Ab initio prediction of superdense tetragonal and monoclinic polymorphs of carbon

The design and synthesis of three-dimensional denser carbons are one of the hot issues in condensed matter physics because of their fascinating properties. Here we identify by ab initio calculations several tetragonal and monoclinic polymorphs of carbon that adopt the $t32, t{32}^{*}, m32$, and $m{32}^{*}$ structures in $P\overline{4}{2}_{1}c, P{4}_3{2}_{1}2, P{2}_1/c$, and $C2$ symmetry, respectively. These carbon polymorphs have large 32-atom unit cells in all-$s{p}^3$ bonding networks comprising five- and six-membered rings that are dynamically stable, as verified by a phonon mode analysis. Electronic band structure calculations show that they are insulators with band gaps in the range of 5.19–5.41 eV, close to the calculated band gap of 5.34 eV for diamond. Remarkably, these carbon phases possess an extremely high atom number density exceeding that of diamond. The present results establish different types of carbon phases and offer insights into their outstanding structural and electronic properties.

Figure 1

Crystalline structures of (a) $t32$, (b) $t{32}^{*}$, (c) $m32$, and (d) $m{32}^{*}$ carbon polymorphs in $P\overline{4}{2}_{1}c, P{4}_3{2}_{1}2, P{2}_1/c$, and $C2$ symmetry, respectively.

Figure 2

(a) The energy-volume and (b) the enthalpy-pressure relations for $t32, t{32}^{*}, m32$, and $m{32}^{*}$ carbon compared to BC12, BC8, BT8, $R$8, ST12, bct4, diamond, and graphite. The enthalpy is measured relative to the value for cubic diamond.

Figure 3

(a) Simulated XRD patterns for $t32, t{32}^{*}, m32$, and $m{32}^{*}$ carbon compared to graphite, diamond, bct4, $R$8, BT8, BC8, and ST12 carbon at 0 GPa. An x-ray wavelength of 1.5406 Å is used with a copper source. (b) Experimental XRD patterns for Fe-catalyzed carbon black heat treatment at $1400{}^{\circ }\mathrm{C}$ [35]. Symbols: $\text{g}=\text{graphite}, \text{cd}=\text{cubic}$ diamond, $▾$ denotes the peak for $n$-diamond.

Figure 4

Calculated phonon band structures (a)–(d) and electronic band structures (e)–(h) for $t32, t{32}^{*}, m32$, and $m{32}^{*}$ carbon at 0 GPa.