Stability of Electrodeposition at Solid-Solid Interfaces and Implications for Metal Anodes

We generalize the conditions for stable electrodeposition at isotropic solid-solid interfaces using a kinetic model which incorporates the effects of stresses and surface tension at the interface. We develop a stability diagram that shows two regimes of stability: a previously known pressure-driven mechanism and a new density-driven stability mechanism that is governed by the relative density of metal in the two phases. We show that inorganic solids and solid polymers generally do not lead to stable electrodeposition, and provide design guidelines for achieving stable electrodeposition.

Figure 1

Schematic of the electrodeposition problem with metal electrode-solid electrolyte interface. The metal surface $z=f(x,t)$ grows on deposition of metal ions, the rate of which is proportional to the current. The local geometry alters the kinetics of deposition at the interface.

Figure 2

Contributions of different terms to the stability parameter $\chi$ for (a) $v>1$ and (b) $v<1$ with Li metal electrode. The property values used for the plots were $G_e=3.4\mathrm{GPa}$, ${\nu }_e=0.42$, ${\nu }_s=0.33$, $V_M=1.3\times 10^{-5}{\mathrm{m}}^3/\mathrm{mol}$, $V_{M^{z+}}=0.3\times 1.674\times 10^{-4}{\mathrm{m}}^3/\mathrm{mol}$, $k=10^8/\mathrm{m}$, $A=0.4/k$ (Ref. [19]) for (a) and $v=0.1$ for (b). The surface tension term is evaluated by choosing $\gamma$ as the average surface energy of Li for (100), (110), and (111) planes, giving a value $0.556\mathrm{J}/{\mathrm{m}}^2$ [35]. This term is generally small at the wave numbers of perturbation and its contribution has not been shown. The deviatoric stress term is always destabilizing. For $v>1$ the hydrostatic stress term is destabilizing at low $G_s/G_e$ and stabilizing at high $G_s/G_e$, whereas for $v<1$, it is stabilizing at low $G_s/G_e$ and destabilizing at high $G_s/G_e$.

Figure 3

Stability diagram showing the range of shear moduli over which electrodeposition is stable and its dependence on the volume ratio $v$ of the cation and metal atom. Regions with stable electrodeposition are shaded green. The critical curves separating stable and unstable regions are plotted using ${\nu }_e=0.42$ (Li metal) and ${\nu }_s=0.33$, 0.5 (incompressible). Several Li solid electrolytes are also plotted in the diagram where the ratio $G_s/G_e$ has been calculated using $G_e=G_{\mathrm{Li}}=3.4\mathrm{GPa}$. For LGPS (${\mathrm{Li}}_{10}{\mathrm{GeP}}_2{\mathrm{S}}_{12}$), $V_{\mathrm{Li}}^{+}$ was calculated from the coordination number, whereas for all others, the procedure mentioned in the Supplemental Material [31] was used. The solid polymer electrolyte shown is a 10% by weight solution of oxymethylene-linked polyethylene oxide (PEMO) and lithium bis-trifluoromethane sulfonimide (LiTFSI) in dimethoxyethane [38].