Anharmonic vibration in fluorite structures

The high-temperature neutron diffraction measurements of UO2 and CaF2 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 Vj(r) = V0,j + ½αj(x2 + y2 + z2) + βjxyz + 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 αj and βj parameters in both UO2 and CaF2, and their ability to reproduce the experimental observations over a wide range of elevated temperature is demonstrated. The parameters derived for CaF2 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 Ca2+ and F- cannot reproduce the physical behaviour of this system.