Phase-field simulation for voltage profile of LixSn nanoparticle during lithiation/delithiation

Tin has become one of the most promising anode materials due to its large theoretical capacity. The multi-phase transformations occurring during the (de-)lithiation process have posed a severe challenge to study their thermodynamic, kinetic and elastic properties via computational methods. In this work, a phase-field framework consisting of phase-concentration equations and Allen-Cahn equations is established. Two concepts to deliver thermodynamic and elasticity data as input quantities for the phase-field model are proposed, namely from density functional theory calculations and the thermodynamic energy of stoichiometric compounds. Using the formulated and configured phase-field model, voltage profiles, composition profiles, phases, and stress distributions of the electrode during the charging/discharging cycles are simulated. The effects of varying applied current densities and the homogeneity/inhomogeneity of the eigenstrain within the electrode on the voltage profile are discussed. According to simulation results, the establishment of stable voltage output remains a challenge under a higher C-rate due to inhomogeneous phase or stress distribution within the nanoparticle. A simulation-based derivation of linkages between electrode morphology, charging rate, stress, and capacity retention could enable an advanced design of electrode microstructures.