Ultrasonic Attenuation and Elastic Constants for Uranium Dioxide

Elastic-constant measurements for c₁₁,c₁₁-c₁₂ and c₄₄ have been made over the temperature range of 4.2 to 300^∘{}K. Anomalies are found in all three elastic constants near the N\'eel point, but particularly large anomalies are seen for c₄₄. Ultrasonic attenuation measurements at 50 MHz for all three elastic constants are also given as a function of temperature. Both c₁₁ and c₁₁-c₁₂ have small attenuations confined to the immediate vicinity of TN. There is a very large attenuation associated with c₄₄, and the attenuation extends over a broad temperature range. c₄₄ is seen to vary as T^-1 in the paramagnetic region. This behavior has led to an analysis of c₄₄ in the paramagnetic region, in terms of a coupling between elastic strains and the triplet ground state for the U⁴⁺ ion. The magnitude of the strain coupling parameter is deduced from the data to be 722 cm^-1 per unit strain. Dynamical Jahn-Teller interactions are discussed as the source of this coupling. The attenuation for c₄₄ 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 sec. The c₁₁, the c₁₁-c₁₂, and part of the c₄₄ 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 c₄₄ data reflect the angular dependence of the exchange energy, particularly of the U---O---U bond. The c₁₁ and c₁₁-c₁₂ attenuation data below TN 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 sec is estimated for relaxation due to long-range order fluctuations below TN. There are no such fluctuations above TN.