β-Rhombohedral Boron: At the Crossroads of the Chemistry of Boron and the Physics of Frustration

Proton disorder in ice and spin disorder in magnetic pyrochlore materials may be described with the same type of Hamiltonian used to describe defects in boron, that of a ferromagnetic Ising model on corner-sharing tetrahedra. Within a nearest neighbor-interaction approximation, this Hamiltonian has an exactly degenerate and disordered ground state with a macroscopic amount of residual entropy. First, without the vacancies corresponding to B13, the valence electrons will occupy globally anti-bonding electronic states. Second, the vacancy sites are in a triangular configuration, and the HOMO band has locally anti-bonding character within the triangle. These sites have globally bonding character, such as that between B13 and its surrounding atoms. The large kinetic barrier is a serious obstacle for the experimental determination of phase boundaries. Direct mapping of the phase boundaries in high-pressure and temperature experiments has not been successful at low pressure and temperature due to slow kinetics.