Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume 29, Issue 1, Pages 118-145Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792517000067
Keywords
Asymptotic Analysis; Phase-Field Model; Stability Analysis; Interface Dynamics; Numerical Methods
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Funding
- Einstein Foundation Berlin
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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-Larche 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.
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