Figure 3: Analytical model of the clamped Si pillar to predict the change of the driving force of the reaction.
(a) A schematic view of <110> crystalline Si with wall fixed at the end. The scheme represents morphological expansion and induced stresses during lithiation of <110> pillars and walls before the physical contact (‘Before contact’, t2<g/2). (b) A schematic view of the one side of Si pillar contacted with the wall physically (‘After contact’, t2≥g/2). The displacement of lithiated Si is confined as a half of the gap (g/2). (c) Normal (σn) and tangential (σt) stress at the interfaces in the crystalline Si and LixSi for the depth of lithiation (t1/t0) when g/t0 is 0.3. (d) Mean stress (σm) at the interfaces in the crystalline Si (solid) and LixSi (dotted) for the depth of lithiation (t1/t0) when g/t0 is 0.3. (e) Corresponding change of free energy due to mechanical stress (ΔGσ) for the depth of lithiation (t1/t0) when g/t0 is 0.3. Black dash line represents free energy of Li deposition versus free energy of lithiation of Si (
). Red vertical lines indicate the contact and reaction stoppage on lithiation of Si, respectively.
