New self-intercalated С$_{28}$,Ti@C$_{28}$, and Zn@C$_{28}$ hyperdiamonds: Crystal structure and elastic and electronic properties

New dense crystal forms of small fullerenes with unusual (combined covalent-van der Waals) atomic bonding, namely, the so-called self-intercalated hyperdiamonds (SIHDs) are suggested. The SIHD systems consist of C₂₈ fullerenes and Ti@C₂₈ and Zn@C₂₈ endofullerenes compacted into diamond lattices, in which the voids are filled with the same fullerenes. The electron density functional method in the tight binding approximation is applied to simulate the structure and to calculate the elasticity parameters, electronic characteristics, and formation energy of C₂₈, Ti@C₂₈, and Zn@C₂₈ SIHDs. It is found that the values of the bulk modulus of the SIHDs are much (2.3–2.7 times) greater than those of the initial hyperdiamonds. It is found that the C₂₈ SIHD is a semiconductor with a band gap of about 1.3 eV, whereas the Ti@C₂₈ and Zn@C₂₈ SIHDs exhibit metal-like electronic spectra. For the alternative diamond-like C₂₈ phases (hyperdiamond, hyperlonsdaleite, and SIHD), the theoretical shape of the x-ray diffraction spectra is calculated.