In this work, we analyze the stability of electrodeposition at the interface between a solid electrolyte and a metal anode, both of which are assumed to be linearly elastic. Based on the derived stability criteria, we show that the condition for stability is sensitive to the mechanical response (shear modulus) and relative density of metal in the two phases . We illustrate this using the constructed stability diagram which shows stable regimes of shear modulus and molar volume of metal ion. This stability diagram qualitatively resembles the stability diagram for stress-driven phase transition at solid-solid interfaces (encountered in, for example, stylolites) studied by Angheluta et al. . Our analysis shows that it is possible to use a soft solid electrolyte provided the density of metal (e.g. Li) is greater in the solid electrolyte than the metal anode. This finding provides new ways to suppress dendrite growth at metal electrode/solid electrolyte interfaces. Two out of the four regions in the stability diagram represent stable electrodeposition regimes. To determine electrodeposition stability for candidate materials for solid electrolytes, we use first-principles calculations of the elastic tensor  and estimate of molar volume from ionic radii tabulated by Shannon  and Marcus et al. . We find that typical inorganic solid electrolytes have higher shear modulus, but lower molar volume than that required for stable electrodeposition. On the other hand, solid polymer electrolytes have higher molar volume but lower shear modulus than the requirement, leading once again to unstable electrodeposition. Our results suggest that a composite material with a combination of high (low) Li molar volume and high (low) shear modulus is required to suppress dendrites.
Recently, the high anisotropy of Li was proposed to play an important role in determining stability of electrodeposition at different Li surfaces . To investigate anisotropy effects, we performed linear stability analysis of electrodeposition at different metal surfaces in contact with solid electrolyte. The deformation equations were solved using the Stroh formalism with the same boundary conditions. Results show that both high density and low density stable regimes exist, with the critical shear modulus curves shifted depending on the Li surface in contact with the solid electrolyte. This presents an opportunity to realize safer high energy density solid-state batteries with metal anodes.
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Figure 1: Stability diagram showing stable and unstable electrodeposition regimes depending on shear modulus and molar volume ratio of metal . Change in the critical shear modulus curves due to Poisson's ratio is also shown.