Thermal vibration amplitudes in fluorite lattices

Abstract

Calculations are presented of the thermal vibration amplitudes of the atoms in the two fluorite structures CaF 2 and UO 2. The calculations are carried out by setting up the dynamic matrix for a rigid-ion model with effective charges and calculating the eigenvalues and eigenvectors at a number of points in reciprocal space. The computed B-factors are compared with those found by willis et al. from neutron diffraction experiments. Willis's hypothesis of a shift in the position of the anions along 〈111〉 directions is rejected : first, on the grounds that it leads to vibration amplitude values which disagree with calculated values; second, on the basis of an approximate calculation of the asymmetry of the interatomic potential in this direction and the resulting shift in position which such an asymmetry would cause.