Raman study ofCeO2: Second-order scattering, lattice dynamics, and particle-size effects

Polarized Raman-scattering spectra are obtained from oriented single crystals of ${\mathrm{CeO}}_{2}$. Second-order features are assigned to phonon overtones from the X and L points on the Brillouin-zone boundary on the basis of selection rules and by analogy to another fluorite structure compound, ${\mathrm{BaF}}_{2}$, in which the phonon dispersion curves are known. Complete selection rules for second-order scattering from these high-symmetry points are determined. A rigid-ion model is constructed for the phonon dispersion curves by fitting several of these features and the known zone-center optical modes. The ${\mathit{F}}_{2\mathit{g}}$ Raman-active mode at 465 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in ${\mathrm{CeO}}_{2}$ shifts and broadens with decreased particle size [G. W. Graham, W. H. Weber, C. R. Peters, and R. Usmen, J. Catalysis 130, 310 (1991)]. It is shown using the calculated dispersion curves that this particle-size effect cannot be explained with the spatial-correlation model.