THE CRYSTAL DYNAMICS OF URANIUM DIOXIDE

Abstract

The frequency/wave-vector dispersion relation for normal modes of vibration propagating along the [00ζ], [ζζ0], and [ζζζ] directions in uranium dioxide at 296 °K has been determined by studying the coherent one-phonon scattering of slow neutrons from a single-crystal specimen. Analysis of the results shows that a simple rigid-ion model of the crystal with axially symmetric forces between near-neighbor ions can provide qualitative agreement with experiment. A more complicated model, in which the ionic polarizabilities are taken into account, is needed to obtain quantitative agreement with the dispersion curves and with the known dielectric properties. Such a model provides an interpolation formula for computing the frequency distribution function and other related quantities, such as the Debye–Waller factors and lattice specific heat. Information concerning the anisotropy of the Debye–Waller factor for the oxygen ions and the configuration of the "magnetic" electrons in UO₂ is derived by comparing these calculations with the appropriate experimental data. The optic-mode frequencies and dielectric constants of UO₂ are shown to satisfy the Lyddane, Sachs, and Teller relation. The slopes of the acoustic-mode branches at small wave vectors are consistent with independently measured elastic constants.