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. (C) 2014 Elsevier Ltd. All rights reserved.