The high-pressure phase of boron, γ-B28: Disputes and conclusions of 5 years after discovery

Abstract

γ-B28 is a recently established high-pressure phase of boron. Its structure consists of icosa-hedral B12 clusters and B2 dumbbells in a NaCl-type arrangement (B2)δ+(B12)δ− and displays a significant charge transfer δ ∼ 0.5–0.6. The discovery of this phase proved to be essential for the understanding and construction of the phase diagram of boron. It was first experimentally obtained as a pure boron allotrope in early 2004 and its structure was discovered in 2006. This paper reviews recent results and contentious issues related to the equation of state, hardness, putative isostructural phase transformation at ∼40 GPa, and debates on the nature of chemical bonding in this phase. Our analysis confirms that (a) calculations based on density functional theory give an accurate description of its equation of state, (b) the reported isostructural phase transformation in γ-B28 is an artifact, (c) the best estimate of hardness of this phase is 50 GPa, (d) chemical bonding in this phase has a significant degree of ionicity. Apart from presenting an overview of the previous results within a consistent view grounded in experiment, thermodynamics and quantum mechanics, we present new results on Bader charges in γ-B28 using different levels of quantum-mechanical theory (GGA, exact exchange, and HSE06 hybrid functional), and show that the earlier conclusion about a significant degree of a partial ionicity in this phase is very robust. An additional insight into the nature of the partial ionicity is obtained from a number of boron structures theoretically constructed in this work.