2007/12/04 by Michael Widom, M. Widom, M. Mihalkovic +1 · 2 citations
Materials Science · Physics and Astronomy · #Boron and Carbon Nanomaterials Research #Graphene research and applications #Machine Learning in Materials Science #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.77.064113
12 pages, 5 figures
arxiv created 2007/12/04 · openalex publication_date 2008/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report that the \ensuremathβ-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 \ensuremathα-rhombohedral (red) form, implying that the \ensuremathβ phase cannot be stable at low temperatures. Furthermore, the \ensuremathβ form 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 \ensuremathβ-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 \ensuremathβ-rhombohedral structure through a phase transition at moderate temperature.