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Model analysis of silicon-based electrodes for lithium ion batteries
Active materials for Lithium-ion batteries

Silicon is one of the most promising anode materials to be used in the next generation high energy density lithium-ion batteries due to its large storage capacity, abundant material content and environmental benignity. Although theoretical capacity of pure silicon can be over 10 times as high as that of graphite, the highly increased Li storage can lead to huge volume change together with large internal stress, which accelerates the electrode degradation. In order to achieve the commercial goal of high-performance anodes in the near future, a good compromise is to blend silicon and graphite into a single composite, benefiting from the high capacity of silicon and the good structural stability of graphite.
Although silicon and graphite are both electrochemically active with lithium ions during cycling, they have very different lithiation mechanisms. In contrast to the conventional intercalation carbonaceous materials, silicon exhibits unique electrochemical behaviors as an alloying material. A huge voltage hysteresis is observed between charge and discharge voltage curves, and more interestingly this voltage hysteresis is proved to be dependent on lithiation depth. Numerous experimental efforts have been made to reveal the mechanisms underlying the complex behaviors of silicon, but theoretical studies have not been well established.
Herein, we first build a mechanistic model to link the electrochemical behaviors of silicon to its complex multi-phase electrochemical reactions, crystallisation and amorphisation processes. This model reproduces the path-dependent voltage hysteresis of silicon at different lithiation depth. In particular, the two sloping voltage plateaus at low lithiation state can be interpreted by two electrochemical phase transformations of Li-Si phases, while the emergence of a single voltage plateau at high lithiation depth is found to be correlated with the amorphization of the crystalline Li15Si4 phase. Furthermore, the model uses the homogeneous crystallisation theory to describe the abrupt growth of the crystalline Li15Si4 phase at the end of lithiation process, and the effects of crystallization rate and surface energy barriers are studied to clarify their roles in determining the performance behaviors of silicon.
We next explore the role of silicon in the composite Si/Gr electrodes using a multi-material model for Si/Gr electrode considering different properties and electrochemical kinetics of each individual material. It is found that the voltage curves of the Si/Gr electrode involve a superposition of silicon and graphite features, which are well consistent with experimental data. It is found that lithiation of the composite electrode begins with Si, and the lithiation reaction rate of graphite is only comparable to that of Si at high lithiation state of the composite electrode. In contrast, delithiation occurs serially from graphite at first and then from silicon. Finally, a dimensionless competing factor is proposed to describe the relative reaction rate of each electrode material. This competing factor is proved to be an effective index to identify the active regions of different electrode materials and we demonstrate how it can be used to design cycling protocols for mitigating electrode degradation of the Si/Gr electrode.

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Gregory Offer, Huizhi Wang