The role of surface energy in propagation of stress-induced cracks in Li-intercalated micro hollowsphere silicon anodes - the forward lithiation process

Due to the promisingly high theoretical capacity to incorporate substantial amounts of lithium, silicon anodes in lithium-ion batteries experience high degrees of volumetric changes during cycling, leading to battery failure and capacity fading due to pulverization and fracture of the anode material. In this work, an analytical model based on the concentration-driven reaction-diffusion equation for concentration and linear elasticity has been developed to study the time-evolution of all significant stresses: radial, hoop, and hydrostatic, under the forward lithiation process, in a unified model. This model combines diffusion-induced stress (DIS), reaction-induced stress (RIS), and surface effects coupled with multiple functional parameters at low Li concentrations at the outer surface of the hollow silicon sphere under potentiostatic operation. In our study, the dynamic stoichiometric ratio of Li in Li-Si alloy was used to interpolate Young's modules and further incorporated in BOLS theory to obtain the cumulative effect. To illustrate the importance of surface effects, we used analytical solutions to the coupled problem in spherical geometry to study a hollow sphere with an inner and outer radius of 200 and 500 nm, respectively. When the aforementioned surface effects are considered, radial stress at the outer boundary of the sphere reaches -4 MPa, leading to the stress becoming compressive. Similarly, its value closer to the mid-center of the shell thickness (~350 nm) shows 0.81 MPa without surface effects, whereas it becomes compressive with surface effects, reaching approximately -2.31 MPa. With a systematic increase in surface energy parameters, radial and hoop stress at the external interface becomes more compressive. Additionally, it is observed that the RIS plays a dominant role over the DIS in a coupled system; thus, as the intercalation reaction progresses, the maximum peak of radial stress increases. In the analysis, we have discovered the significance of a figure of merit in determining the impact of RIS on the nature of hoop stress at the outer surface. We are currently studying the effects of a more suitable model for time-dependent boundary conditions for the rational design of anodes under plastic deformation during cycling, including the potential of machine learning methods.