Generalized Theory for Diffusion-Induced Stress

Abstract

The charging/discharging rate plays an important role in determining the structural integrity of metal-ion batteries, such as lithium-ion and sodium-ion batteries. In this work, we follow the approach by Green and Lindsay [Journal of Elasticity 2, 1 (1972)] and incorporate the contribution of the time derivative of the concentration of solute atoms to strain energy in Helmholtz and Gibbs free energies. Using the free energies, we obtain the chemical potential of the solute atoms and a generalized constitutive relation with the contribution of the concentration of the solute atoms and the time derivative of the concentration of the solute atoms. We use the generalized constitutive relation to analyze the stress evolution in an infinite, elastic cylinder under the condition that the stress-limited diffusion is negligible. The numerical results reveal that the term of the time derivative of the concentration of the solute atoms in the constitutive relation contributes to tensile hoop stress on the surface of the cylinder, which can initiate surface cracks and cause structural damage during the influx of the solute atoms. The generalized constitutive relation provides an approach to investigate the effect of charging/discharging rate on the structural integrity of electrodes in metal-ion batteries during electrochemical cycling.

Chemical stress in a largely deformed electrode: Effects of trapping lithium

“…The hoop component of the Piola-Kirchhoff stress at the surface of the spherical electrode is compressive, and its magnitude reaches maximum at the early stage of the lithiation and gradually decreases with the increase of the lithiation time. Such a trend is similar to the one given by Yang 55 and suggests that the chemical stress within the spherical electrode is primarily controlled by the concentration gradient of lithium. Thus, both the mobile lithium and immobile lithium are expected to contribute to the evolution of the eigen-strain, thereby leading to significant stress levels in the spherical electrode during the lithiation.…”

A physics-inspired neural network to solve partial differential equations – application in diffusion-induced stress

“…Diffusion-induced stress (DIS) due to the concentration gradient during mass transport and/or the deformation of active materials during charging and discharging has been proven to be one of the most important factors contributing to the failure of LIBs. 1,2 DIS can be calculated generally from partial differential equations (PDEs) for mechanical equilibrium and mass transport, in which mechanical equations consist of constitutive equations and equilibrium equations and the mass transport equation is the diffusion equation. The methods to solve such a set of PDEs can follow the techniques in thermo-elasticity, as used first by Prussin.…”

Cycling-induced structural damage/degradation of electrode materials–microscopic viewpoint

“…Most results have suggested that the initiation of a crack induced by the insertion of metal atoms (solute atoms) takes place away from the surface of electrode materials, since the stress calculation reveals that the inner portion of the electrode materials experiences tensile stress and the material surface is at compressive state during lithiation. Recently, the effect of the time derivative of local concentration of metal atoms (solute atoms) was incorporated in both the constitutive relation for diffusion-induced stress and the chemical potential of diffusive specie (solute atoms) [30]. The numerical results reveal the possibility that a crack induced by the insertion of metal atoms (solute atoms) can be initiated on the surface of electrode materials due to that the surface can experience in-plane tensile stress during lithiation.…”