Differential Raman and differential fluorescence measurements have been carried out for the first time in order to investigate the phonon dispersion relations of KTa${\mathrm{O}}_3$ crystals. The derivative with respect to wavelength of the intensity of Raman scattered light has been measured as a function of photon energy at room and at liquid-nitrogen temperatures (L.N.T.). The measurements were carried out on pure KTa${\mathrm{O}}_3$, 5%-Li-doped KTa${\mathrm{O}}_3$, and KTa${\mathrm{O}}_{0.9}$${\mathrm{Nb}}_{0.1}$${\mathrm{O}}_3$. Similar differential measurements were carried out on the fluorescence of ${\mathrm{Er}}^{3+}$ ions in KTa${\mathrm{O}}_3$ and KTa${\mathrm{O}}_{0.9}$${\mathrm{Nb}}_{0.1}$${\mathrm{O}}_3$ crystals. Characteristic linewidths observed in this way are 15 ${\mathrm{cm}}^{-1\mathrm{}}$. These linewidths allowed the determination of the energies to within ±2 ${\mathrm{cm}}^{-1\mathrm{}}$. All the zone-center phonon energies have been measured from first-order Raman lines in KTa${\mathrm{O}}_3$:Li and KTa${\mathrm{O}}_{0.9}$${\mathrm{Nb}}_{0.1}$${\mathrm{O}}_3$ at L.N.T. They are in excellent agreement with the generalized Lyddane-Sachs-Teller theory. By comparing the energies of pairs of phonons measured from the differential Raman spectra with energies of single phonons at Van Hove critical points measured from the differential fluorescence spectra, we were able to interpret in detail the second-order Raman data in terms of combinations of pairs of phonons at two critical points. In doing so we obtained the energies of six phonons at the [100] zone boundary and three additional phonons at another critical point. Three additional phonon energies at this same critical point are inferred. The shape of one of the differential Raman lines measured at different conditions has been analyzed. It is shown that this line shape fits the derivative of a suitably broadened density-of-states function. The broadening parameter is shown to change from $\eta =1\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ in pure KTa${\mathrm{O}}_3$ at L.N.T. to $\eta =2.8\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ in KTa${\mathrm{O}}_3$:Li at L.N.T. and $\eta =6.5\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ in pure KTa${\mathrm{O}}_3$ at room temperature.

• Received 20 July 1973

DOI:https://doi.org/10.1103/PhysRevB.9.2723