The study of dendritic growth and roughening during electrodeposition has gained renewed interest in light of the safety concerns associated with dendritic shorting in the current Li-ion batteries. A precise understanding of the growth of dendrites during electrodeposition could enable the use of metal anodes, especially Li, which could lead to significantly higher energy density batteries. Solid electrolytes present a new avenue for attacking this problem of stable electrodeposition, besides improving the safety of energy storage technology. Replacing the organic liquid electrolyte by a solid electrolyte creates a solid-solid interface whose properties alter the kinetics of electrodeposition. Monroe and Newman analyzed the electrodeposition stability of Li/solid polymer electrolyte system within linear elasticity theory and showed using a kinetic model that solid polymer electrolytes with a sufficiently high modulus are capable of suppressing dendrite growth [1]. However, the propagation of the interface is often accompanied by a change in density of the metal which is thus, an important order parameter that should affect the stability of electrodeposition at the interface. In the theory of stress-driven phase transformation at solid-solid interfaces studied in geological systems, it has been shown that interfacial stability or roughening condition depends on the density change at the interface [2].

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 [3]. 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. [2]. 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 [4] and estimate of molar volume from ionic radii tabulated by Shannon [5] and Marcus et al. [6]. 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 [7]. 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.