Exchange‐Quadrupole Forces and Phonon Dispersion for the Simplest Cubic Crystals

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Abstract
Systematic discrepancies between the experimentally observed phonon dispersion law and that predicted by the theory of the lattice with polarizable ions in the short wavelength region are discussed. The discrepancies appear to be due to the quadrupole deformation of ions, primarily of anions. The adiabatic lattice potential which depends on the displacements, uls, on the dipole moments, P1s, and on the quadrupole moments, Qlsαβ, of all the atoms is determined and equations for the lattice vibrations are derived. Besides the Coulomb forccs the adiabatic potential includes the short‐range forces which are due to the alteration of the exchangc interaction of neighboaring atoms with the quadrupole deformation of one of them. Equations for the Fourier components of dynamic variables using the Ewald transformation for sums of the Coulomb potential of dipole and quadrupole interactions are given.

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