The formation of dendrites within the solid-state electrolyte of a Lithium (Li) ion battery is exacerbated by the presence of voids at the interface between the electrolyte and the Li anode. It is assumed that voids initiate and grow by the focussing of Li flux at the periphery of pre-existing small imperfections along the interface between the solid electrolyte and Li anode. Void growth in the Li anode, driven by stripping of the $\mathrm{L}{\mathrm{i}}^{+}$ ions from the anode, is accompanied by creep within the anode. Consequently, the initiation and growth of these voids involve electrochemical stripping of $\mathrm{L}{\mathrm{i}}^{+}$ from the anode, creep deformation of the anode and flux of $\mathrm{L}{\mathrm{i}}^{+}$ through the adjacent solid electrolyte. Here we present a numerical analysis of this problem. We consider a single-ion conductor electrolyte, with Butler–Volmer kinetics governing the interfacial flux and the Li anode modelled as a power-law creeping solid. The study reveals that void growth can only initiate from relatively large pre-existing interfacial imperfections of size $>$ 1200 $\mathrm{\mu }$m along the interface of the solid electrolyte (LLZO) and the Li anode. In contrast, experimental observations suggest that voids as small as $1$ $\mathrm{\mu }$m can initiate along the LLZO/Li interface and thus the simple picture described above involving power-law creep of the Li anode coupled with Butler–Volmer kinetics, even with interfacial diffusion accounted for, is insufficient to explain these observations. Our calculations reveal that the degree of flux focussing on the periphery of small imperfections must exceed that predicted by Butler–Volmer kinetics in order for interfacial voids to initiate and grow.

锂（Li）离子电池的固态电解质中树枝状晶体的形成由于电解质与锂阳极之间的界面处存在空隙而加剧。假定空隙是由于沿固体电解质和Li阳极之间的界面上预先存在的小缺陷的周围的Li助焊剂的聚集而引发并增长的。锂阳极上的空洞生长是由于汽提的原因$\mathrm{大号}{\mathrm{一世}}^{+}$阳极中的离子伴随着阳极内部的蠕变。因此，这些空隙的引发和生长涉及电化学剥离。$\mathrm{大号}{\mathrm{一世}}^{+}$ 从阳极开始，阳极的蠕变变形和 $\mathrm{大号}{\mathrm{一世}}^{+}$通过相邻的固体电解质。在这里，我们对这个问题进行数值分析。我们考虑一种单离子导体电解质，其中Butler-Volmer动力学控制界面通量，Li阳极建模为幂律蠕变固体。研究表明，空洞的增长只能从相对较大的先前存在的界面缺陷中引发$>$ 1200 $\mathrm{\mu }$m沿着固体电解质（LLZO）和Li阳极的界面。相比之下，实验观察表明，空隙小至$\mathrm{1个}$ $\mathrm{\mu }$m可以沿着LLZO / Li界面引发，因此上述涉及Li阳极的幂律蠕变与Butler-Volmer动力学相结合的简单图片，即使考虑了界面扩散，也不足以解释这些观察结果。我们的计算表明，集中在小缺陷周围的通量程度必须超过Butler-Volmer动力学所预测的程度，才能使界面空隙引发和生长。