## 3 Results
### Phase of the Oxide
As an example, in the 5 MD-series, the mean crystallite size increases in the order 5 MD-sg (22.9 nm) < 5 MD-a (43.7 nm) < 5 MD-b (43.9 nm), whereas in the 5 MF-series, it varies in the order 5 MF-sg (38.7 nm) > 5 MF-b (22.5 nm) > 5 MF-a (20.5 nm). Additional information on the phase-purity of the prepared samples and its spatial homogeneity is inferred by measuring Raman scattering from several random locations in each specimen (Figure S7). No appreciable differences in the relative intensities and in the positions of the bands at the probed locations are observed in pure single-phase samples (Figure S7a,b). On the contrary, changes in the spectral profile at a random location indicate local deviations from the average chemical composition and segregation in a secondary phase (Figure S7c). The obtained results by these measurements are in agreement with the indications emerged from the XRD analysis. Figure 4 shows the averaged Raman spectra of pure single-phase samples, obtained from the spectra acquired at random locations in each sample. These spectra provide a global picture of the entire sample. The vibration modes theoretically predicted for the spinel-group [62; 63] include five Raman-active phonon modes, namely three triply degenerate modes having F\({}_{2g}\) symmetry, one doubly degenerate mode with E\({}_{g}\)-symmetry and an A\({}_{1g}\)-symmetry mode. The lowest frequency F\({}_{2g}\)(1) mode might be due to the translation motion of the BO group [64] or originate from a complete translation of the AO\({}_{4}\) unit within the spinel lattice [65; 66]. The E\({}_{g}\) mode is associated with symmetric bending of O anion with respect to octahedral B cation [67; 68]. Higher frequency F\({}_{2g}\)(2) and F\({}_{2g}\)(3) modes arise from the asymmetric stretching and asymmetric bending of oxygen, respectively [65; 67; 69]. Finally, the A\({}_{1g}\) mode is attributed to the vibration along the direction joining an oxygen atom to the tetrahedral A cation. In the A\({}^{2+}\)B\({}^{3+}\)\({}_{2}\)O\({}_{4}\) spinel structure, cations occupy both octahedral and tetrahedral sites. Depending on the sites occupied by the A and B cations, normal, inverse or partial inverse spinel structures can be formed [65]. Frequencies and intensities of the Raman bands are sensitive to the type of cations, A\({}^{2+}\) or B\({}^{3+}\), that occupy octahedral and tetrahedral sites. For example, the spectrum of chromate spinels (ACr\({}_{2}\)O\({}_{4}\)) changes with changing A cations [65]. All predicted Raman active modes are detected in the spectrum of ZnCr\({}_{2}\)O\({}_{4}\), whereas the lowest wavenumber band F\({}_{26}\)(1) is absent in that of MgCr\({}_{2}\)O\({}_{4}\). By comparing the spectra of FeCr\({}_{2}\)O\({}_{4}\) and MgCr\({}_{2}\)O\({}_{4}\), noticeable changes in the relative intensity of bands are observed. Since in the chromate spinels, A\({}^{2+}\) and Cr\({}^{3+}\) cations are ordered in the tetrahedral and octahedral coordinated sites respectively, the observed variations in the Raman spectra can be attributed to the different divalent cations [65]. The same considerations hold if the trivalent cation changes. This may even cause the appearance of new vibration modes, as reported for FeAl\({}_{2}\)O\({}_{4}\) and FeCr\({}_{2}\)O\({}_{4}\)[65]. In addition, the presence of defects that generate distortions of the crystalline lattice contributes to shift the Raman bands and change their relative intensities [66]. However, in the case of HESOs, assessing the type of sites occupied by cations in the lattice is made even more difficult than in common spinels due to the inherent complexity of five-cation systems. In the present samples, the F\({}_{26}\)(1) mode is detected between 160 and 220 cm\({}^{-1}\), whereas the very weak E\({}_{g}\) mode is located between 250 and 420 cm\({}^{-1}\). Their relative intensities and frequency positions do not appreciably vary with the metal combinations (compare spectra shown in Figure 4).