Research ArticleMATERIALS SCIENCE

Mechanism of strength reduction along the graphenization pathway

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Science Advances  20 Nov 2015:
Vol. 1, no. 10, e1501009
DOI: 10.1126/sciadv.1501009
  • Fig. 1 PCG model obtained from liquid-quench MD simulation.

    (A) Full-size representation. (B to E) Enlargement on serpent-like GBs (B), subgrain boundaries (C), point defects (D), and amorphous domains (E). Black: bonds between two atoms that either are nonthreefold or belong to an NHR; white: other bonds; blue spheres: twofold atoms; red spheres: fourfold atoms; red lines in (B) and (C): some grain orientations; blue arrow in (C): a nonclosing Burger’s circuit around a dislocation core.

  • Fig. 2 Graphenization of the PCG model.

    (A to C) Snapshots of the system after thermal annealing at 4000 K for (A) 2.5 ns, (B) 5 ns, and (C) 25 ns. (D to I) Evolutions (with annealing time) of (D) potential energy per atom, (E) average grain size, (F) fractions of rings that are hexagons, (G) fractions of rings that are pentagons and heptagons, and (H and I) the connectivity (in terms of edge-sharing polygons) of NHRs: (H) fractions of NHRs having two NHR neighbors and (I) fractions of NHRs having one NHR neighbor and three or more NHR neighbors . The color code for (A) to (C) is the same as in Fig. 1.

  • Fig. 3 Tensile properties along the graphenization path.

    (A) Typical tensile curves for PCG before (blue) and after (red) 25 ns of thermal annealing at 4000 K [data for pristine graphene along the AC (yellow) and ZZ (green) directions are given for comparison]. (B to E) Evolutions (with annealing time) of (B) failure strain (ε*), (C) failure stress (σ*), (D) fracture energy (E), and (E) Young’s modulus (Y). Blue circles: tensile tests along the horizontal (x) direction; red squares: tensile tests along the vertical (y) direction.

  • Fig. 4 Prefracture states of PCG annealed for 5 and 25 ns (from tensile tests along y).

    (A and B) Snapshots of the systems close to failure (A: 5 ns at ε = 11.15%; B: 25 ns at ε = 7.90%) exhibiting numerous nonpropagating nanocracks in (A), as indicated by red arrows. (C to E) Enlargements of the boxed areas in (A) and (B) color-coded according to bond distance (blue, <0.15 nm; cyan, 0.15 to 0.1533 nm; green, 0.1533 to 0.1567 nm; yellow, 0.1567 to 0.16 nm; brown, 0.16 to 0.1675 nm; orange, 0.1675 to 0.175 nm; red >0.175 nm). (F) Evolution (with strain) of the number of broken sp2 bonds (nanocracks). (G) Evolution (with strain) of the average length of sp2 bonds (H, atoms forming the bonds in a hexagonal environment; D, atoms forming the bonds in a defective environment). Fracture in the two systems will eventually propagate from the nanocracks shown in (C) and (D).

  • Fig. 5 Effects of the number of PFCs on fracture properties.

    (A) Number of PFCs as a function of annealing time. (B to D) Evolutions (with the number of PFCs) of (B) fracture strain, (C) fracture stress, and (D) fracture energy.

  • Fig. 6 Initial steps in the catastrophic fracture of PCGs annealed for 5 and 25 ns (from tensile tests along y).

    (A and B) Evolutions (with nominal strain) of the length of chemical bonds involved in the fracture process for annealing times of (A) 5 ns and (B) 25 ns (dashed line: average distance at which PFCs form). (C to J) Snapshots at different strain levels [bonds are colored as in Fig. 4 (C to E); atoms (spheres) are colored according to the corresponding curves in (A) and (B)].

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/10/e1501009/DC1

    Fig. S1. Determination of Young’s modulus.

    Fig. S2. Effects of initial bond length on the appearance of PFCs.

    Fig. S3. Reversibility of PFCs.

    Fig. S4. Formation of the first PFC.

    Fig. S5. Individual fracture stress versus fracture strain plots.

    Table S1. Effects of strain rate and interatomic potential on fracture properties.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Determination of Young’s modulus.
    • Fig. S2. Effects of initial bond length on the appearance of PFCs.
    • Fig. S3. Reversibility of PFCs.
    • Fig. S4. Formation of the first PFC.
    • Fig. S5. Individual fracture stress versus fracture strain plots.
    • Table S1. Effects of strain rate and interatomic potential on fracture properties.

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