Multiscale Analysis of Lithiation of Si Anode of Li-Ion Batteries: First Principle Calculation and Finite Element Analysis

Silicon is known to have large Li storage capacity up to 4.4 Li atoms per Si atom in Li22Si5 compounds, but the large volume change and the mechanical stress during the charge-discharge cycles have damaged the electrode structures leading to rapid capacity fade. Recently, Cui et al. have applied the silicon nanowire structures to avoid the mechanical stresses induced by the volume change and demonstrated promising capacity of the silicon nanowire anode for Li ion batteries. However, there are many issues on the lithiation in silicon anode to understand its physics of mechanism. The kinetics of Li diffusion in Si anode is a main issue because the mechanical failure of Si active material significantly affects the stress state during cycles. In this presentation, we analyze the Li diffusivity in bulk-Si and LixSi (x>1) systems using first principle calculation and obtain the Li diffusion coefficient as function of Li concentration using kinetic Monte Carlo simulation. We also study the difference of lithiation between crystalline silicon and amorphous silicon. Based on the first principle calculation, we check the mechanical stability of Si anode in various shape and charged condition using the diffusion-induced macroscopic model based on finite element method. Our multiscale analysis can provide reliable predictions on the stability with respect to the stress deviation according to size and shape of Si nanowire including charge rates. We also construct a non-dimensional design criteria equation for allowable stresses based on Buckingham-Pi theorem. Moreover, we analyze stress of more complex Si nanowire called Si nanotube and explain why pre-lithiated Si nanowire could have better cycle-ability compared to pristine one. The multiscale approaches of Si anode from atomic scale to continuum scales help understand the mechanical failure of the Si anode in terms of the microstructure variations, and suggest a guideline to improve the Si anode performance for LIBs. ACKNOWLEDGEMENT This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2012R1A3A2048841) and by the Industrial Strategic technology development program (10041589) funded by the Ministry of Knowledge Economy (MKE, Korea)