The phonon structure in the cubic paraelectric phase $\left(F\overline{4}3c\right)$ of ${\text{Co}}_3{\text{B}}_7{\text{O}}_{13}X$ $\left(X=\text{Cl},\text{Br},\text{I}\right)$ boracites has been studied theoretically by density-functional theory and experimentally by Raman spectroscopy. The calculated Raman frequencies are in good agreement with those determined from the polarized Raman spectra. In addition to the four Raman-allowed phonons of $A_1$ symmetry, a low-frequency broadband of same symmetry is observed in the spectra of ${\text{Co}}_3{\text{B}}_7{\text{O}}_{13}\text{Cl}$ and ${\text{Co}}_3{\text{B}}_7{\text{O}}_{13}\text{Br}$. The position and width of this band correspond to those of the partial phonon density of states of the halogen vibrations: an indication for disorder and instability of the halogen sublattice. In the case of ${\text{Co}}_3{\text{B}}_7{\text{O}}_{13}\text{I}$, an even greater number of spectral features reflecting the underlying phonon density of states are observed. An “instability” $F_2$ mode that involves displacements of the $X$ atoms along $⟨111⟩$ and of the Co atoms along $⟨100⟩$ directions is also identified. It is shown that this mode is closely related to the halogen and metal sublattice instabilities, which trigger the cubic to orthorhombic transition at lower temperature.

• Received 8 December 2008

DOI:https://doi.org/10.1103/PhysRevB.79.104115