FePO₄ has emerged as a promising cathode material for next-generation Li-ion rechargeable batteries. Nanoparticles of FePO₄ have shown remarkably high charge and discharge rates, which is desirable in battery applications, while larger particles have relatively poor performance. The reasons why nanoparticles are so efficient are not completely understood but may originate in the tendency of Li_xFePO₄ to separate into Li-rich and Li-poor regions in large particles. The ionic conductivity of LiFePO₄ and FePO₄ is known to be low, but intermediate concentrations such as Li_0.5FePO₄are thought to have larger conductivities, leading to faster charge and discharge. Nanoparticles appear to be able to sustain intermediate concentrations of Li throughout the particle.

Our work aims to understand how FePO₄ nanoparticles can accommodate intermediate concentrations of Li. Li_xFePO₄is a complex material with anisotropic, concentration-dependent elastic and lattice constants and a complicated free energy dependence on Li concentration. In addition, Li preferentially ‘wets’ certain particle surfaces, which introduces a geometric component into the model and leads to microstructure.

We developed a multiphysics phase-field model to study phase segregation in LiFePO₄nanoparticles, and how the phase segregation affects discharge voltage profiles [1]. The model includes spinodal decomposition, anisotropic, concentration-dependent elastic moduli, misfit strain, and facet-dependent surface wetting within a Cahn-Hilliard framework. Elastic and structural constants, diffusivity, and surface energy are highly anisotropic and concentration dependent, necessitating a 3D treatment. Simulations are carried out on particles of varying sizes in 3D in order to examine modification to phase segregation. The stability of a phase at an intermediate composition, sometimes seen experimentally, is also examined.

Spinodal decomposition into Li-rich and –poor phases is modified and can be suppressed by mesoscopic effects, which influences the kinetic and mechanical performance of this material as a battery electrode. We are able to consider all of the described phenomena in a fully 3D geometry. Our mesoscale model can predict the stress and distribution of intercalated Li, and the consequent voltage as the particle is charged or discharged. Our simulations agree well with experimental studies, and show the halting of phase separation for particles of about 10 nm diameter as well as the emergence of new microstructures.

The figure shows the lowest energy stationary microstructures of particles as a function of radius (vertical) and average lithiation (horizontal). Volumes with less than 50% lithiation are made translucent, and when symmetry is observed one of the hemispheres is removed. Surface wetting plays an important role determining the phase-distribution of smaller particles, but elasticity becomes more significant at larger sizes.

[1] Welland, M.J., Karpeyev, D., O’Connor, D.T., Heinonen, O, “Miscibility gap closure, interface morphology and phase microstructure of 3D Li_xFePO₄ nanoparticles from surface wetting and coherency strain”, ACS Nano, DOI 10.1021/acsnano.5b02555.