The large volume change during lithium-ion insertion/extraction leads to huge stress and even failure of active materials. To well understand such a problem, the two-phase lithiation process of film and hollow core-shell electrodes is simulated by using a non-linear diffusion lithiation model. The dynamic evolution of lithium-ion concentration and diffusion-induced stress are obtained. Based on the dimensional analysis, a phase diagram is determined to demonstrate the relationship between critical failure, structure dimensions and mechanical properties. As a case study, the critical state of charge in Sn films are measured and compared with theoretical results. Because of the large storage capacity and high energy density, lithium-ion batteries (LIBs), one of the most promising secondary cells, [1][2][3] have been widely used in portable electronic devices. Recently, more research interest has focused on their potential applications in electric vehicles.2,4,5 As typical high-capacity electrode materials (e.g., Si, Ge, Sn, and some transition metal oxides) can host a large amount of Li-ions, this makes them promising candidates for demanding applications.6,7 For instance, Si has the highest theoretical specific capacity in the phase of Li 22 Si 5 (up to 4200 mA h g −1 ), which is nearly ten times higher than that of fully-lithiated graphite in LiC 6 (372 mA h g −1 ). 8,9 Other electrode materials such as Ge and Sn also have considerable theoretical specific capacities (1623 mA h g −1 for Li 22 Ge 5 and 700 mA h g −1 for Li 22 Sn 5 ). 4,7,10 However, the large number of Li-ions inserting into high-capacity electrode materials may result in a huge volume change (400% for full lithiation of Si), 6 and a series of shortcomings: fracture or pulverization of active materials, breakage of a conduction path for electrons and lose of electrical contact, and destruction of solid electrolyte interphase formed by the reaction between active materials and electrolyte. They can rapidly fade electrochemical properties of active materials and result persistent decrease of their long-term coulombic efficiency.
11-15To solve these problems, extensive efforts have been made over the last decade. It is shown that nanostructure-based battery electrodes such as nanofilms, nanowires and nanoparticles, can alleviate diffusion-induced stress and improve their cycle life through structural optimization and geometric restriction. [16][17][18][19][20] For example, a facile and scalable in situ chemical vapor deposition technique was developed for one-step fabrication of three-dimensional porous networks anchored with Sn nanoparticles (5-30 nm) and encapsulated with graphene shells of about 1 nm as a superior LIB anode. 21 However, the irreversible capacity loss caused by stress damage during the first cycle is still serious. 6,22,23 Due to complicated lithiation deformation mechanisms, 11,24 the study on the structural change and stress evolution of high-capacity electrode materials during charging and discharging is necessary for the contr...