Morphology Control and Suppression of Lithium Dendrite Growth in Solid-State Electrolytes Based on Phase-Field Simulation
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摘要: 传统液态电解质的易燃易爆性带来的安全隐患，推动了基于固态电解质系统的全固态锂电池开发. 然而，锂枝晶生长问题仍然是阻碍固态锂电池商业化应用的一个亟待解决的关键难题. 因此，深入探究固态电解质内锂枝晶生长的形貌调控机制及抑制策略，对于提高固态锂电池的循环寿命并推动其广泛应用至关重要. 该工作基于相场法，通过构建力-电化学的多场耦合模型，动态地演示了锂枝晶生长形貌及其力学行为，并探讨了模型参数/条件对锂枝晶形貌的调控和抑制作用. 结果表明：低水平的界面反应率系数能有效减缓锂枝晶的生长速度，同时还极大地降低了其根部承受大机械应力的范围；通过改变固态电解质材料内锂离子的各向异性扩散程度，可以实现枝晶形貌从纤维状到扁平状的转变；多晶成核对于晶间相互靠近的侧枝具有抑制作用，最高应力为单晶成核的3~5倍；高弹性模量的固态电解质对于锂枝晶生长有显著的力学抑制作用. 该研究有望为固态电解质的优化设计以抑制固态锂金属电池的枝晶生长提供参考.Abstract: The safety concerns regarding the flammability and explosivity of traditional liquid electrolyte (LE) lithium batteries have spurred the development of all-solid-state lithium batteries with solid-state electrolytes (SSE). However, the issue of lithium dendrite growth remains a critical challenge to be urgently addressed to commercialize solid-state lithium batteries. Hence, a thorough investigation of the morphology control mechanisms and suppression strategies for lithium dendrite growth within solid-state electrolytes is crucial for improving the cycle life of solid-state lithium batteries and promoting their widespread application. Based on the phase-field method, a multi-physical fields coupling model integrating mechanics and electrochemistry, was constructed to dynamically demonstrate the morphology and mechanical behavior of lithium dendrite growth. Then the model parameters and different conditions were explored to regulate and suppress the morphology of lithium dendrite. The results indicate that, a low-level interfacial reaction rate coefficient can effectively slow down the growth rate of lithium dendrite, while also significantly narrowing the high mechanical stress range at the dendrite root. With the change of the lithium-ion anisotropic diffusion degree within solid-state electrolyte materials, the transition of dendrite morphology from fibrous to flat can be achieved. The polycrystalline nucleation exhibits inhibitory effects on the lateral branches close to each other, with the maximum stress being 3 to 5 times higher than that of single-crystal nucleation. Solid-state electrolytes with a high elastic modulus exert notable mechanical inhibitory effects on lithium dendrite growth. This work can serve as a valuable reference for the optimization design of solid-state electrolytes to suppress dendrite growth in solid-state lithium metal batteries.
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Key words:
- electro-chemo-mechanical coupling /
- dendrite growth and suppression /
- all-solid-state battery /
- phase-field method
edited-byedited-by1) 我刊青年编委赵莹来稿 -
图 1 固态电解质内锂枝晶生长的相场模拟
Figure 1. Phase-field simulation of lithium dendrite growth within solid-state electrolyte
图 2 求解域及边界条件示意图
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. Schematic diagram of solving domain and boundary conditions
图 4 不同网格单元尺寸下，a线上相场序参量ξ随时间的一维分布
Figure 4. The 1D distributions of phase-field order parameter ξ over time on the a-line under different grid cell sizes
图 5 不同时间步长下，相场序参量ξ和锂离子浓度$ \tilde{c}_{+}$的二维分布
Figure 5. The 2D distributions ofξ and $ \tilde{c}_{+}$ at different time steps
图 6 不同时间步长下，枝晶生长过程中各区域的Von Mises应力分布
Figure 6. Distributions of Von Mises stresses in different regions during dendrite growth at different time steps
图 7 不同时刻下，a线和b线上的Von Mises应力分布
Figure 7. Distributions of Von Mises stresses on the a-line and the b-line at different time steps
图 8 不同时间步长下，锂枝晶生长过程中的正应力分布
Figure 8. Distributions of normal stresses during lithium dendrite growth at different time steps
图 9 不同时间步长下，a线和b线上的正应力分布
