Figure 1

Energy $E$ and tension $f=dE/dr$ as a function of distance $r$ for the carbon dimer. Shown are results obtained using the original formulation of the potentials and the screened version (denoted by +S) that unlock the asymptotic behavior of the interaction.Reuse & Permissions

Figure 2

(a) Screening of the bond $i$-$j$: If an atom $k$ moves into the vicinity of the bond $i$-$j$ we construct an ellipsis through atoms $i$, $j$, and $k$ such that bond $i$-$j$ constitutes one of the half axes. The square root of the coefficient $C_{ijk}$ is then the ratio of the lengths of second half axis to first half axis. The $C_{ijk}$ is an empirical measure for how close atom $k$ sits to bond $i$-$j$. (b) Our screening approach distinguishes two cutoff radii. The bond $i$-$j$ always exists if $r_{ij}<r_1$. For $r_2<r_{ij}$ we compute the screening function of panel (a) and determine whether bond $i$-$j$ exists from the value of $C_{ijk}$. If an atom sits in the inner gray region where $r_1<r_{ij}<r_2$ we interpolate between the screened and unscreened cutoff function [see Eq. (11)]. For reasons of computational efficiency we furthermore turn the interaction completely off for $r_{ij}>r_2^{*}$.Reuse & Permissions

Figure 3

The bond-order $b_{ij}$ of bond $i$-$j$ that sits at the surface of an exemplary diamond $\left(110\right)$ surface depends on all neighbors. This includes neighbor $k$ that sits on an opposite surface. At sufficient separation the influence of $k$ on $b_{ij}$ needs to vanish.Reuse & Permissions

Figure 4

Cohesive stress $\sigma$ (derivative of the energies obtained by separating a bulk crystal normal to certain surfaces normalized by their area) for carbon, silicon, and 3C silicon-carbide. Here we show this function for the creation of low-index $\left(100\right)$, $\left(110\right),$ and $\left(111\right)$ surfaces. Broken lines show results for the unscreened interatomic potentials. Solid lines show their screened counterparts and DFT results. Curves are shifted vertically to be distinguishable. The $\left(111\right)$ surface is cut at the shuffle plane.Reuse & Permissions

Figure 5

Bond length $r$ before the crack tip (left three curves) and after the crack tip (right three curves) for a crack on the $\left(110\right)$ surface with a $\left[1\overline{1}0\right]$ crack front in carbon, silicon, and 3C silicon carbide as a function of the stress intensity factor $K$. The bond length $r$ is here scaled by the bond length $r_0$ in the bulk crystal, and the stress intensity factor is scaled by the factor $K_G$ obtained from Griffith's criterion using relaxed surface energies.Reuse & Permissions

Figure 6

Carbon: Fraction of $s{p}^3$ in amorphous carbon that is quenched from a $5000\mathrm{K}$ melt to $300\mathrm{K}$ with a time constant of $0.5\mathrm{ps}$. Experimental data are from Ref. 96, DFT data are from Ref. 95, and NOTB data are from Ref. 36.Reuse & Permissions

Figure 7

Silicon: Volume per atom as a function of temperature when quenching from the liquid phase to $300\mathrm{K}$ at a rate of $1\mathrm{K}{\mathrm{ps}}^{-1}$ and zero external pressure. The periodic cell contained 4001 atoms in all cases. Experimental data are taken from Ref. 101.Reuse & Permissions

Figure 8

Silicon carbide: Pair distribution functions for stochiometric silicon carbide. The final amorphous structure was obtained by quenching a box of 4000 atoms from the melt to $300\mathrm{K}$ at a rate of $1\mathrm{K}{\mathrm{ps}}^{-1}$ and zero external pressure. Curves are shifted vertically to be distinguishable. The experimental data are taken from Ref. 103.Reuse & Permissions