Ab initio Raman spectrum of the normal and disordered $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ spinel

Ab initio calculations, based on density functional theory, of the vibrational Raman spectra of both normal and cationic disordered $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ spinel are reported. The vibrational properties of the disordered system are obtained in two steps. First, the interatomic force constants of small defective supercells are computed in a fully ab initio way. Later, these force constants are used to build the dynamical matrices of larger disordered systems. The calculated Raman spectrum presents the mode near $727{\mathrm{cm}}^{-1}$ which is due to the presence of cationic disorder and which is commonly attributed to a breathing mode (BM) of $\mathrm{Al}{\mathrm{O}}_4$ tetrahedra. Contrary to previous interpretations, the $727{\mathrm{cm}}^{-1}$ mode is due to phonons which are silent in the perfect crystal and become Raman active in the disordered structure because of the coupling with the BM of the $\mathrm{Mg}{\mathrm{O}}_4$ tetrahedra.

Figure 1

$\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ spinel phonon dispersion from DFT calculation. Dots are measurements from Ref. 24. Right panel: Phonon density of states.

Figure 2

Raman spectrum of $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ spinel. Upper panel: measurements from Ref. 4 on synthetic and natural spinel. Lower panel: DFT calculation on the perfect $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ crystal. The spectrum is convoluted with a uniform Gaussian broadening having $5{\mathrm{cm}}^{-1}$ width.

Figure 3

Raman spectrum from DFT calculation on the perfect crystal and on a partially inversed structure [$x=0.3$ in Eq. (1)]. The spectrum of the partially inversed structure is obtained from an average over several random configurations. The spectra are convoluted with a uniform Gaussian broadening having $5{\mathrm{cm}}^{-1}$ width.

Figure 4

Raman spectrum of the partially inversed structure of Fig. 3. The spectrum is projected on the in-phase breathing modes of the oxygen tetrahedra centered on the Mg (Al) atoms: Mg- (Al)-TBM, upper (lower) panel. The overlap intensity is shifted for clarity.