Figure 9. Distributions of normal stresses on the a-line and the b-line at different time steps
图 11 界面反应率系数对锂枝晶形貌和应力分布的影响
Figure 11. The influences of the interface reactivity coefficient on the lithium dendrite morphology and the stress distribution
图 12 固态电解质内锂离子的各向异性扩散对枝晶形貌和离子浓度分布的影响
Figure 12. The influences of anisotropic diffusion of lithium ions in solid-state electrolytes on the dendrite morphology and the lithium ion concentration distribution
图 13 多晶成核设置下的锂枝晶生长形貌及应力分布
Figure 13. Lithium dendrite growth morphologies and stress distributions under polycrystalline nucleation settings
图 14 液态/固态电解质内锂枝晶生长的形貌对比
Figure 14. Morphological comparison of lithium dendrite growth in liquid/solid-state electrolytes
图 15 不同弹性模量的固态电解质内锂枝晶形貌及应力变化情况
Figure 15. Morphologies and stresses of lithium dendrites in solid-state electrolytes with different elastic moduli
表 1 应力耦合的相场模型对比
Table 1. Comparison of mechanically coupled phase-field models
model mechanically coupled phase-field model reference model 1 $ \begin{gathered} \frac{\partial \xi}{\partial t}=-L_\sigma\left(\frac{\delta \varSigma}{\delta \xi}+\Delta \mu_{\mathrm{m}}\right)-L_\eta h^{\prime}(\xi)\left\{\exp \left[\frac{(1-\alpha) z F \eta_{\mathrm{a}}}{R T}\right]-\widetilde{c}_{+} \exp \left[-\frac{\alpha z F \eta_{\mathrm{a}}}{R T}\right]\right\} \\ \Delta \mu_{\mathrm{m}}=\frac{\partial g_{\text {mech }}\left(\boldsymbol{\varepsilon}^{\mathrm{E}}\right)}{\partial \xi} \end{gathered}$ [13, 16] model 2 $ \begin{gathered} \frac{\partial \xi}{\partial t}=-L_\sigma\left(\frac{\delta \varSigma}{\delta \xi}+\Delta \mu_{\mathrm{m}}\right)-L_\eta h^{\prime}(\xi)\left\{\exp \left[\frac{(1-\alpha) z F \eta_{\mathrm{a}}}{R T}\right]-\tilde{c}_{+} \exp \left[-\frac{\alpha z F \eta_{\mathrm{a}}}{R T}\right]\right\} \\ \Delta \mu_{\mathrm{m}}=\beta \sigma_{\mathrm{m}}+\frac{1}{2} \frac{\partial g_{\text {mech }}\left(\boldsymbol{\varepsilon}^{\mathrm{E}}\right)}{\partial \xi} \end{gathered}$ [15, 17] β is the stress factor, and σm is the average of the maximum and minimum stresses of dendrite model 3 $ \begin{gathered} \frac{\partial \xi}{\partial t}=-L_\sigma \frac{\delta \varSigma}{\delta \xi}-L_\eta h^{\prime}(\xi)\left\{\exp \left[\frac{(1-\alpha) z F \eta_{\mathrm{a}}}{R T}\right]-\widetilde{c}_{+} \exp \left[-\frac{\alpha\left(z F \eta_{\mathrm{a}}+\mu_{\mathrm{m}}\right)}{R T}\right]\right\} \\ \Delta \mu_{\mathrm{m}}=V_{\mathrm{Li}} \Delta P \end{gathered}$ [14, 18] ΔP is the hydrostatic pressure acting on the reaction front and VLi is the molar volume of lithium 
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表 2 相场模拟参数
Table 2. Phase-field simulation parameters
parameter symbol value reference interface migration coefficient Lσ/(m3/(J·s)) 1×10-6 [21] interface reaction rate coefficient Lη/s-1 0.5 [13] gradient energy coefficient κ/(J/m) 1×10-7 [13] lithium metal site density cs/(mol/m3) 7.64×104 [11] diffusion coefficient of lithium metal electrode De/(m2/s) 2×10-15 [2] diffusion coefficient of solid electrolyte Ds/(m2/s) 1×10-14 [2] conductivity of lithium metal electrode de/(S/m) 1×107 [11, 22] solid-state electrolyte conductivity ds/(S/m) 0.1 [14] elastic modulus of lithium metal electrode Ee/GPa 7.8 [23] elastic modulus of solid electrolyte Es/GPa 0.2 [24] Poisson’s ratio of lithium metal electrode νe 0.42 [25] Poisson’s ratio of solid electrolyte νs 0.3 [26] Molar volume of lithium in lithium metal electrode VLi/(m3/mol) 1.3×10-5 [14]
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表 3 采用的固态电解质及其弹性模量
Table 3. Adopted solid-state electrolytes and corresponding elastic moduli
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