Electronic Structures and Mechanical Properties of Boron and Boron-Rich Crystals (Part I)

Boron and boron-rich crystals are hard materials, which have unique properties compared with other hard materials, such as diamond. Various ways of the arrangement of icosahedra yield many complicated crystal polymorphs and their derivatives. Although the crystals are basically hard, these are internally flexible for the mechanical and chemical properties. This flexibility is a consequence of conspiracy between the soft part and the hard part of the structure. The soft part is conveyed by the icosahedral unit, and the hard part is by the bonds connecting icosahedra. This article attempts to provide a consistent description for the unique characters of boron and boron-rich solids from the electronic-structure calculations. Recent developments of the first-principles calculation provide significant contributions to our understanding of the unusual properties of this class of materials. In particular, a combination of high-pressure experiment is successful in providing convincing evidence for our understanding, while it gives rise to unforeseen developments, such as discovery of superconductivity. Throughout analyses of many properties of boron solids, care is repeated for the effects of special arrangement of atoms and atom relaxation for those of complicated structures, which otherwise would mislead our intuitive interpretations. Special emphasize is placed on the phase stability and phase transitions at high pressure, because of recent successive discoveries of novel hard materials, such as. gamma-orthorhombic boron and diamond-like BC5 compound. The first part of this review describes the ground state of boron and boron-rich crystals. The energy gap, native defects, and phonon properties are discussed.