Infrared Dielectric Dispersion and Lattice Dynamics of Uranium Dioxide and Thorium Dioxide

Abstract

Measurements at room temperature of the infrared reflectivity of single crystals of Th${\mathrm{O}}_{2}$ and U${\mathrm{O}}_{2}$ have been carried out and analyzed by Kramers-Kronig relations. A single strong resonance is found in each case with ${\ensuremath{\omega}}_{\mathrm{TO}}=279(\ifmmode\pm\else\textpm\fi{}2)$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\omega}}_{\mathrm{LO}}=568(\ifmmode\pm\else\textpm\fi{}4)$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{0}\ensuremath{-}{n}^{2}=15.5$ for Th${\mathrm{O}}_{2}$; ${\ensuremath{\omega}}_{\mathrm{TO}}=278(\ifmmode\pm\else\textpm\fi{}2)$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\omega}}_{\mathrm{LO}}=556(\ifmmode\pm\else\textpm\fi{}4)$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{0}\ensuremath{-}{n}^{2}=17.7$ for U${\mathrm{O}}_{2}$ (TO=transverse optic; LO=longitudinal optic). The best classical dispersionformula fit to the reflectivity yields the following parameters: for Th${\mathrm{O}}_{2}$, ${\ensuremath{\omega}}_{0}=282.7$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{0}\ensuremath{-}{n}^{2}=14.85$, $\overline{\ensuremath{\gamma}}=16.2$ ${\mathrm{cm}}^{\ensuremath{-}1}$; for U${\mathrm{O}}_{2}$, ${\ensuremath{\omega}}_{0}=283.2$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{0}\ensuremath{-}{n}^{2}=15.80$, $\overline{\ensuremath{\gamma}}=18.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The low-frequency (0.3-Mc/sec) dielectric constant of Th${\mathrm{O}}_{2}$ was measured to be 18.9\ifmmode\pm\else\textpm\fi{}0.4. For U${\mathrm{O}}_{2}$ the mode frequencies are in excellent agreement with those obtained by neutron spectroscopy, and can be reconciled with existing infrared absorption data by taking into account particle-size corrections which can shift the polar mode frequency by a factor $\ensuremath{\sim}{({\ensuremath{\epsilon}}_{0}+\frac{2}{{n}^{2}}+2)}^{\frac{1}{2}}\ensuremath{\sim}1.8$ for small spherical samples. The above data are used to evaluate (Szigeti-type) effective charges (${{{Z}^{\ensuremath{'}}}_{\mathrm{Th}}}^{+4}=2.33$, ${{{Z}^{\ensuremath{'}}}_{\mathrm{U}}}^{+4}=2.42$) and to discuss several approximate relations between the long-wave elastic and optical properties of the fluorite (Ca${\mathrm{F}}_{2}$-type) lattice. Absorption bands were measured in the two-phonon-combination region in U${\mathrm{O}}_{2}$ and their assignment is discussed.