Experiments on single crystal ${\mathrm{Li}}_X{\mathrm{FePO}}_4$ nanoparticles indicate rich nonequilibrium phase behavior, such as suppression of phase separation at high lithiation rates, striped patterns of coherent phase boundaries, and nucleation by binary-solid surface wetting and intercalation waves. These observations have been successfully predicted (prior to the experiments) by one-dimensional (1D) depth-averaged phase-field models, which neglect any subsurface phase separation. In this paper, using an electro-chemo-mechanical phase-field model, we investigate the coherent nonequilibrium subsurface phase morphologies that develop in the $ab$ plane of plateletlike single-crystal plateletlike ${\mathrm{Li}}_X{\mathrm{FePO}}_4$ nanoparticles. Finite element 2D plane-stress and plane-strain simulations are performed in the $ab$ plane and validated by 3D simulations, showing similar results. Using a realistic material model from previous work, we show that the anisotropy of the interfacial tension (or gradient penalty) tensor and its relation to electro-auto-catalytic surface intercalation reactions plays a crucial role in determining the subsurface phase morphology. With the standard assumption of an isotropic interfacial tension tensor, subsurface phase separation in the bulk is observed and its morphology is independent of the reaction kinetics at the surface, but for strong anisotropy, phase separation is controlled by surface reactions, as assumed in 1D models. Moreover, the driven intercalation reaction suppresses phase separation during lithiation, while enhancing it during delithiation, by electro-auto-catalysis, in quantitative agreement with in operando imaging experiments in single-crystalline nanoparticles, given measured reaction rate constants.

• Received 26 February 2018
• Revised 9 June 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.085406