Anisotropic behavior in the lithiation of a silicon nanopillar. (January 2023) - Li, Yong; Zhang, Kai; Pan, Yihui; Yang, Fuqian
Abstract: 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 crystalline 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 Li 15 Si 4, which exhibits cubic structure, and illustrate geometrical profiles of the lithiated Si nanopillars of [110] and [111] in longitudinal direction at Li 15 Si 4 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. Graphical abstract: Unlabelled Image Highlights: An anisotropic chemo-mechanical model in the frameworks of crystal mechanics is proposed. Orientation-dependent material constants are determined by using direction-cosine matrix. The anisotropic expansions in Si nanopillars are in accordance with experimental observation.