Identifying the intermediate phase of tin oxides as Sn$_3$O$_4$ through Raman spectroscopy from theory and experiment

The existence of an intermediate phase within the tin oxide system was first reported in 1882. However, its stoichiometry and its crystal structure have been dubious and heavily debated ever since, despite a multitude of structural investigations. Here we show that a combined Raman spectroscopic investigation based on \textit{ab initio} methods and experiments offers an alternative to diffraction studies, which are not conclusive for this material system. It allows us to unambigiuously identify the intermediate phase as Sn$_3$O$_4$ and to rule out the other likely candidate, Sn$_2$O$_3$. We assign the one-phonon Raman signals of Sn$_3$O$_4$ to the mode symmetries of the corresponding point group $C_{2h}$ and confirm the space group as $P2_1/c$ with 14 atoms per unit cell.