  The crystal structure of boron is unique among chemical elements, highly
complex, and imperfectly known. Experimentalists report the beta-rhombohedral
(black) form is stable over all temperatures from absolute zero to melting.
However, early calculations found its energy to be greater than the energy of
the alpha-rhombohedral (red) form, implying beta cannot be stable at low
temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in
conflict with the thermodynamic requirement that entropy vanish at low
temperature. Using electronic density functional theory methods and an
extensive search of the configuration space we find a unique, energy minimizing
pattern of occupied and vacant sites that can be stable at low temperatures but
that breaks the beta-rhombohedral symmetry. Even lower energies occur within
larger unit cells. Alternative configurations lie nearby in energy, allowing
the entropy of partial occupancy to stabilize the beta-rhombohedral structure
through a phase transition at moderate temperature.
