Anisotropic behavior in the lithiation of a silicon nanopillar

There are reports on experimental observation of anisotropic expansion/swelling in the lithiation of crystal silicon (Si) nanopillars/nanowires. Such anisotropic expansion/swelling can cause the cracking of Si electrodes, leading to the capacity fading in Si-based lithium-ion batteries (LIBs). In this paper, we propose an anisotropic chemo-mechanical model that takes into account anisotropic characteristics of the physical properties of crys-talline Si, including stiffness tensor (matrix), diffusion tensor and partial-molar volume tensor. Using direction -cosine matrix for the tensor transformation, we determine the orientation-dependent elastic constants, diffusion coefficients and partial molar volumes in the anisotropic chemo-mechanical model instead of using phenomenal parameters associated with experimental results. For the purpose of demonstration, we analyze the lithiated Si phase of Li15Si4, which exhibits cubic structure, and illustrate geometrical profiles of the lithiated Si nanopillars of [110] and [111] in longitudinal direction at Li15Si4 state. The numerical results reveal that the cross section of the [111]-oriented Si nanopillar remain circular and the cross section of the [110]-oriented Si nanopillar evolves to elliptical shape. Such results are in good accordance with the experimental observation reported by Lee et al. [P. Natl. Acad. Sci. 109(11) (2012) 4080-4085]. The numerical results also show that the anisotropic expansion likely reduces von-Mises stress in the [110]-oriented Si nanopillar, retarding mechanical degradation of the Si -based electrodes. This work provides a new insight into the anisotropic expansion and stress generation in crystalline electrodes.