Vibrations of icosahedron-based networks: Application to amorphous boron

The structure of amorphous boron is believed to be an icosahedron-based random network. The vibrational properties of such a network are studied theoretically using a Bethe lattice of connected icosahedra. The local symmetry of each icosahedron, along with the use of effective fields, greatly reduces the complexity of the problem. We show that many intraicosahedral vibrations are not affected by the intericosahedral forces. The peak with the highest frequency, which appears commonly in various spectra of amorphous boron, has been ascribed to the intericosahedral vibrations. It is therefore concluded that the intericosahedral force is stronger than the intraicosahedral force. Examination of the density of states at the low-frequency side leads to a relatively large noncentral force for the intericosahedral bond. These conclusions support the view that the intericosahedral bond has a strong covalent character, which is consistent with available experimental data. Raman scattering and infrared absorption are discussed using the shell model and the bond-polarizability model. In these calculations, the spectra are analyzed using the correlations of atomic displacements between different molecular units.