Phase-field modeling on sodium ion batteries particles of NaxFePO4
Sodium-ion batteries have been considered as a promising alternative to lithium-ion batteries. In contrast to LixFePO4, where transformation from a lithium-poor phase FePO4 into a lithium-rich phase LiFePO4 occurs directly, the system of NaxFePO4 goes through an intermediate state at Na2/3FePO4. In addition, the volume expansion of NaxFePO4 upon full insertion is much larger than that of LixFePO4 . A volume mismatch between phases may induce large concentration gradients at a mesoscopic scale and thus also large stress magnitudes, which can cause particle fracture and capacity loss.
In this work, a mechanically coupled phase-field model for NaxFePO4 is studied for the first time. As a major novelty, the multiwell potential of this material is constructed, and the relevant material parameters are determined, which can provide a significant input for the future phase-field work for NaxFePO4. The model captures the important feature that distinguishes NaxFePO4 from LixFePO4, i.e. phase segregation into a sodium-poor phase FePO4 and a sodium-rich phase Na2/3FePO4. The simulation of the time dependent insertion process in electrode particles including the coupling to mechanics is achieved using the advanced numerical technologies of mesh adaptivity and time step adaptivity, as well as parallelization.
A direct comparison between NaxFePO4 and LixFePO4 is made in terms of the microstructure evolution and the stress evolution. The dynamics of so-called single wave propagation is obtained in the particles of NaxFePO4, and both, the classical shrinking-core and the mirror symmetry of phase segregation can be destroyed to minimize the system free energy. The morphology of the interface between phases that goes across the particle dynamically changes to minimize its proportion. When mechanics is accounted for, the interface gets more widened for NaxFePO4, and the miscibility gap of this material 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 a steeper concentration inhomogeneity in each phase for NaxFePO4. It is predicted that the particle surface of the species-rich phase is more prone to cracking due to the tensile stresses located there. Compared with LixFePO4, the stress magnitudes at the interface are smaller in NaxFePO4 due to the relatively widened interface.