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Sharp-interface formation during lithium intercalation into silicon

Published online by Cambridge University Press:  28 March 2017

E. MECA ,
A. MÜNCH  and
B. WAGNER
E. MECA
Affiliation:
Weierstrass Institute, Mohrenstraße 39, 10117 Berlin, Germany email: [email protected]
A. MÜNCH
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GGUK email: [email protected]
B. WAGNER
Affiliation:
Weierstrass Institute, Mohrenstraße 39, 10117 Berlin, Germany email: [email protected] Technische Universität Berlin, Institute of Mathematics, Straße des 17. Juni 136, 10623 Berlin, Germany email: [email protected]
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Abstract

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–Larché 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 sharp-interface 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.

Keywords

Asymptotic AnalysisPhase-Field ModelStability AnalysisInterface DynamicsNumerical Methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 1 , February 2018 , pp. 118 - 145
Copyright
Copyright © Cambridge University Press 2017 

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