One-dimensional analysis of the coupling between diffusion and deformation in a bilayer electrode

Diffusion-induced deformation during electrochemical cycling plays an important role in determining structural durability of the electrodes in lithium-ion batteries. In this work, we investigate the coupling between diffusion and stress in the boundary conditions of a bilayer electrode, and analyze the evolution of the lithium concentration and stress. Numerical simulations are performed under four different combinations of the boundary conditions between diffusion and mechanical deformation. The stress distributes uniformly in the bilayer electrode for all four cases. The concentration of lithium at the interface is discontinuous for the cases with fixed boundary conditions and is continuous for the cases with a surface at stress-free state. For the bilayer electrode fixed at both surfaces, the magnitude of the stress in the bilayer electrode increases with the increase of the diffusion time. This study reveals the importance of incorporating the coupling between diffusion and stress in the boundary condition in the analysis of the structural durability of lithium-ion batteries and in the design of multilayered and/or gradient electrodes.

A simple model for diffusion-induced dislocations during the lithiation of crystalline materials

Assuming that the lithiation reaction occurs randomly in individual small particles in the vicinity of the reaction front, a simple model of diffusion- induced dislocations was developed. The diffusion-induced dislocations are con- trolled by the misfit strain created by the diffusion of solute atoms or the phase transformation in the vicinity of the reaction front. The dislocation density is proportional to the total surface area of the ＂lithiated particle＂ and inversely pro- portional to the particle volume. The diffusion-induced dislocations relieve the diffusion-induced stresses.

Entropy change-induced elastic softening of lithiated materials

To understand the ＂elastic softening＂ of Li-Si alloys for the development of Li-ion batteries, the effect of stress-induced change of entropy on the mechanical properties of lithiated materials is examined within the theories of thermodynamics and linear elasticity, An approach is presented whereby the change of Gibbs free energy is governed by the change of the mixture entropy due to stress-induced migration of mobile atoms, from which the contribution of the change of the mixture entropy to the apparent elastic modulus of lithiated materials is determined. The reciprocal of the apparent elastic modulus of a lithiated material is a linear function of the concentration of mobile Li-atoms at a stress-free state and the square of the mismatch strain per unit mole fraction of mobile Li-atoms.

Relation between surface stress and surface energy for an elastic sphere： Effects of deformation and Maxwell stress

Surface stress is a physical quantity associated with the change of surface energy due to surface deformation, as introduced by Gibbs [1]. In principle, a surface stress tensor can be derived from the work associated with the variation of the total excess free energy of the surface and the surface strain due to surface deformation [2]. Using this concept, four main equations [3-6] relating surface stress to surface strain and surface charging have been developed and widely used to measure the surface stress due to surface adsorption and surface charging.

Generalized Butler-Volmer relation on a curved electrode surface under the action of stress

According to the principle of thermal activation process, the energy state of a material under the action of stress is a function of local stress. A generalized Butler-Volmer relationship for the electrode reaction on the surface of a curved electrode is derived,which takes account of the effects of local stress and the radius of mean curvature. From this relationship, the overpotential is found to be proportional to hydrostatic stress and the activation volume under the condition of open circuit. The conditions for the deposition of the material made solely from solute atoms and the formation of surface pits and porous structures are obtained,using the generalized Butler-Volmer relationship.