Computational discovery of a new rhombohedral diamond phase

We identify by first-principles calculations a new diamond phase in $R\overline{3}c$ ($D_{3d}^6$) symmetry, which has a 16-atom rhombohedral primitive cell, thus termed R16 carbon. This rhombohedral diamond comprises a characteristic all-$s{p}^3$ six-membered-ring bonding network, and it is energetically more stable than previously identified diamondlike six-membered-ring bonded BC8 and BC12 carbon phases. A phonon mode analysis verifies the dynamic structural stability of R16 carbon, and electronic band calculations reveal that it is an insulator with a direct band gap of 4.45 eV. Simulated x-ray diffraction patterns provide an excellent match to recently reported distinct diffraction peaks found in milled fullerene soot, suggesting a viable experimental synthesis route. These findings pave the way for further exploration of this new diamond phase and its outstanding properties.

Figure 1

(a) The primitive rhombohedral crystalline structure of R16 carbon in $R\overline{3}c$ ($D_{3d}^6$) symmetry with the lattice parameters of $a=4.492$ Å and $\alpha =90.{87}^{\circ }$. There are two inequivalent crystallographic sites, occupying the $4c(0.4049,0.4049,0.4049)$ and $12f(0.5929,0.0558,0.8809)$ positions, denoted by ${\mathrm{C}}_1$ (black) and ${\mathrm{C}}_2$ (red), respectively. (b) Structure of R16 carbon viewed along the [111] direction. (c), (d) Polyhedral views of BC8 carbon. (e), (f) Polyhedral views of the crystal structure of supercubane [38].

Figure 2

The total energy as a function of volume per atom for R16 carbon in comparison with graphite, diamond, bct-${\mathrm{C}}_4$, BC8, supercubane, and BC12 carbon. The dashed line indicates the energy level of the linear carbyne chain.

Figure 3

(a) Simulated XRD patterns for diamond, graphite, BC8, BC12, and R16 carbon. (b) Experimental XRD patterns for the milled fullerene soot using steel media [41]. The x-ray wavelength is 1.5406 Å with a copper source.

Figure 4

Energy fluctuation of R16 carbon in AIMD simulations at 2000 K. Inset structures depict the structural changes at steps of 1000 and 4000 during the simulations.

Figure 5

(a) Phonon band structures and phonon density of states (PDOS) for R16 carbon. The highest vibrational frequency is about 1400 ${\mathrm{cm}}^{-1}$. (b) Electronic band structures and density of states (DOS) for R16 carbon. The direct band gap is 4.45 eV at the $\mathrm{\Gamma }$ point. The calculations are performed using LDA method at zero pressure.