Body-Centered Tetragonal ${\mathbf{C}}_4$: A Viable $s{p}^3$ Carbon Allotrope

We have investigated by first principles the electronic, vibrational, and structural properties of bct ${\mathrm{C}}_4$, a new form of crystalline $s{p}^3$ carbon recently found in molecular dynamics simulations of carbon nanotubes under pressure. This phase is transparent, dynamically stable at zero pressure, and more stable than graphite beyond 18.6 GPa. Coexistence of bct ${\mathrm{C}}_4$ with $M$ carbon can explain better the x-ray diffraction pattern of a transparent and hard phase of carbon produced by the cold compression of graphite. Its structure appears to be intermediate between that of graphite and hexagonal diamond. These facts suggest that bct ${\mathrm{C}}_4$ is an accessible form of $s{p}^3$ carbon along the graphite-to-hexagonal diamond transformation path.

Figure 1

Crystal structure of bct ${\mathrm{C}}_4$: (a) three-dimentional view, (b) view along the $b$ axis, and (c) along the $c$ axis. In (c), if pairs of carbon atoms in the gray boxes are flipped across the planes denoted by dashed lines, bct ${\mathrm{C}}_4$ transforms to (d) hexagonal diamond.

Figure 2

Relative enthalpies of bct ${\mathrm{C}}_4$, $M$ carbon, hexagonal diamond, and cubic diamond with respect to graphite. Black circle, white circle, and white squares represent enthalpies of fcc solid ${\mathrm{C}}_{60}$ [21], (7,0) CNT, and (8,0) CNT [22], respectively.

Figure 3

Electronic band structures of bct ${\mathrm{C}}_4$ at 0 GPa calculated using LDA (small crosses) and GWA (large circles). Energy is measured from the valence top. The figure on the right shows the first Brillouin zone of the bct lattice.

Figure 4

(a) Simulated XRD patterns of bct ${\mathrm{C}}_4$, graphite, and $M$ carbon. (b) Experimental XRD patterns [9]. X-ray wavelength is 0.3329 Å.