Fig. 4

In situ X-ray scattering analysis of P_K = 0.33 and P_K = 0.2. a, b The evolution of X-ray scattering profile with time during hydrothermal synthesis along P_K = 0.33 (a) and P_K = 0.2 (b). c, d Phase fraction evolution calculated from the intensities of diffraction peaks in a, b, respectively. e, f X-ray scattering profiles of the δ′ phase (e) and α phase (f). The inset figure in d shows the asymmetrical tail of the peak at q = 4.45 Å⁻¹. The broad peak around q = 1.5–2.5 Å⁻¹ is caused by imperfect background removal, and is discussed in Supplementary Note 3. g, h Refined structures of the δ′ phase (g) and α phase (h). Manganese (purple), potassium (green), and oxygen (red) are represented by spheres, and the unit cell is identified by gray lines (see Supplementary Notes 5 for refinement details). The partially filled spheres represent the site fraction of the atoms