Development of stresses in silicon nanolayer under lithiation

Constitutive equations are developed for the mechanical response of a host medium driven by diffusion of guest atoms under an arbitrary three-dimensional deformation with finite strains. The model distinguishes two states of a guest atom: mobile and immobilized (due to alloying of host and guest atoms). Derivation of reaction-diffusion equations for transport and immobilization of guest atoms, as well as stress-strain relations for the viscoplastic behavior of the host material, is grounded on the free-energy imbalance inequality. The governing equations are applied to the analysis of stresses in an amorphous silicon nanolayer under lithiation. Good agreement is revealed between results of numerical simulation and observations on evolution of thicknesses of lithiated and non-lithiated domains and volume growth of the lithiated layer.