Finite element method based analysis of diffusion induced stresses of Sn micropillar anode for Li ion batteries in alloying process

Abstract

Sn is promising anode material for Li ion batteries due to its high theoretical capacity (993.5 mAh/g) while having favorable mechanical properties such as low strength and ductility as well as room temperature creep that allows for relaxation of the lithiation induced stresses. Severe volume expansion (260%) during lithiation results in extreme diffusion induced stresses that in turn lead to the mechanical degradation of Sn anode. Aspects of diffusion induced stress evolution strongly depend on the lithiation kinetics and material properties of anode. Phase transformations of Sn during lithiation significantly alter the material properties. Furthermore, lithiation kinetics of Sn is varied by cycling condition such as scale and morphology of anode material and c-rate. Therefore, to precisely investigate lithiation induced stress evolution of Sn micropillar, FEM simulations are conducted by incorporating Li concentration-dependent material properties in simulation. Consequently, in case of diffusion-controlled lithiation of Sn, concentration-dependent material properties including increase in the diffusivity of Li in Sn, significantly affect the concentration profile that hence results in different stress states. Rather than assuming a simple continuous diffusion profile of Li, in-situ XRD and electrochemical methods were used to reveal a unique stepwise phase transformation that depend on the length scale of anode as well as the c-rate. In case of pillar with small scale or discharged at slow c-rate (0.1C), stepwise two phase reactions occur in three step, which significantly relax the generated DIS since volume expansion in each two phase reaction step is below 80%. However, in Sn micropillar which is large or rapidly discharged (over 2C), one-step two phase reaction towards Li$_7$Sn$_3$ occurs and volume expansion of 179% lead to severe DIS evolution in Sn micropillar. Therefore, use of Sn anode which has small scale and enough SEI formation in pre-cycling can be necessary to achieve the high performances.