Lattice dynamics of calcium fluoride: Part I. Lyddane, sachs, teller formula, diffuse x-ray scattering, and specific heat

Abstract

The reported violation of the Lyddane, Sachs, Teller formula in calcium fluoride has been shown to arise from an error due to the non-application of a symmetry operation in the second neighbor fluorine-fluorine interaction in Cribier's work. By correct deduction of the force constants, the diffuse X-ray scattering measurements are shown to be in accord with the Lyddane, Sachs, Teller formula, but the specific heat calculation on this model is in disagreement with the experimental data.Reflection measurements in the infrared and dispersion of refractive index are shown to be consistent with the principal infrared absorption frequency near 40 μ and not near 51 μ as assumed in the previous model. The calculation of the specific heat using this new infrared frequency agreed with the measurements only at very low and very high temperatures.The two curves are brought into agreement by assuming that the non-Coulomb cross interaction force constant β 1 between first neighbor calcium and fluorine decrease with the wave vector. The diffuse X-ray scattering was recalculated on the model, which explained the specific heat data, and was again found to be in agreement with the Lyddane, Sachs, Teller formula. It is suggested that detailed infrared and inelastic neutron scattering studies be made on this crystal.