Chemical-Mechanical Coupling: Stress Effect on Lithiation of Amorphous Si
Authors: Wang Miao , Xiao Xinran 
Published: February 2020

Si is a promising high capacity anode material for Li-ion batteries (LIBs). Nevertheless, the large volume variation of Si during lithiation/delithiation cycles can induce high stresses. This presents a great challenge to the structural integrity of LIBs. The high stresses and large volume variation are also attributed to rapid capacity fading of LIBs with Si anode. Understanding the stress evolution and its effect on Si lithiation is of great importance for Si electrode design.
The in situ stress inside Si during lithiation/delithiation has been measured for amorphous Si (a-Si) thin film(Bucci et al., 2014; Pharr et al., 2014; Sethuraman et al., 2010a; Zhao et al., 2012a). The measured stress can reach as high as 1.5 GPa in both compression and tension. The stress also influence the lithiation process(Luo et al., 2014; McDowell et al., 2012). It is reported that, after the crystalline Si (c-Si) nanosphere has been lithiated for some time, the lithiated thickness (thickness of LixSi shell in the first lithiation) growth rate reduced significantly(McDowell et al., 2012). The phenomenon was primarily attributed to the high compressive stress at the reaction front that eventually prohibited Li from further insertion. However, the mechanism of how stress affected the Si lithiation is not clear.
In literature, two categories of chemical-mechanical coupling theories have been proposed for the stress effect on Li diffusion into Si: (I) by influencing Li diffusivity, and (II) by influencing the chemical potential of Li in Si.
In category (I), it assumes that the Li diffusivity is modulated by the stress induced activation free energy barrier shift(Gao et al., 2013; Haftbaradaran et al., 2010; Sukharev et al., 2007). The rate of reaction depends on the activation energy (i.e. free energy between the ground state and transition state). So far, the relationship is qualitative only. The activation energy is adjusted by either hydrostatic stress(Kim, 2011; Sukharev et al., 2007) or biaxial stress (in thin film)(Liu et al., 2012) with a coefficient which varies in a wide range.
In category (II), it postulates that the chemical potential of Li in Si changes because the free energy difference between Si and LixSi is altered by stress. This effect is still quite argumentative given multiple different treatments in literature(An and Jiang, 2013; Bucci et al., 2014; Cui et al., 2012; Gao et al., 2013; Haftbaradaran et al., 2011; Sethuraman et al., 2010b; Swaminathan and Qu, 2007; Yang, 2005). For example, some proposed that only the hydrostatic stress influence the chemical potential for ideal dilute solution(Yang, 2005) or non-ideal dilute solution(Gao et al., 2013) whereas others casted the chemical potential as a function of both hydrostatic stress and deviatoric stress components(Bucci et al., 2014; Chen et al., 2014).
In this work, we will investigate the chemical-mechanical coupling phenomena in lithiation/delithiation of amorphous Si using numerical simulations. It should be noted that the abovementioned chemical-mechanical coupling theories have been formulated using both the small strain(Bucci et al., 2014; Sethuraman et al., 2010b; Swaminathan and Qu, 2007) and large strain(Cui et al., 2012) framework. Nevertheless, the Li transport was commonly considered by a normalized Li concentration calculated using the dimension of unlithiated Si. As a result, the analytical/simulation results could not be compared directly to the dimension/shape changed observed in experiments. In our previous work, a model that couples the lithiation/delithiation of Si with its accompanied volume change and stress generation has been developed (Wang et al., 2016). The current work will use this model to investigate some of the existing chemical-mechanical coupling theories. Since it is difficult to decouple stress effect from Li diffusion in any single case study, we examine the theories using more than one geometry: a-Si thin film(Li et al., 2015) and a-Si nanospheres(McDowell et al., 2013). Asymmetric cycling behavior of Si was observed for both geometries and the trend was opposite to each other. By simulating these experiments, the chemical-mechanical coupling theories that predict the trend observed in experiments will be identified.