context: Simultaneously, the predicted structural changes of O3-Nax[Ni0.5Mn0.5]O2 during Na+ extraction/insertion are presented in Fig. 5a. With extraction of 0.75 mol of Na from O3-Na1[Ni0.5Mn0.5]O2, the c-lattice parameter gradually increased from ∼15.97 to ∼17.40 Å because of the reinforced repulsive force between O2− anions. Then, after an additional 0.25 mol Na extraction, it decreased to ∼15.24 Å owing to MeO2 slab gliding arising from the structural instability, which matched well with the structural change of other layered-type cathode materials for SIBs. Furthermore, as shown in Fig. 5b, we compared the c-lattice parameters of various O3-/P3-NaxCa0.01[Ni0.5Mn0.5]O2 verified through Rietveld refinement based on operando XRD results and those of O3/P3-Nax[Ni0.5Mn0.5]O2 predicted through the first-principles calculations. We confirmed that despite the occurrence of a partial two-phase reaction, the c-lattice parameter was increased in general during extraction of Na ions from O3-Na1[Ni0.5Mn0.5]O2 to P3-Na0.25[Ni0.5Mn0.5]O2. In the case of Na0[Ni0.5Mn0.5]O2, although two phases were detected in the XRD patterns of NaxCa0.01[Ni0.5Mn0.5]O2 from the operando XRD analysis, the average value of c-lattice parameters on the two phases was similar to the c-lattice parameter predicted through first-principles calculations. Moreover, this result implies that at the Na0[Ni0.5Mn0.5]O2 composition, coexistence of O3′ and O3′′ phases is more favorable than perfect phase transition to the O3′′ phase, which agrees with the experimental results of previous research studies.