Figure 1

We split the atom population between representative atoms (large circles on the figure) and constrained atoms (small gray circles). The average positions of the latter are estimated from the position of the former using finite-element interpolation. Among the representative atoms, we make a distinction between nonlocal atoms (black circles) whose energy only depends on representative atoms (as shown by the dashed circle whose radius equals the cutoff distance of the interatomic potential), and the local atoms (white circles) which interact with constrained atoms.Reuse & Permissions

Figure 2

Lattice parameter of nickel as a function of temperature using an embedded atom model (EAM) potential [22]. The melting temperature of this potential is 1478 K [23]. The QC calculation involved a cell of dimensions $200\mathrm{nm}\times 100\mathrm{nm}$ with a regular mesh containing 50 nodes. The lattice parameter was calculated as an average over the dimensions of the cell.Reuse & Permissions

Figure 3

Computational mesh at an indenter displacement of 1.5 nm at 100 K, showing details of the nonlocal, fully atomistic region under the indenter as a dissociated edge dislocation nucleates. Elements between the representative atoms are drawn, rather than the representative atoms at the element vertices, to accentuate the deformation due to dislocation motion. Dislocation nucleation occurs in two stages. A first dipole of $\frac{1}{6}⟨112⟩$ Shockley partial dislocations (SPD’s) is nucleated under the surface (1 and 2). SPD 1 propagates into the bulk while SPD 2 reaches the surface, creating a stacking fault between them as shown by the dashed line. Later a second dipole of SPD’s (3 and 4) is nucleated at the same location as the first dipole. SPD 3 propagates into the bulk to form a dissociated dislocation with SPD 1. SPD 4 moves to the surface, removing the stacking fault, and creating a step on the surface by combining with SPD 2. As temperature increases this mechanism occurs closer to the surface and on planes closer to the midline. The inset shows the entire initial mesh.Reuse & Permissions

Figure 4

Force vs indentation depth curve. The forces are averaged over a period of 0.5 ps to reduce thermal noise. The slope decreases with increasing temperature in accordance with the evolution of elastic coefficients. More interestingly, dislocation nucleation occurs at lower displacements with increasing temperature.Reuse & Permissions