Defect-induced Raman spectra in dopedCeO2

Polarized Raman-scattering spectra are obtained from oriented single crystals of yttria-doped ${\mathrm{CeO}}_{2}$. The temperature and dopant dependencies of Raman spectra strongly suggest that many structures in the Raman spectra of yttria-doped ${\mathrm{CeO}}_{2}$ are induced by the defect space including an ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ vacancy. The contribution to the frequency distributions of Raman-active modes from the whole Brillouin zone are estimated from the imaginary part of the simple projection of the phonon displacement-displacement Green's functions of undoped ${\mathrm{CeO}}_{2}$ crystals onto several defect spaces. The observed spectra are well explained by the linear combination of the calculated frequency distributions from the defect space consisting of the four metal ions and from that consisting of the six next-nearest-neighbor ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions surrounding an ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ vacancy. Brillouin-scattering spectra of ${\mathrm{CeO}}_{2}$ are also measured in order to calculate the phonon-dispersion curves of ${\mathrm{CeO}}_{2}$. The dependencies of type and concentration of defect space on dopant concentration in doped ${\mathrm{CeO}}_{2}$ are also discussed.