Vibrations of Bethe lattices with an icosahedral basis: Application to amorphous boron

A model of an icosahedron-based random-network is constructed by using a Bethe lattice, and the vibrational spectrum has been calculated. Reasonable agreement with experimental spectra from amorphous boron is obtained. Comparison to the phonon spectra of crystalline boron with a similar structure shows the importance of the correlation in the phase of displacements between adjacent icosahedra. The even and odd vibrations have distinct frequencies in the crystal case. In a random network, the difference in the phase between intermolecular bonds is averaged, so that the highest frequency band becomes both IR and Raman active.