Evaluation of Chemical Potentials, Bulk Modulus and Volume Expansion Ratio of Li-Si Alloys with Variety of Li Concentrations Using First-Principles Calculations (Supporting Information)

<p dir="ltr">This study investigates silicon as a promising anode material for future all-solid-state lithium-ion batteries. However, when lithium insertion and extraction are repeated near the maximum capacity, the associated volumetric expansion and contraction cause structural degradation, leading to accelerated deterioration of charge-discharge cycle performance. To fundamentally address this issue, this study analyzes the basic chemical and mechanical properties of Li–Si alloys (Li<i>_x</i>Si; 0 < <i>x</i> ∼ 5) using first-principles calculations. In particular, this study evaluates the chemical potential—which has not been thoroughly investigated before—as well as the bulk modulus, including compositions and polymorphs that had not been previously studied. The analysis shows that, the chemical potential becomes as high as +75 kJ mol⁻² when the composition ratio approaches the maximum one of 4.4 in Li–Si alloys. This is consistent with the fact that no Li–Si alloys with a composition beyond this ratio have been observed. In addition, the calculations revealed that the chemical potential takes positive values at several points before reaching the maximum composition, suggesting that lithium insertion into the silicon anode may not proceed smoothly in these cases. Regarding the bulk modulus, this study finds that it generally decreases with increasing lithium content, consistent with previous reports. However, in the case of LiSi, which has three different polymorphs, significant variation in the bulk modulus is observed. Furthermore, by calculating the volumetric expansion during lithium insertion, including compositions not previously examined, this study finds that the volume expansion is approximately proportional to the lithium composition ratio which is in agreement with earlier studies, although the slope of the increase varies slightly.</p>