Atomic structure and vibrational properties of icosahedral α-boron and B₄C boron carbide

The Raman and infrared spectra of α-rhombohedral boron B₁₂ and of B₄C boron carbide have been determined by accurate first-principles calculations based on density-functional perturbation theory. Our results account for all the features observed experimentally, including the characteristic Raman-active mode around 530 cm^-1, which is attributed to the libration of the icosahedra. A comparison of the calculated vibrational spectra with experimental data allows the first unambiguous determination of the atomic structure of B₄C. Analysis of our data shows that the high bulk moduli of α-rhombohedral boron and of B₄C boron carbide - 220 and 240 GPa, respectively - are mainly determined by the stiff intramolecular bonding within each icosahedron. This finding is at variance with the current interpretation of recent neutron diffraction data on B₄C in terms of a postulated larger stiffness of the intermolecular bonds in icosahedral solids (inverted molecular compressibility). Our results show that icosahedral boron-rich solids should be considered as members of a new class of covalently bonded materials.