Theoretical prediction of fracture conditions for delithiation in silicon anode of lithium ion battery

Structural instability such as fractures of a silicon anode in a lithium ion battery, intrinsically induced by the large variation of the ratio, Li/Si, upon lithiation and delithiation, limits its potential for commercial use. Here, we study mechanical properties during delithiation in lithiated silicon particles to identify the conditions under which fracture is preventing during delithiation in terms of Li contents and silicon particle sizes. We employed the first principles calculation within the density functional framework combined with the continuum based calculation for the macroscopic mechanical properties. The theoretical limit for the largest crystalline silicon particle size that can prevent fractures upon complete delithiation is ∼0.6 μm at the lithium flux per unit surface area of 5.657 × 10−2 s−1 nm out of amorphous Li3.75Si, much larger than the critical fracture size (0.15 μm) that occurs during the first lithiation of crystalline Si. Furthermore, fractures during delithiation are nearly unaffected by the silicon particle size for a residual lithium fraction larger than x ∼ 2.1 in amorphous LixSi.