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Schematic of a Si island on substrate under cyclic lithiation and delithiation. (a) Geometry of the entire system and (b) the free-body diagram of half of the island. Free-body diagrams at the end of (c) intercalation half-cycles and (d) deintercalation half-cycles.
The rigid-perfectly plastic cohesive law used for modeling the interfacial sliding with differential sliding resistance during lithiation and delithiation half cycles. Here, denotes the interfacial sliding strength during the lithiation half-cycle and denotes the sliding strength during the delithiation half-cycle.
Finite element simulations of deformation in a periodic array of islands. Ratcheting of the islands after (a) 1 cycle and (b) 10 cycles with differential sliding resistance and . Ratcheting of the islands after (c) 1 and (d) 10 cycles with differential yield stress for Si and . Elasticreversible response of an array of islands with after (e) 1 cycleand (f) 10 cycles. The thickness direction has been magnified by a factor of 4.
Plan view of a 250 nm thick Si continuous film cycled at C/2.5 rate. (a) Film has fractured after 1 cycle. (b) The gap between the islands has substantially widened after 30 cycles. The matching edges and roughened surface of the islands suggest that the lateral dimensions of the islands have shrunk. The scale bars correspond to 2 μm of the actual dimensions (reprinted with permission from J. P. Maranchi et al., J. Electrochem. Soc., 153, A1246, 2006. Copyright 2006, The Electrochemical Society).
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