“…Combined with the Bragg rule: 2 d sin θ = λ ( d , θ , λ represents the interplanar spacing, the angle between incident X-ray and corresponding crystal plane, and the wavelength of the X-ray, respectively) and ionic radii (( r (Mg 2+ ) = 0.72 Å, CN = 6), ( r (Ge 4+ ) = 0.39 Å, CN = 4), ( r (Mn 2+ ) = 0.83 Å, CN = 6), ( r (Mn 4+ ) = 0.56 Å, CN = 6), a large radius Mn 2+ ion may occupy a smaller radius Mg 2+ ion, where the Mn 2+ ion is self-reduced from the Mn 4+ ion at high temperature. 27 This point is further proved by Rietveld refinement using GSAS software, where all the samples belong to the orthorhombic Pbca (61) space group. The reliable factors are converged into χ 2 < 3, illustrating that the refined results are trustworthy in Fig.…”