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The purpose of this paper is to predict the existence of novel 3D covalent ultra-hard carbon allotropes in view of synthesizing them eventually. Stability and spectroscopic characteristics of the rarely occurring tricarbon linear molecule from quantum chemistry calculations are extended to the solid state based on crystal chemistry considerations and quantum density functional theory ground state calculations letting devise rhombohedral rh-C3 (h-C9) and hexagonal h-C6 proposed as ultra-hard carbon allotropes like lonsdaleite. Two crystallographic different carbons forming linear C2-C1-C2 unit are characterized as sp3-like C2 with an angle of 106.17° smaller than ideal 109.4°, and sp1 C1. The calculated elastic constants are positive and their combinations obey the required stability criteria; furthermore they point to a strong anisotropy of the mechanical properties of the two allotropes rh-C3 (h-C9) and h-C6 with exceptionally large C33 values (1636 GPa and 1610 GPa, respectively), exceeding that of lonsdaleite (1380 GPa). The phonon dispersion curves stress furthermore the dynamical stability of the two carbon allotropes by showing positive frequencies throughout the hexagonal Brillouin zone. A significant separation between the highest frequencies of the optic modes illustrates the rigidity of the bonding within linear C3 building block and the whole structure. Both allotropes are characterized by large bulk moduli and high hardness values that are only slightly less than those of lonsdaleite and diamond. Weak metallic behavior of both new carbon allotropes were identified from electronic band structure calculations and explained by the mixed sp1-sp3 hybridizations, likewise other carbon allotropes from literature: m-C12 (sp1-sp2) and h-C18 (sp2-sp3).

John B [...]

The boron-rich boron sub-oxide rhombohedral B6O considered in B12O2 full formulation has a large O-O spacing of ~3 Å and a central vacant position that can receive interstitial atoms X, forming a central O-X-O alignment in the dodecaboron cage as observed in well-known triatomic B12 compounds as B12{C-C-C}, B12{N-B-N}, etc. Plane wave density functional theory (DFT) based calculations of unrestricted geometry relaxation of B12{O-X-O}, X = B, C, N, and O let one identify new ternary sub-oxides, all found cohesive while showing different d(X-O) distances ranging from d(B-O) = 1.95 Å down to d(O-O) = 1.73 Å with intermediate d(C-O) = 1.88 Å. The different magnitudes were assigned to the chemical affinities of X-inserts versus host oxygen with the increasing development of X-O bonding along the series with larger cohesive B12{O-O-O}. From the atom projected charge density, B presents none, while significant magnitudes are shown on C and N, the latter developing bonding with terminal oxygen atoms especially N. The presence of unpaired valence electrons leaves nonbonding charge density on X = C, N interstitial compounds, which, besides the relative isolation of the central C and N lead to the onset of magnetic moments: M(C) = 1.9 μB, and M(N) = 1 μB in a ferromagnetic ground state. Atom-resolved assessments are provided with the magnetic charge density and electron localization function electron localization function (ELF) projections on one hand and the site and spin projected density of states and the chemical bonding based on the overlap integral Sij within the COOP criterion, on the other hand.