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

In the periodic table boron occupies a peculiar, crossover position: on the first row, it is surrounded by metal forming elements on the left and by non-metals on the right. In addition, it is the only non-metal of the third column. Therefore it is perhaps not surprising that the crystallographic structure and topology of its stable allotrope at room temperature (β-boron) are not shared by any other element, and are extremely complex. The formidable intricacy of β- boron, with interconnecting icosahedra, partially occupied sites, and an unusually large number of atoms per unit cell (more than 300) has been known for more than 40 years. Nevertheless boron remains the only element purified in significant quantities whose ground state geometry has not been completely determined by experiments. However theoretical progress reported in the last decade has shed light on numerous properties of elemental boron, leading to a thorough characterization of its structure at ambient conditions, as well as of its electronic and thermodynamic properties. This review discusses in detail the properties of β-boron, as inferred from experiments and the ab-initio theories developed in the last decade.