Abstract
The high-temperature neutron diffraction measurements of UO 2 and CaF 2 made recently by Willis are examined by means of the generalized formulation of the structure factor which recognizes the antisymmetric properties of atoms occupying non-centrosymmetric lattice sites. Numerical analysis of the neutron data in terms of an anharmonic vibration formalism developed for effective one-particle potential fields of the type V j (r) = V 0 , j + ½ α j ( x 2 + y 2 + z 2 ) + β j xyz + quartic terms shows that certain unusual features of the observations are readily accounted for by the antisymmetric ( β ) components associated with the tetrahedral point symmetry of the anionic sites. Values are derived for the α j and β j parameters in both UO 2 and CaF 2 , and their ability to reproduce the experimental observations over a wide range of elevated temperature is demonstrated. The parameters derived for CaF 2 are compared with theoretical estimates obtained from an Einstein-type model of the vibrating lattice, using the various expressions for the interionic interaction in fluorite that have been proposed by Benson & Dempsey. Despite evident limitations in this model, it is possible to conclude that the Pauling radii for Ca 2+ and F - cannot reproduce the physical behaviour of this system.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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