Effect of metal substitution in ${\mathrm{ZrSe}}_3$-type compounds: Vibrational states of ${\mathrm{Zr}}_{1\mathrm{-}\mathrm{t}}$${\mathrm{Hf}}_{\mathrm{t}}$${\mathrm{S}}_3$

The pseudobinary ${\mathrm{ZrS}}_3$–${\mathrm{HfS}}_3$ system exhibits a complete range of solid solubility, the structure being of the ${\mathrm{ZrSe}}_3$ type with Zr and Hf distributed at random over the metal sublattice in the ternary region. The unit-cell dimensions, as well as the virtually-temperature-independent diamagnetic susceptibility of ${\mathrm{Zr}}_{1\mathrm{-}\mathrm{t}}$ ${\mathrm{Hf}}_{\mathrm{t}}$ ${\mathrm{S}}_3$, evolve approximately linearly with the compositional parameter t. Examination of the vibrational states of ${\mathrm{Zr}}_{1\mathrm{-}\mathrm{t}}$ ${\mathrm{Hf}}_{\mathrm{t}}$ ${\mathrm{S}}_3$ by Raman spectroscopy has proven to be an efficient tool for probing the lattice properties of the parent members ${\mathrm{ZrS}}_3$ and ${\mathrm{HfS}}_3$. One-mode behavior of most of the long-wavelength optical modes in ${\mathrm{Zr}}_{1\mathrm{-}\mathrm{t}}$ ${\mathrm{Hf}}_{\mathrm{t}}$ ${\mathrm{S}}_3$ confirms the identity of the eigenvectors, which remain unperturbed under the Zr-to-Hf substitution as they involve essentially only the motions of the sulfur atoms. Continuous and slight variation of the eigenfrequencies with the composition reflects minor changes in force constants when one metal atom is replaced by another. The two-mode behavior of the rigid sublattice displacements of the metal against the sulfur atoms perpendicular to the b axis gives rise to a broad structure in the Raman spectrum of ${\mathrm{HfS}}_3$ resulting from an impurity mode of the Zr originally present in the Hf starting material. The accidental degeneracy of the $A_g$ and $B_g$ modes at 151 ${\mathrm{cm}}^{\mathrm{-}1}$ in ${\mathrm{ZrS}}_3$ is lifted by the metal substitution, thus confirming previous findings obtained under hydrostatic pressure.