Imperfect Crystal and Unusual Semiconductor: Boron, a Frustrated Element

Abstract

All elements, except for helium, appear to solidify into crystalline forms at zero temperature, and it is generally assumed that the introduction of lattice defects results in an increase in internal energy. beta-Rhombohedral boron, a thermodynamically stable form of elemental boron at high temperature, is known to have a large amount of partial occupied sites, seemingly in conflict with our common knowledge. By using lattice Monte Carlo techniques combined with ab initio calculations, we find that the beta-phase is stabilized by a macroscopic amount of intrinsic defects that are responsible not only for entropic effects but also for a reduction in internal energy. These defects enable the conversion of two-center to three-center bonds and are accompanied by the presence of localized, nonconductive electronic states in the optical gap. In addition we find that the ab initio Ising model describing the partial occupancy of beta-boron has macroscopic residual entropy, suggesting that boron is a frustrated system analogous to ice and spin ice.

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

“…Effects of such complicated defects have been studied by Widom and Mihalkovič [159]. Further studies followed [160,161]. Now, we have confirmed that the presence of defects is essential for the boron crystal stability.…”

“…Now, we have confirmed that the presence of defects is essential for the boron crystal stability. Ogitsu et al have set forth an idea that the electronic structure of β-rhombohedral boron can be characterized as a frustrate system [161]. A similar idea was once aroused by Golikova in terms of "amorphous concept" [162,163].…”

Raman effect in icosahedral boron-rich solids

“…for the extraordinary strong correlation is probably the interaction of 3d atoms with the unique system of the antiferromagnetically organized, partially occupied regular boron sites B(16)-B(20), as recently described by Ogitsu et al [54,55] A systematic Raman study on the changes in the intraand inter-icosahedral force constants upon the interstitial accommodation of foreign atoms in β-rhombohedral boron is in progress.…”

“…Ogitsu et al [54,55]. describe the partial occupancies of the sites B (13) The claimed purity of our samples (Wacker, Munich) is 99.9999% for any contaminant except carbon (typically 60 ppm).…”

First-principles characterization of the structure and electronic structure ofα−Sand Rh-S chalcogenides

“…In the same spirit, and as a way to validate our methodology, we also investigated the structural properties of the ground state of pure sulfur (α-S). Sulfur is one of the very few elements for which full first-principles relaxation calculations have not been performed (boron being another element known for the difficulties that its crystalline ground state presents 6 ).…”