3D chemo-mechanical modeling of microstructure evolution and anisotropic deformation in NaxV2(PO4)3 cathode particles for sodium-ion batteries

The cathode material Na${}_x$V${}_2$(PO${}_4$)${}_3$ of sodium-ion batteries displays complicate phase segregation thermodynamics with anisotropic deformation during (de)intercalation. A virtual multiscale modeling chain is established to develop a 3D anisotropic chemo-mechanical phase-field model based on first-principles calculations for Na${}_x$V${}_2$(PO${}_4$)${}_3$. This model accounts for diffusion, phase changes, anisotropic misfit strain, and anisotropic elasticity. The multiwell potential of Na${}_x$V${}_2$(PO${}_4$)${}_3$ is constructed, which captures phase segregation into a sodium-poor phase NaV${}_2$(PO${}_4$)${}_3$ and a sodium-rich phase Na${}_3$V${}_2$(PO${}_4$)${}_3$. The elastic properties of NaV${}_2$(PO${}_4$)${}_3$ are determined by first-principles for the first time. Furthermore, we address how elastic effects and crystal orientation influence the full 3D microstructure evolution, including phase evolution, interface morphology, and stress evolution in Na${}_x$V${}_2$(PO${}_4$)${}_3$ particles. We find that the quasi-equilibrium single wave propagation along [010] is determined by the anisotropic elasticity tensor. The anisotropic elasticity tensor leads to the striking behavior of warping of the interface. Furthermore, the phase boundary motion is thermodynamically affected by the crystal orientation, which is controlled by minimization of the interface area. It is found that the [010] crystal orientation is mechanically more reliable and recommended for Na${}_x$V${}_2$(PO${}_4$)${}_3$ electrode design. Apart from yielding information about the properties of Na${}_x$V${}_2$(PO${}_4$)${}_3$, the findings of this work may offer an opportunity to achieve improved mechanical stability of the phase separating electrode materials by engineering the crystal orientation.