Long-Wavelength Normal Modes of Crystals with Coulomb Interactions

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Abstract
An investigation is made of the behavior of the normal modes of vibration in the long‐wavelength limit for infinite crystal lattices in which Coulomb interactions are present. The work is applicable to point ion models with any crystal structure. Rules are derived which are helpful in determining the long‐wavelength behavior of the normal modes from symmetry considerations. A study is made of the conditions under which the branches of the phonon dispersion relations will approach definite frequencies in the long‐wavelength limit. Finally, a number of examples are presented which illustrate the preceding analysis.

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