Polar vibrations and the effective charges of the icosahedral boron solid

Abstract

Boron crystals exhibit polar vibrations, despite the fact that the crystal is comprised of the same chemical species. In this paper, occurrence of the first-order polar vibrations for the icosahedral B12 molecule and α-boron crystals is demonstrated within the harmonic approximation, by using the shell model. The dynamic effective charges are expressed by both the normal coordinates and the cartesian coordinates, while the tensor nature of the effective charges is emphasized. By use of different expressions for the effective charges, the dielectric properties of anisotropic and multi-mode polar vibrations are formulated for general crystals whose symmetry is higher than the monoclinic system. Numerical estimations have been examined for the B12 molecule and α-boron. It is shown that the effective charge of the B12 molecule is very small (≈ 10−2), while that of α-boron is enhanced by the deformation of the isosahedra. The non-central coreshell force has the dominant effect of this enhancement. Although there still remains some uncertainties in the interpretation of experimental spectra, the present calculation provides some restrictions on the allowable values of the force constants and leads to relationships between the frequencies of Raman and i.r. bands and the intensity of i.r. bands.