Abstract
The short range ion-ion interactions in calcium fluoride are assumed to have the form φ ij = A ij exp(− r/ ρ). By calculating the electrostatic contribution to the elastic constants of calcium fluoride and comparing the results with the experimentally observed constants, it is determined that ρ = 0.28 × 10 −8 cm, A +- for Ca ++−F − is 3.09×10 −9 ergs, and A -- for F −−F − is 1.04 × 10 −9 ergs. These results indicate that the Ca ++−F − interaction is about ten times larger than the F −−F − interaction in this crystal. The deviation from the Cauchy relation is investigated by means of a model which allows relative motion between the sublattices making up the crystal, the model proves inadequate, however, and it is concluded that the failure of the Cauchy relation is due to a many-electron interaction between ions which cannot be approximated by a central interaction.
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