Three-Body Interactions and Short-Range Force Constants in Alkaline-Earth Fluorides

Abstract

By assuming the binding forces in CaF2, SrF2, and BaF2 to be predominantly ionic, the cohesive energies and short-range force constants are calculated on the basis of a semiempirical adaption of the Heitler–London approximation. While the model attributes the major part of short-range central force interactions to first neighbor M2+–F− pairs, the nonorthogonality of free-ion orbitals associated with second neighbor F−–F− pairs contributes significantly to three-body effects. These are estimated by multipole expansion of electrostatic potentials due to point-charge clusters representing the distribution of overlap charge throughout the lattice. A comparison with earlier Born–Mayer calculations is presented. For CaF2 the substitution of Huggins radii for Pauling radii improves the agreement of Born–Mayer theory with effective one-particle force fields inferred from the observed temperature dependence of neutron diffraction intensities. Simultaneously, this substitution brings the description closer to the present model crystal composed of essentially undeformed ions. Hence it is dubious whether the inadequacy of Pauling radii in this case provides valid evidence of deformations of crystal ions relative to their free states. However, the presently obtained 3%–4% discrepancies between predicted and observed cohesive energies probably indicate some deviation from the ideally ionic state.