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Research Papers

Modified Stoney Equation for Patterned Thin Film Electrodes on Substrates in the Presence of Interfacial Sliding

[+] Author and Article Information
Hamed Haftbaradaran, Sumit K. Soni, Brian W. Sheldon

 School of Engineering,  Brown University, Providence, RI 02912

Xingcheng Xiao

General Motors Global Research & Development Center, 30500 Mound Road, Warren, MI 48090

Huajian Gao1

 School of Engineering,  Brown University, Providence, RI, 02912Huajian_Gao@Brown.edu

1

Corresponding author.

J. Appl. Mech 79(3), 031018 (Apr 05, 2012) (6 pages) doi:10.1115/1.4005900 History: Received August 07, 2011; Revised December 19, 2011; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

Mechanical stresses and failure are believed to be a major cause for the limited cycle life of lithium-ion batteries employing high capacity Si electrodes. Recent experiments have shown that patterned Si thin film electrodes on substrate exhibit improved cycling stability and substantial sliding at the film/substrate interface. To facilitate experimental studies of stress evolution in such systems, we have developed a modified Stoney equation which accounts for the effect of interfacial sliding on the relationship between curvature and stress in patterned thin films on substrate.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Optical micrographs of Si islands on a Ti substrate, indicating substantial in-plane expansion/contraction during lithiation and delithiation. (a) The original size of the islands is around 17 μm; (b) under lithiation, the Si islands expand by roughly 30% in the plane of the substrate, indicating substantial interfacial sliding, and (c) after delithiation, the Si islands are seen returning towards the original size. The scale bar is 50 μm.

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Figure 2

Modified Stoney equation for two-dimensional patterned films on substrate. (a) The geometry of the problem, and (b) the reciprocity theorem for determining the curvature of the system; (c) comparison of FEM calculations and theoretical predictions of curvature for two-dimensional patterned films on substrate.

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Figure 3

Modified Stoney equation for three-dimensional patterned films on substrate, and comparison with FEM calculations. (a) The geometry of the problem, and (b) the reciprocity theorem for determining the curvature of the system.

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Figure 4

Comparison of FEM calculations and theoretical predictions of curvature for (a) circular patches where the solid line is the theoretical prediction; (b) square patches where the solid line is based on a fitting scheme

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Figure 5

Stress evolution obtained according to the volume-averaged Stoney equation versus capacity. The modified Stoney equation in Eq. 16 has been used in the solid curves and to estimate the maximum stress in the center of island. (a) For the second cycle; the predicted stress at the center of the island is −0.8 GPa at the capacity of 300 mAh/g and (b) for the fourth cycle; the predicted stress at the center of island is −1.05 GPa at the capacity of 402 mAh/g. The deviation of the fitted curve form the observed values in part (b) is attributed to plastic flow in the island.

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