Solid electrolytes based on Li₇La₃Zr₂O₁₂ (LLZO) garnet may enable lithium-metal electrodes. The negatively charged crystal sublattices form channels that facilitate cation transport and produce room-temperature ionic conductivity of 0.4 mS/cm [1]. LLZO’s shear modulus is large enough to suppress dendrite nucleation arising from morphological instability [2, 3]. LLZO has cation transference near unity, so diffusion does not limit the current density as it does for liquid electrolytes. Although the modulus and transference of LLZO are both high, a ‘critical current’ is still observed, above which Li dendrites form [4]. Experiments show that preconditioning to improve interfacial contact can raise critical currents significantly [4]. Close inspection by TEM reveals an extended space charge layer [5] at the boundaries, which was predicted theoretically more than 30 years ago [6]. A recent model by Braun et al. [7] shows the importance of Lorentz forces and stress in explaining how apparent screening lengths are stretched for LLZO [5]. The role of mechanical stress in determining the critical current remains unclear.

The study of space charging in lithium-ion conductors requires additional consideration of deformation stress, which is beyond the capability of typical Poisson-Boltzmann theory. Moreover, a dynamic model that accounts for the resistive character of the material is needed to rationalize the response when both current and surface charge are significant. Recently, Newman’s concentrated-solution theory was generalized in a thermodynamic consistent way to account for the coupling of all these electrical, mechanical, and electrochemical processes [8]. In this generalized scheme, the momentum balance links mechanical stress, related to thermodynamic pressure, with the Lorentz force, which arises from space charge. Onsager–Stefan–Maxwell multicomponent-diffusion theory brings in irreversible thermodynamics to allow modelling of current flow. We will discuss how this generalized framework can be applied to the study of Li|LLZO|Li cells.

This model illustrates cation-concentration, stress, and electric-potential profiles that arise in solid electrolytes as they respond to potential bias and/or Faradaic currents. That information provides clues about the mechanism of mechanical failure that underpins the observations of critical current. We will discuss the key results of a parametric study of important mechanical properties, such as bulk modulus, critical stress, and partial molar volume of the crystal lattice. In addition, LLZO under different doping conditions will be simulated to understand the migration and segregation of doping cations (such as Al³⁺ and Ga⁺), and show how the presence of dopants may impact critical currents.

Reference:

1. R. Murugan, et al. Angew. Chem 46, 7778 (2007).
2. C. Monroe and J. Newman, J. Electrochem. Soc. 151, A880 (2004).
3. C. Monroe and J. Newman, J. Electrochem. Soc. 152, A396 (2005).
4. A. Shara, et al. J. Power Sources 302, 135 (2016).
5. K. Yamamoto, et al. Angew. Chem 49, 4414 (2010).
6. A. A. Kornyshev and M. A. Vorotyntsev, Electrochim. Acta, 26(3), 303 (1981).
7. S. Braun, et al. J. Phys. Chem. C 119, 22281 (2015).
8. P. Goyal and C. W. Monroe, J. Electrochem. Soc. 164, E3647 (2017).