The Effect of Phase Separation on Diffusion Induced Stresses in Spherical and Cylindrical Electrode Particles

Experiments have frequently shown that phase separation in lithium-battery electrodes could lead to mechanical failure, poor cycling performance, and reduced capacity. Here, a phase-field model is utilized to investigate how phase separation affects the evolution of the concentration and stress profiles within the spherical/cylindrical electrode particles, during both insertion and extraction half-cycles. To this end, the governing equations are derived and then discretized using the central finite difference method. The resulting algebraic equations are solved numerically with the aid of the Newton-Raphson method to determine both the concentration and stress fields in the electrode particles. For further verification, the results are compared against predictions of an analytical core-shell model. The results suggest that, within the range of parameters considered here, phase separation could lead to a more than five-fold increase in the maximum tensile stress at the particles surface

Competing effects of current density and viscoplastic deformation on the critical conditions for dendrite growth into solid-state lithium battery electrolytes

All-solid-state lithium (Li) batteries provide a promising pathway toward high energy and power density. Dendrite penetration through the solid electrolyte causing battery short-circuit, however, persists to be one of the challenges impeding their widespread application. Here, considering a pre-existing surface crack in the electrolyte initially filled with an infinitely thin layer of Li, and assuming Li deposit to behave in accordance with rigid-viscoplasticity, we seek for the steady state Li-filled crack opening profile that could potentially form at a given constant current density. Treating the chemical potential of Li ions in the electrolyte and the electric potential to be uniform along the crack face, the model accounts for the coupling between stress buildup in the dendrite, deposition rate, viscoplastic flow of Li deposit, and crack opening induced by electrolyte deformation using singular integral equations of fracture mechanics. The model establishes limiting conditions for crack growth before a steady state dendrite is reached, triggering a cycle of crack growth and dendrite elongation. Using material properties adopted from literature, the model predicts that the critical condition can be met for a microcrack at typical current densities. The effect of pressure applied to the cell is further discussed

Estimation of the Stress Intensity Factors for Surface Cracks in Spherical Electrode Particles Subject to Phase Separation

Experiments have frequently shown that phase separation in lithium-ion battery electrodes could lead to the formation of mechanical defects, hence causing capacity fading. The purpose of the present work has been to examine stress intensity factors for pre-existing surface cracks in spherical electrode particles during electrochemical deintercalation cycling using both analytical and numerical methods. To this end, we make use of a phase field model to examine the time-dependent evolution of the concentration and stress profiles in a phase separating spherical electrode particles. By using a geometrical approximation scheme proposed in the literature, stress intensity factors at the deepest point of the pre-existing surface cracks of semi-elliptical geometry are calculated with the aid of the well-established weight function method of fracture mechanics. By taking advantage of a sharp-interphase core-shell model, an analytical solution for the maximum stress intensity factors arising at the deepest point of the surface cracks during a complete deintercalation half-cycle is also developed. Numerical results for evolution of the concentration profile and the distribution of the hoop stresses in the particle are presented; further, the stress intensity factors found numerically based on the phase field model are compared with those predicted by the analytical core-shell model. The results of the numerical model suggest that the maximum stress intensity factor could significantly vary with changes in the surface flux, increasing potentially by a factor of two within the range of parameters considered here, when the concentration difference between the two phases is decreased

A surface locking instability for atomic intercalation into a solid electrode

By introducing a coupling between internal stresses and activation energy for diffusion in the classical theory of diffusion induced stresses, a class of nonconventional solutions has been found for atomic intercalation into a solid electrode, indicative of a surface locking instability once the product between electrode dimension and charging rate exceeds a critical value. This finding may have important implications for the lithium ion battery technology

Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration

Poor cyclic performance of electrodes in lithium-ion rechargeable cell batteries is calling for efforts to develop continuum models of diffusion under very large stresses and high solute concentrations. The present work is aimed to develop such a model based on input from atomistic simulations. We consider four fundamental features of highly nonlinear behavior associated with diffusion at high solute concentrations. First, the effect of solute-induced stresses on the activation energy of solute diffusion could be important. Second, the solute concentration may be subject to an upper limit if there exists a stoichiometric maximum concentration. Third, the strong influence of the change in local chemical environment on the interaction energy between solute and host atoms could play a significant role. Fourth, we include the effect of the solute concentration on the Young's modulus of the host material. A continuum model is developed and validated based on atomistic simulations of hydrogen diffusion in nickel. The influences of each feature above are clearly discussed through parametric studies. (C) 2010 Elsevier B.V. All rights reserved