Ultrasonic Attenuation and Elastic Constants for Uranium Dioxide

Abstract

Elastic-constant measurements for $c_{11}$,$c_{11}-c_{12}$ and $c_{44}$ have been made over the temperature range of 4.2 to 300°K. Anomalies are found in all three elastic constants near the Néel 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 $c_{11}-c_{12}$ 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 $T^{-1\mathrm{}}$ 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 ${\mathrm{cm}}^{-1\mathrm{}}$ 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 ${10}^{-11\mathrm{}}$ sec. The $c_{11}$, the $c_{11}-c_{12}$, 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 $c_{11}-c_{12}$ 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×${10}^{-10\mathrm{}}$ sec is estimated for relaxation due to long-range order fluctuations below $T_N$. There are no such fluctuations above $T_N$.