Ultrasonic Attenuation and Elastic Constants for Uranium Dioxide

Abstract

Elastic-constant measurements for ${c}_{11}$,${c}_{11}\ensuremath{-}{c}_{12}$ and ${c}_{44}$ have been made over the temperature range of 4.2 to 300\ifmmode^\circ\else\textdegree\fi{}K. Anomalies are found in all three elastic constants near the N\'eel point, but particularly large anomalies are seen for ${c}_{44}$. Ultrasonic attenuation measurements at 50 MHz for all three elastic constants are also given as a function of temperature. Both ${c}_{11}$ and ${c}_{11}\ensuremath{-}{c}_{12}$ have small attenuations confined to the immediate vicinity of ${T}_{N}$. There is a very large attenuation associated with ${c}_{44}$, and the attenuation extends over a broad temperature range. ${c}_{44}$ is seen to vary as ${T}^{\ensuremath{-}1}$ in the paramagnetic region. This behavior has led to an analysis of ${c}_{44}$ in the paramagnetic region, in terms of a coupling between elastic strains and the triplet ground state for the ${\mathrm{U}}^{4+}$ ion. The magnitude of the strain coupling parameter is deduced from the data to be 722 ${\mathrm{cm}}^{\ensuremath{-}1}$ per unit strain. Dynamical Jahn-Teller interactions are discussed as the source of this coupling. The attenuation for ${c}_{44}$ is analyzed in terms of relaxation theory and it is shown that the relaxation time deduced varies exponentially with temperature, with relaxation times of the order of ${10}^{\ensuremath{-}11}$ sec. The ${c}_{11}$, the ${c}_{11}\ensuremath{-}{c}_{12}$, and part of the ${c}_{44}$ data are discussed in relation to an Ising-model calculation of Garland and co-workers. Only qualitative statements can be made, but it seems reasonable that the ${c}_{44}$ data reflect the angular dependence of the exchange energy, particularly of the U---O---U bond. The ${c}_{11}$ and ${c}_{11}\ensuremath{-}{c}_{12}$ attenuation data below ${T}_{N}$ are qualitatively in agreement with the Landau-Khalatnikov theory of relaxation by critical scattering from long-range order fluctuations. A relaxation time of 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ sec is estimated for relaxation due to long-range order fluctuations below ${T}_{N}$. There are no such fluctuations above ${T}_{N}$.