Raman scattering in the ternary phaseHfS3−xSex

The mode behavior of long-wavelength optical phonons in the ternary phase $\mathrm{Hf}{\mathrm{S}}_{3-x}{\mathrm{Se}}_x$ has been investigated by Raman spectroscopy through the whole composition range $0\le x\le 3$. Previous studies on the parent compounds have shown that $\overrightarrow{\mathrm{k}}=\overrightarrow{0}$ Raman-active modes can be classified according to largely rigid chain modes (group I), internal deformation chain modes (group II), and a stretching mode of the diatomic chalcogen $X_2$ pair within the chains (group III). A mixed one-, two-, and three-mode behavior is observed in the $\mathrm{Hf}{\mathrm{S}}_{3-x}{\mathrm{Se}}_x$ system, depending respectively on modes of group I, II, and III. This behavior reflects the quite different and specific atomic interactions governing these different groups. More precisely, the mode-number progression from group I to group III appears to be related to the corresponding shortening of the range of atomic interactions involved. In particular, three-mode behavior is observed for diatomic $X_2$ modes. This behavior results from vibrations of S-S, Se-Se, and S-Se pairs of chalcogen atoms covalently bound. The picture of diatomic $X-X^{\prime }$ ($X, X^{\prime }=\mathrm{S},\mathrm{S}\mathrm{e}$) "molecules" is substantiated by an estimate of the S-Se mode frequency based on a molecular model, in good agreement with experimental data. In addition, we took advantage of one-mode behavior of group I to establish a one-to-one correspondence between compatible phonons in the pure end member crystals and thus resolve some discrepancies in mode assignment from different authors.