Stress level estimates in coated or uncoated silicon nanoparticles during lithiation

Abstract

This work is devoted to the modeling of the mechanical behavior of coated or uncoated silicon nanoparticles, which constitute the anode active material in some lithium ion batteries, during their first lithiation at room temperature. The lithiation process induces a large volume expansion of the particles and a high level of stresses, which can lead to the fragmentation of the particles. Several approaches are proposed in order to estimate the volume expansion and the stress levels experienced by the particles. An original semi-analytical small strain model is first presented, which adapts the solution proposed by Seck et al. (2018) of the elastic-viscoplastic composite sphere problem subjected to radial loading, to the lithiated particle problem, in particular by considering the variation of phases properties during lithiation. The lithium concentration in the silicon particle is given by a sigmoid function (called logistic function) in order to mimic the reaction front between the phases. The implementation of the approach using the Hencky strain tensor Miehe et al. (2002) is proposed to take into account the large strains experienced by the particles. A complete description of the formulation is provided and the advantages are discussed. The importance of the large strains model is established by comparing it with the small strain one concerning the predictions of the pushing-out effect and the size effect of particles on their internal stresses during lithiation. Comparisons between our simulations and experimental data from Tardif et al. (2017) measuring the operando strain experienced by the pristine silicon gives the yield stress of the lithiated silicon. In addition, carbon-coated silicon nanoparticles are finally studied. We develop original closed-form expressions to predict the maximal stresses experienced by the coating at the end of the lithiation. Those expressions are used to re-estimate the fracture stress of pyrolitic carbon, considering a critical review of both pyrolitic carbon and lithiated silicon elastic properties. Finally, the mechanical effect of the coating on silicon during lithiation is studied.