Far Infrared Dielectric Dispersion in BaTi${\mathrm{O}}_3$, SrTi${\mathrm{O}}_3$, and Ti${\mathrm{O}}_2$

The room temperature reflectivity of BaTi${\mathrm{O}}_3$, SrTi${\mathrm{O}}_3$, and Ti${\mathrm{O}}_2$ has been measured from 5000 to 70 ${\mathrm{cm}}^{-1\mathrm{}}$. These data have been analyzed by the Kramers-Kronig method and by classical dispersion theory. All of the infrared-active fundamental vibrations allowed by crystal symmetry have been measured and characterized by their dispersion parameters. Of particular interest is the low-frequency mode which recent theories show is responsible for ferroelectricity in BaTi${\mathrm{O}}_3$ and SrTi${\mathrm{O}}_3$ and is found at 33.8 and 87.7 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. The unusually large damping found for this mode can explain the observed microwave loss tangents. The strength of the mode accounts for the large values of the low-frequency dielectric constant. This mode, as well as the highest frequency mode, 510 and 546 ${\mathrm{cm}}^{-1\mathrm{}}$ in BaTi${\mathrm{O}}_3$ and SrTi${\mathrm{O}}_3$, respectively, is associated with Ti${\mathrm{O}}_6$ octahedra vibrations. A previously unreported mode at 183 and 178 ${\mathrm{cm}}^{-1\mathrm{}}$ for BaTi${\mathrm{O}}_3$ and SrTi${\mathrm{O}}_3$, respectively, has also been found and assigned to a cation-(Ti${\mathrm{O}}_3$) vibration. In rutile, three resonances are observed for the ordinary ray and one for the extraordinary ray, as required by theory. As with the titanates, the high dielectric constant is associated with the low-frequency mode. An analysis of the strengths of all of the resonances shows that they involve resonable effective charges for ionic crystals.