Preprint 9-2016

Sharp-Interface Formation during Lithium Intercalation into Silicon

Author(s) : Esteban Meca , Andreas Münch , Barbara Wagner

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 9-2016

MSC 2000

74N20 Dynamics of phase boundaries

35Q72 Other equations from mechanics

35B25 Singular perturbations

74S10 Finite volume methods

Abstract :
In this study we present a phase-field model that describes the process of in- tercalation of Li ions into a layer of an amorphous solid such as a-Si. The gov- erning equations couple a viscous Cahn-Hilliard-Reaction model with elasticity in the framework of the Cahn-Larch ́e system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dy- namics of triple points where the sharp interface in the bulk of the layer intersects the free boundary. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

Keywords : Asymptotic Analysis, Phase-Field Model, Interface Dynamics, Numerical Methods