Figure 1

(Color online) The failure of the original Brenner potential. (a) A crack on a diamond (111) plane with a [110] crack front shows crack tip blunting and does not propagate at 10% strain in contrast to common experimental wisdom. (b) Quasistatically pulling a $5,5$ carbon nanotube leads to ductile behavior whereas quantum calculations and low-temperature experiments predict brittle fracture. (c) Diamond transforms to graphite under shear loading. In addition to underestimating the necessary shear stress, the Brenner potential shows the wrong transition behavior in one of the loading directions. DFT calculations predict a different rotation of the graphene planes after the transition for the “positive” (left) and “negative” (right) shear direction. Insets: Results obtained using the modifications presented in this paper.Reuse & Permissions

Figure 2

Cutoff formulation for the bond $ij$. (a) Four cutoff radii are used. The interaction is always computed if $r_{ij}<r_1$. For $r_1<r_{ij}<r_4$ screening is considered. The inner gray region switches between these two cases and the outer gray region smoothly zeroes the potential. (b) Screening of the bond $ij$: Ellipses (dashed-line) are constructed through all third atoms $k$ with $i\text{−}j$ being the first half axis. The coefficient $C_{ijk}$ is then given by the square of the fraction of the second half axis to the first half axis. For further details see text.Reuse & Permissions

Figure 3

(Color) Properties of quenched a-C. (a) Hybridization (fraction of ${\text{sp}}^3$ sites) as a function of density for a-C. (b) Ring statistics of the a-C samples at a density of $2.9\text{g}/{\text{cm}}^3$. Inset: Pair distribution for the same samples. The data has been averaged over ten consecutive runs. 512 atom samples are used in the Brenner and DFTB calculations while the DFT data was computed using 64 atom samples (Ref. 21). The hybridization was determined by counting neighbors within a cutoff of $1.85\text{Å}$.Reuse & Permissions

Figure 4

(Color) Crack propagation on the diamond (110) plane. Solid lines give the bond length of the bond behind the crack tip for an increasing stress intensity factor (loading). For a decreasing stress intensity factor (unloading) the bond length of the bond in front of the crack tip is displayed. These are the dashed lines. The stress intensities are increased in steps of $0.05K_G$. For more information on the DFT calculations and the specific crack configuration used see Refs. 25, 26. (a) $\left[1\overline{1}0\right]$ crack front (b) [001] crack front. Inset: Cohesive force function $\partial E_{110}\left(z\right)/\partial z$ of the unrelaxed diamond (110) surface as a function of surface separation $z$.Reuse & Permissions