Figure 3.

Na—1/2 ordering and the corresponding Mn charge ordering. a) 3D view of the Na—1/2 superstructure solved by SXRD and relaxed by DFT. The corresponding Mn charge orderings relaxed from DFT are labeled by purple (3+) and grey (4+). The Mn³⁺ and Mn⁴⁺ superplanes are labeled by green and blue planes, respectively. Na_disp refers to the Na ions that are displaced away from the octahedral sites. b) Projective view of inset (a) in the direction perpendicular to the MnO₂ plane (the hexagonal c direction). The left figure shows the basal structure of one Na layer and one MnO₆ layer and the right figure illustrates the interlayer stacking in detail. Points at the intersections of dashed triangular pattern corresponds to Mn lattice from layer 1, with the Mn³⁺ and Mn⁴⁺ marked in purple and grey, respectively, showing the Mn charge stripe along the b direction, as also can be seen in inset (a). The Na triangular lattice is a projection of three neighboring layers, labeled in small grey dots, with the actual Na occupation in the three layers labeled by big circles in different colors. c) Section of the two types of (101) superplanes with Na and Mn³⁺ or Mn⁴⁺. d) Elementary Na–O–Mn units of Mn³⁺ and Mn⁴⁺ superplanes for Na-1/2 ordering. Representative bonds are marked by colors, with the corresponding bond length from DFT simulation.