Anisotropic compositional expansion in elastoplastic materials and corresponding chemical potential: Large-strain formulation and application to amorphous lithiated silicon

A general large-strain thermodynamic approach with anisotropic (tensorial) compositional expansion/contraction in elastoplastic material under stress tensor is developed. The dissipation rate due to compositional expansion/contraction is introduced. Adapting and utilizing a previously formulated postulate of realizability, we derived a simple equation for the deviatoric part of the compositional deformation rate. This leads to a nontrivial generalization of the concept and expression for the chemical potential. It receives a contribution from deviatoric stresses, which leads to an increase in the driving force for both the compositional expansion and contraction and to some new phenomena. Our model provides a remarkable description of the known experimental and atomistic simulation data on the biaxial stress evolution during lithiation–delithiation of LixSi on a rigid substrate with just one constant kinetic coefficient. In contrast to known approaches, it does not involve plasticity, because the yield strength is higher than the stresses generated during lithiation–delithiation. This allowed us to suggest a method for reduction in internal stresses by cyclic change in Li concentration with a small amplitude, and our simulations were in qualitative agreement with known experiments. The coupled diffusion and mechanical model was applied to lithiation and delithiation of thin-film, solid, and hollow spherical nanoparticles. The importance of the contribution of the deviatoric stress on the diffusion is demonstrated.