Research ArticleMATERIALS SCIENCE

Dislocation behaviors in nanotwinned diamond

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Science Advances  21 Sep 2018:
Vol. 4, no. 9, eaat8195
DOI: 10.1126/sciadv.aat8195
  • Fig. 1 Schematics of the nt-diamond microstructure, slip modes, and the computational model.

    (A) A polycrystalline nt-diamond microstructure consists of subparallel nanoscale twin lamella embedded in submicrometer-sized grains. Grains have random orientations. (B) Three dislocation slip modes in nt-diamond: slip transfer (slip mode I), confined layer slip (slip mode II), and paralleled to TB slip mode (slip mode III). (C) Computational model for studying interactions between dislocations and a twin plane. (D) The local enlarged drawing for the purple rectangle in (C) showing detailed dislocation structure, where the blue line is the dislocation line.

  • Fig. 2 Interactions between dislocations and the twin plane by slip transfer mode in nt-diamond.

    (A) Glide-set 0° perfect and glide-set 30° partial dislocations reacting with the twin plane. (B) Reaction heat and activation energy of interaction in (A). (C) Glide-set 60° perfect and glide-set 90° partial dislocations reacting with the twin plane. (D) Reaction heat and activation energy of reactions in (C). (E) Shuffle-set 0° and 60° perfect dislocations reacting with the twin plane. (F) Reaction heat and activation energy of reactions in (E).

  • Fig. 3 CRSSs for dislocation motion for the three different slip modes in nt-diamond.

    (A) The CRSS for the slip transfer and the confined layer slip mode. A dislocation pileup model is used for the slip transfer mode, and principles of virtual work are used for the confined layer slip mode. (B) CRSS for the slip parallel to the twin plane. Hall-Petch effect by decreasing grain size is used to evaluate CRSS for dislocation slip within the twin plane. The inset is the activation energy as a function of resolved shear stress for dislocation slip in the twin plane and slip in crystal’s interior.

  • Fig. 4 Calculated hardness compared to experimental observations for nt-diamond as a function of twin thickness.

    (A) The population of yielded grains as a function of uniaxial stress, based on the Sachs model, which is illustrated schematically in the inset. When the proportion of yielded grains reaches 90%, the corresponding uniaxial stress is defined as the yield stress. The curve is an example for an nt-diamond sample with twin thickness of 5 nm and grain size of 20 nm. (B) Calculated hardness of nt-diamond as a function of twin thickness compared to experimental ones (8, 9). The inset shows the proportion of yielded grain by different slip modes at grain size of 20 nm.

  • Table 1 Calculated reaction heat, activation energy, and barrier strength for dislocation reactions by slip transfer mode.
    Types of dislocationDislocation reactions equationReaction heat (eV/Å)Activation energy (eV)Barrier strength (GPa)
    Glide-set 30° partial
    dislocation
    Bα → Bδ + δα1.56.953.7
    Bα → BTαT + αTα2.46.752.1
    Glide-set 90° partial
    dislocation
    αD → Aδ03.937.2
    αD → αδ +αTδ + DTαT2.94.649.3
    Glide-set 0° perfect
    dislocation
    BC → Bδ + δC−0.96.243.7
    BC → BTαT + αTCT−0.910.231.7
    Bα + αC → Bδ + δC06.953.7
    Bα + αC → BTαT + αTCT06.752.1
    Glide-set 60° perfect
    dislocation
    BD → Bδ + δD2.79.955.3
    Bα + >αD →αTDT + BTαT + 2αTδ3.06.752.1
    Shuffle-set 0° perfect
    dislocation
    BC → BC07.824.1
    BC → BTCT08.219.2
    Shuffle-set 60° perfect
    dislocation
    BD → BC + CD7.116.347.7
    BD → BTCT + CD7.116.347.7

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaat8195/DC1

    Fig. S1. Dislocation energy as function of supercell size.

    Fig. S2. Schematic of process for dislocation reaction with twin plane.

    Fig. S3. Calculated shear stress–dependent activation energy of dislocation reaction with twin plane.

    Fig. S4. Hardness of nt-diamond at grain size of 125 nm.

    Table S1. Calculated kink energy Ef and activation energy Wm of kink migration for dislocation reactions by slip transfer mode.

    Table S2. Fitted parameters used in Eq. 10.

    Table S3. The parameters used to calculate the critical resolved shear stress of slip transfer mode, confined layer slip mode, and paralleled to twin plane slip mode.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Dislocation energy as function of supercell size.
    • Fig. S2. Schematic of process for dislocation reaction with twin plane.
    • Fig. S3. Calculated shear stress–dependent activation energy of dislocation reaction with twin plane.
    • Fig. S4. Hardness of nt-diamond at grain size of 125 nm.
    • Table S1. Calculated kink energy Ef and activation energy Wm of kink migration for dislocation reactions by slip transfer mode.
    • Table S2. Fitted parameters used in Eq. 10.
    • Table S3. The parameters used to calculate the critical resolved shear stress of slip transfer mode, confined layer slip mode, and paralleled to twin plane slip mode.

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