The frequency spectrum of clusters of small ionic particles is calculated when the particle mutual interaction is described by a dipole-dipole interaction Hamiltonian. The crystallites are spheres of known bulk dielectric properties. The actual geometry of the cluster is taken into account. Clusters of increasing size (pair, triplet, quadruplet, etc.) have been solved analytically. As expected, the dipolar broadening of the frequency spectrum of (optically active or inactive) surface modes increases with cluster size and compactness. From the spectrum of few-particle clusters, one obtains the long-wavelength modes of large linear or planar aggregates of such clusters by application of the Bloch-Floquet theorem.Application is made to ir optical absorption of NiO. The present approach is intermediate between the continuum model of a structureless powder on the one hand and microscopic calculations for single microcrystals of prescribed shape on the other hand.

• Received 9 February 1976

DOI:https://doi.org/10.1103/PhysRevB.14.1715