Figure 1

(Color online) Simulations of a low-density (1.5 g/cc) amorphous carbon precursor system after 200 ps of high-temperature annealing which show the effect of the periodic boundary conditions of the simulation cell on the fully evolved structure. The development of extended $s{p}^2$ ordering is highlighted by rendering as surfaces all rings in which the atoms are exclusively $s{p}^2$ bonded. (a) 4096-atom amorphous carbon $\left(a\text{-C}\right)$ precursor generated by liquid quenching at 1.5 g/cc. (b) (0D, isolated cluster) Final structure after annealing of the system in panel (a) at 4000 K for 200 ps with all three periodic boundary conditions removed. (c) (1D, nanowire) Same as (b) but with two periodic boundary conditions removed. (d) (2D, freestanding sheet) Same as (b) but with one periodic boundary condition removed and an annealing temperature of 3500 K. (e) (3D, bulk) Same as (b) but with all three periodic boundary conditions intact and annealing temperatures of 4000 K (left panel) and 3500 K (center and right panels). In the color version of this figure (online), some additional structural information not critical to the discussion is indicated: Atoms are colored by coordination: red $\left(sp\right)$, green $\left(s{p}^2\right)$, and blue $\left(s{p}^3\right)$. Ring surfaces are colored by ring length: blue (5), green (6), red (7), and yellow (8).Reuse & Permissions

Figure 2

Fraction of $s{p}^2$ atoms in the main cluster as a function of annealing time for 1.5 g/cc systems annealed at 4000 K under 0D, 1D, 2D, and 3D periodic boundary conditions.Reuse & Permissions

Figure 3

Normal vector orientation plot (see Sec. 2A) for $s{p}^2$ rings in a 1.5 g/cc 3D system annealed for 200 ps at (a) 3500 K [structure shown in Fig. 1e, center and right panels], and (b) 4000 K [structure shown in Fig. 1e, left panel].Reuse & Permissions

Figure 4

(Color online) Void fraction as a function of density for systems simulated under 3D periodic boundary conditions at a temperature of 5000 K and after rapid quenching to 300 K. At densities below 2.5 g/cc, the simulated systems have a nonzero void volume. Also shown are the void fractions for 1.5 and 2.5 g/cc systems annealed for 200 ps at 3500 K (open symbols). At 1.5 g/cc, the void fraction increases on annealing, while at 2.5 g/cc the void fraction remains close to zero. A probe and exclusion radius of $r_{\text{excl}}=1.3\text{Å}$ are used to calculate the void volume (see text).Reuse & Permissions

Figure 5

(Color online) Fraction of $s{p}^2$ atoms in the main cluster as a function of annealing time for 1.5, 2.5, and 3.0 g/cc systems annealed at 3500 K (solid line) and 4000 K (dashed line) under 3D periodic boundary conditions.Reuse & Permissions

Figure 6

(Color online) Simulation of a 2.5 g/cc amorphous carbon precursor system after 200 ps of annealing at 3500 K with 3D periodic boundary conditions on the simulation cell. The cross section in the right-hand panel shows the layered structure within some of the graphitelike domains. Legend for color version of this figure (online) is same as for Fig. 1.Reuse & Permissions

Figure 7

Normal vector orientation plot for $s{p}^2$ rings in a 2.5 g/cc system annealed at (a) 3500 and (b) 4000 K, under 3D periodic boundary conditions for 200 ps. The construction of this plot is the same as in Fig. 3.Reuse & Permissions

Figure 8

(Color online) Simulations of a 3.0 g/cc amorphous carbon precursor system: (a) as-quenched structure and (b) after 200 ps of annealing at 3000 K with 2D periodic boundary conditions on the simulation cell [same scale as (a)]. Legend for color version of this figure (online) is same as for Fig. 1.Reuse & Permissions

Figure 9

The highly curved $s{p}^2$ sheet structure we observe in annealed low-density systems is very similar to a hypothetical structure for glassy carbon proposed by Harris (Ref. 44). (a) A $19\text{Å}$ section of the 1.5 g/cc system annealed at 3500 K for 200 ps under 3D periodic boundary conditions. Several periodic images are included to highlight the medium- and long-range structure. Only bonds are shown, where bonds are drawn between atoms closer than $1.85\text{Å}$. Bonds crossing the boundaries of the section are not drawn. (b) Hypothetical fullerene-related structure proposed for glassy carbon by Harris (Ref. 44). From P. J. F. Harris, “Fullerene-related structure of commercial glassy carbons,” Philos. Mag. 84, 3159 (2004). Copyright 2004. Reprinted by permission of Taylor & Francis Group (http://www.informaworld.com).Reuse & Permissions