 9. Comparison of lithium dendrite height under external pressure, ambient temperature and coupling of these two conditions.
参数名 参数符号 数值 界面迁移率 Lσ/(m3·J–1·s–1) 1×10–6 化学反应常数 Lη/s–1 0.5 各向异性强度 δ 0.05 各项异性模数 ω 4 电极扩散系数 De/(m2·s–1) 1.7×10–15 电解质扩散系数 Ds/(m2·s–1) 2×10–15 电极电导率 σe/(S·m–1) 1×107 电解质电导率 σs/(S·m–1) 0.1 电荷转移系数 α 0.5 势垒高度 W/(J·m–3) 105 电解质初始浓度 c0/(mol·m–3) 1000 电极初始浓度 cs/(mol·m–3) 7.69×104 梯度能量系数 k/(J·m–1) 1×10–10 电极杨氏模量 Ee/GPa 7.8 电解质杨氏模量 Es/GPa 1 电极泊松比 Ve 0.42 电解质泊松比 Vs 0.3 Vegard 应变系数 λi –0.866×10–3 –0.773×10–3 –0.529×10–3 电极比热容 Cpe/(J·kg–1·K–1) 1200 电解质比热容 Cps/(J·kg–1·K–1) 133 电极导热系数 Re/(W·m–1·K–1) 1.04 电解质导热系数 Rs/(W·m–1·K–1) 0.45 扩散势垒 ${E_{{\text{a}}, D_{{\text{Li}}}^{+}}}$/eV 0.34 电化学反应势垒 ${E_{{\text{a}}, {L_\eta }}}$/eV 0.3 
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