In situ Measurement of Biaxial Modulus of Si Anode for Li-ion Batteries
  We report in situ measurement of biaxial moduli of a Si thin-film electrode as a function of its lithium concentration. During lithiation, biaxial compressive stress is induced in the Si film and it undergoes plastic flow. At any state-of-charge (SOC), a relatively small delithiation-relithiation sequence unloads and reloads the film elastically. From the stress and strain changes during a delithiation-relithiation cycle, the biaxial modulus of the film is calculated. Stress change is obtained by measuring the change in substrate curvature using a Multi-beam Optical Sensor; the elastic strain change is obtained from the change in SOC. By repeating these measurements at several different values of SOC, the biaxial modulus was seen to decrease from ca. 70 GPa for Li0.32Si to ca. 35 GPa for Li3.0Si. Such a significant reduction in elastic modulus has important implications for modeling stress evolution and mechanical degradation in Si-based anodes. 
Vijay A. Sethuraman, Michael J. Chon, Maxwell Shimshak, Nathan Van   Winkle, Pradeep R. Guduru
cond-mat.mtrl-sci