Sharp-interface formation during lithium intercalation into silicon

Journal article

In this study we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as amorphous silicon (a-Si). The governing 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 lithium 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 sharpinterface model that also takes into account the dynamics of triple points where the sharp interface intersects the free boundary of the Si layer. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase- field model.

Authors: Meca, E; Muench, A; Wagner, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: European Journal of Applied Mathematics
• Volume: 29
• Issue: 1
• Pages: 118-145
• Publication date: 2017-03-28
• Acceptance date: 2017-02-22
• DOI: 10.1017/S0956792517000067
• EISSN: 1469-4425
• ISSN: 0956-7925
• Keywords: asymptotic analysis; numerical methods; stability analysis; interface dynamics; phase-field model