Solidifying carbon @ APSmarch 2020

Elemental carbon is interesting to study thanks to its material properties and structural diversity, which ranges from nanotubes through graphite to diamond. In our study of slow-cooled carbon droplets condensed in cool-star atmospheres, computational study with semi-empirical potentials is complementary to experiment and ab initio work. We’ve used the long-range carbon bond-order potential to relax, via conjugate gradient, 1.8 g/cc liquid-like carbon tiled-cube and isolated-cluster systems with 13, 20 and 100 atoms, as well as tetrahedral nanodiamond clusters of 17, 22 and 29 atoms. Tiled-cube simulation nearest neighbor histograms show a bond defining gap between 1.7-2.0 Å. Coordination statistics then show a high percentage of sp and sp2 coordination. Ring sizes of 5 - 7 atoms form more prominently than others, with 5 and 6 atom rings especially abundant. Isolated cluster relaxations show a high amount of sp chains forming, and less ring formation than the tiled-cube simulations. We also see a volume increase for the isolated clusters, unlike comparable density functional theory (DFT) simulations. Our isolated diamond-cluster relaxations saw less surface reconstruction than with DFT.

Elemental carbon at low (ambient) pressure sublimates to vapor near 4000K, but liquid carbon is reported after laser ablation. Some meteoritic carbon particles, formed in red giant atmospheres, show a “graphene-core”/graphite-rim structure likely from super-cooled carbon droplets that nucleated graphene sheets on randomly-oriented 5-member rings. Similar core-rim particles form by slow cooling of carbon vapor in the lab (HAL-02238804). Our computations target growth of carbon rings & graphene sheets at the experimental 1.8 g/cc density estimate, by relaxing random liquid-like configurations of 13/20-atom clusters in a supercell. Inter-atom distances characteristic of covalent vs. metallic interactions (with a gap in 1.7-2 Å range) allow us to identify covalent “bonds” with small separation. Local energy minima at T = 0K show sp2 & sp coordination numbers, as in the literature. Ring sizes vary from triangle to heptagon, but pentagons are more abundant than hexagons, also consistent with previous reports. Work remains to see if pent-loops can nucleate the growth of faceted pentacones, as suggested by HRTEM imaging. Unlayered graphene sheets in a frozen matrix may be an effective diffusion barrier.