Transformations at interfaces between solid-state electrolytes (SSEs) and lithium metal electrodes can lead to high impedance and capacity decay during cycling of solid-state batteries, but the links between structural/chemical/mechanical evolution of interfaces and electrochemistry are not well understood. Here, we use in situ X-ray computed tomography to reveal the evolution of mechanical damage within a Li1+x Al x Ge2–x (PO4)3 (LAGP) SSE caused by interphase growth during electrochemical cycling. The growth of an interphase with expanded volume drives fracture in this material, and the extent of fracture during cycling is found to be the primary factor causing the impedance increase, as opposed to the resistance of the interphase itself. Cracks are observed to initiate near the edge of the lithium/LAGP interface, which agrees with simulations. The chemomechanical effects of interphase growth studied here are expected to play a role in a variety of SSE materials, and this work is a step toward designing durable interfaces.

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a b s t r a c tThe theory of Chester and Anand (2011) for fluid diffusion and large deformations of elastomeric gels is implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS. A specialized form of the constitutive equations and the governing partial differential equations of the theory are summarized, and the numerical implementation is described in detail. To demonstrate the robustness of the numerical implementation a few illustrative numerical simulation examples for axisymmetric, plane strain, and three-dimensional geometries are shown. For educational purposes, and also to facilitate the numerical implementation of other coupled multiphysics theories, the source code for the UEL is provided as an online supplement to this paper.

We formulate a unifi ed framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn-Hilliard-type species diffusion with large elastic deformations of a body. The traditional Cahn-Hilliard theory, which is based on the species concentration and its spatial gradient leads to a partial differential equation for the concentration which involves fourth-order spatial derivatives in the concentration; this necessitates use of basis functions in fi nite-element solution procedures that are piecewise smooth and globally C 1-continuous. In order to use standard C 0-continuous fi nite-elements to implement our phase-fi eld model, we use a split method to reduce the fourth-order equation into two second-order partial differential equations (PDES). Specifi cally, we introduce an additional variable-as in the micromorphic theories of continua-and formulate a theory which depends on actual concentration, the micromorphic concentration, and the gradient of the micromorphic concentration. These two PDES, when taken together with the PDE representing the balance of forces, represent the three governing pdes for chemomechanically coupled problems. These equations are amenable to fi nite-element solution methods which employ standard C 0-continuous fi nite-element basis functions. We have numerically implemented our theory by writing a user-element subroutine for the widely used fi nite-element program Abaqus/Standard. We use this numerically implemented theory to fi rst study the diffusion-only problem of spinodal decomposition in the absence of any mechanical deformation. Next, we use our fully-coupled theory and numerical-implementation to study the combined effects of diffusion and stress on the lithiation of a representative spheroidal-shaped particle of a phase-separating electrode material.