The cathode material Na${}_x$FePO${}_4$ ($0<x<1$) of sodium-ion batteries displays complex phase segregation processes with the existence of an intermediate phase, and large volume change during charging/discharging. A chemo-mechanical phase-field model is developed to capture the thermodynamics of phase segregation along with the structural change that occurs in Na${}_x$FePO${}_4$. The multiwell potential of Na${}_x$FePO${}_4$ for the full range of concentration is constructed for the first time. This new model not only captures phase segregation into a sodium-poor phase FePO${}_4$ and a sodium-rich phase $N{a}_{2∕3}FeP{O}_4$ but also the solid-solution phase Na${}_x$FePO${}_4$ ($2∕3<x<1$). The microstructure evolution in the whole processes of sodiation and desodiation is investigated. The stress assisted diffusion induces the striking behavior of the maximum solubility limit going beyond 2/3 even within two-phase coexistence. Further, the formation of an intermediate phase leads to varying solubility limits which agrees with recent experimental observation, as well as a stress reduction behavior. Finally, our work suggests that prolate Na${}_x$FePO${}_4$ particles are mechanically more reliable due to nearly stress-free phases. We expect that the intermediate phase-induced stress reduction behavior provides a new concept for improving mechanical stability and thus better battery performance.

正极材料Na${}_X$磷酸铁${}_4$ （$0<X<\mathrm{1个}$钠离子电池的）显示复杂的相分离过程，存在中间相，并且在充电/放电过程中体积变化很大。建立化学机械相场模型以捕获相分离的热力学以及在Na中发生的结构变化${}_X$磷酸铁${}_4$。Na的多孔势${}_X$磷酸铁${}_4$首次建立了完整的浓度范围。这个新模型不仅捕获了相分离成贫钠的FePO${}_4$ 和富钠相 $ñ{\mathrm{一种}}_{2∕3}FËP{Ø}_4$ 还有固溶相Na${}_X$磷酸铁${}_4$ （$2∕3<X<\mathrm{1个}$）。研究了整个消沉过程的微观结构演变。应力辅助扩散引起最大溶解度极限的惊人行为，甚至在两相共存时也超过2/3。此外，中间相的形成导致变化的溶解度极限，这与最近的实验观察一致，并且具有应力降低行为。最后，我们的工作表明Na${}_X$磷酸铁${}_4$由于几乎没有应力，因此颗粒在机械上更可靠。我们期望中间相诱导的应力降低行为提供了一个新的概念，以改善机械稳定性并因此改善电池性能。