Insights into the Fracture Mechanisms and Strength of Amorphous and Nanocomposite Carbon

Tight-binding molecular dynamics simulations shed light into the fracture mechanisms and the ideal strength of tetrahedral amorphous carbon and of nanocomposite carbon containing diamond crystallites, two of the hardest materials. It is found that fracture in the nanocomposites, under tensile or shear load, occurs intergrain and so their ideal strength is similar to the pure amorphous phase. The onset of fracture takes place at weakly bonded $s{p}^3$ sites in the amorphous matrix. On the other hand, the nanodiamond inclusions significantly enhance the elastic moduli, which approach those of diamond.

Figure 1

Ball-and-stick models for (a) a $n\mathrm{\text{−}}\mathrm{D}/a\mathrm{\text{−}}\mathrm{C}$ network, and (b) a pure $ta\mathrm{\text{−}}\mathrm{C}$ structure. Red (empty) spheres denote $s{p}^2$ ($s{p}^3$) sites. In (a), atoms belonging to the nanocrystal are represented by black spheres.

Figure 2

Bulk modulus as a function of $s{p}^3$ content for $a\mathrm{\text{−}}\mathrm{C}$ and $n\mathrm{\text{−}}\mathrm{D}/a\mathrm{\text{−}}\mathrm{C}$, with nanodiamonds of different diameter $d$. Calculations for bulk diamond (D) and $a\mathrm{\text{−}}\mathrm{D}$ (the fully tetrahedral WWW model of $a\mathrm{\text{−}}\mathrm{C}$) are also shown for comparison.

Figure 3

Stress versus strain curves for the various structures studied in this work. The $ta\mathrm{\text{−}}\mathrm{C}$ and $n\mathrm{\text{−}}\mathrm{D}/a\mathrm{\text{−}}\mathrm{C}$ contain 80% $s{p}^3$ sites in the amorphous matrix; the $a\mathrm{\text{−}}\mathrm{C}$ cell contains 50% $s{p}^3$ sites. Lines are fits to the data points. (a) Tensile load in the (111) direction. (b) Shear load on the $[111]$ plane in the (112) direction.

Figure 4

Ball-and-stick models for fracture in (a) single-phase $ta\mathrm{\text{−}}\mathrm{C}$ and (b) nanocomposite $n\mathrm{\text{−}}\mathrm{D}/a\mathrm{\text{−}}\mathrm{C}$, of similar densities. Beige and empty spheres denote $s{p}^2$ and $s{p}^3$ sites with no broken bonds, respectively. Dark spheres show atoms of the nanodiamond. Pink and blue spheres denote broken $s{p}^2$ and $s{p}^3$ sites, which lost at least one bond, respectively.