Two Phase Lithiation

The two phase lithiation problem deals with lithium diffusion into a circular silicon anode, which results in the formation of a two-phase interface having pure silicon inside and an amorphous Li-Si phase surrounding it. This problem is solved using the Cahn-Hilliard equation with the phase lithium concentration ( $\hat{c}$ ) as the phase field variable. The governing euation for the problem is:

$\dot{\hat{c}} = -\nabla.(-M(\hat{c})\nabla \mu)$

where,

$\mu = c_{max}RT(ln(\frac{\hat{c}}{1-\hat{c}}) + \Omega(1-2\hat{c})) - \kappa \nabla^2 \hat{c}$

The results are summarised in the following figure and they match closely with the figure 3 of L. Chen’s paper.

Two Phase Lithiaton Model