Mechanically Coupled Phase-Field Modeling of Microstructure Evolution in Sodium Ion Batteries Particles of NaxFePO4

The microstructure evolution of the cathode material Na x FePO 4 of sodium-ion batteries is investigated during insertion, using a mechanically coupled phase-field model. A direct comparison between Na x FePO 4 and Li x FePO 4 is made in terms of the microstructure evolution and the stress evolution. The dynamics of single wave propagation in spherical particles of Na x FePO 4 is obtained, and the interface morphology between phases that goes across the particle dynamically changes to minimize its proportion. When mechanics is accounted for, the interface gets more widened for Na x FePO 4, and its miscibility gap is significantly reduced. In contrast to the constant stresses in each phase occurring in shrinking-core dynamics, both, tensile and compressive stresses coexist in each phase, and the related gradient of hydrostatic stress induces Na x FePO 4 a steeper concentration inhomogeneity in each phase. It is expected that the particle surface of the species-rich phase is more prone to cracking. Compared with Li x FePO 4, the stress magnitudes at the interface are smaller in Na x FePO 4. Although the miscibility gap of Na x FePO 4 is smaller, the stress magnitudes at the particle surface are larger in this material, which makes it less mechanically reliable.