Atomic structure of screw dislocations intersecting the $\mathrm{Au}\left(111\right)$ surface: A combined scanning tunneling microscopy and molecular dynamics study

The atomic-scale structure of naturally occurring screw dislocations intersecting a $\mathrm{Au}\left(111\right)$ surface has been investigated both experimentally by scanning tunneling microscopy (STM) and theoretically using molecular dynamics (MD) simulations. The step profiles of 166 dislocations were measured using STM. Many of them exhibit noninteger step-height plateaus with different widths. Clear evidence was found for the existence of two different populations at the surface with distinct (narrowed or widened) partial-splitting widths. All findings are fully confirmed by the MD simulations. The MD simulations extend the STM-, i.e., surface-, investigation to the subsurface region. Due to this additional insight, we can explain the different partial-splitting widths as the result of the interaction between the partial dislocations and the surface.

Figure 1

Schematic view of the interaction of a surface (top line) with different types of dislocations, each represented by the stacking-fault ribbon (gray) with two Burgers vectors indicating the partial dislocations’ orientation. Left: Original configuration without interaction. Right: Due to interaction with the surface, the partial dislocations rotate to align themselves with the Burgers vectors, i.e., toward a more screw-like orientation, thus reducing the line energy. This can lead to a widened (left) or a narrowed (right) partial-splitting width at the surface.

Figure 2

Larger-scale STM image of a single large terrace with herringbone reconstruction on the clean $\mathrm{Au}\left(111\right)$. In the top part, a monoatomic step can be seen (the lower terrace appears black). Note how the herringbone pattern aligns perpendicular to the step $(2700\mathrm{\AA }\times 3000\mathrm{\AA })$.

Figure 3

Larger-scale STM image showing a family of eight screw dislocations (highlighted with circles). Screw dislocations are easily visible even at such low lateral resolution (here ca. $12\mathrm{\AA }∕\mathrm{pixel}$) since a surface step ends at the dislocation. The herringbone reconstruction or dislocations with less pronounced footprints are not visible under these conditions. Note that all dislocations in this family have the same turning sense (clockwise) $(6000\mathrm{\AA }\times 5400\mathrm{\AA })$.

Figure 4

Left: A step segment of 1/3 of a full step height on the central terrace indicates the presence of an edge dislocation with widened partial-splitting width (indicated by circle). It has been found due to the disturbance it causes in the herringbone pattern $(1100\mathrm{\AA }\times 1100\mathrm{\AA })$. Right: Zoom in to atomic resolution. All atoms on a closed loop around the dislocation along a $⟨110⟩$ path have been marked. There is one $⟨110⟩$ vector less in the bottom line (39) than in the top line (40). Comparing to the larger-scale image (left), we believe that an intrinsic stacking fault extends to the lower left, visible as the brighter ribbon connecting to the next step. Analysis of the edge’s step profile is complicated by the presence of two U-turn points of the herringbone $(180\mathrm{\AA }\times 200\mathrm{\AA })$.

Figure 5

Lomer-Cottrell lock pinning a step. Note that the step edges of the Lomer-Cottrell lock are not frizzy at all compared to the ordinary $\mathrm{Au}\left(111\right)$ steps $(500\mathrm{\AA }\times 365\mathrm{\AA })$.

Figure 6

Besides the two clearly visible screw dislocations, the modification of the herringbone pattern indicates the presence of at least three (more or less clearly visible) edge dislocations (indicated by circles) $(3000\mathrm{\AA }\times 3000\mathrm{\AA })$.

Figure 7

Disturbed herringbone pattern in the vicinity of screw dislocations. Normally, the herringbone double lines do not end on a terrace. U-turns like those visible here are only seen close to defects (including steps) (Ref. 22) $(500\mathrm{\AA }\times 480\mathrm{\AA })$.

Figure 8

Schematic explanation of step-profile extraction procedure. Left: Example of a screw dislocation $(500\mathrm{\AA }\times 350\mathrm{\AA })$. The step disappears in the close-packed $\left[1\overline{1}0\right]$ direction. Note the herringbone double lines coming in perpendicular to the step on the upper terrace in $\left[11\overline{2}\right]$ direction and running parallel to the step on the lower terrace. Middle: First the user places straight segments along the step edge (dotted) and extending onto the terrace. Then the program calculates lines perpendicular to these segments (only some shown). Right: Resulting step-height profile for this dislocation. Note the wiggles due to the herringbone reconstruction. To analyze the plateau, one has to zoom in on the transition region.

Figure 9

The six parameters extracted from each step profile. See text for explanation.

Figure 10

(Color online) A: Sketch of the simulated system. The box is the block of atoms, the inserted partial dislocations are indicated in the middle. B: A step on the surface ends at the dislocation. C: The dislocation intersecting the surface, seen from below. Only atoms at the surface and in the dislocation core and stacking-fault ribbon are shown, all other atoms have been removed. The atoms in the stacking-fault ribbon have been colored. It is seen how the splitting width is enlarged near the surface. The partials are zigzagging slightly due to thermal fluctuations.

Figure 11

Comparison of three simulated step profiles (full lines) with corresponding measured ones. Left: Narrowed partial-splitting width. Middle: Widened partial-splitting width, plateau at around 1/3 of full step height. Right: Widened partial-splitting width, plateau at around 2/3 of full step height.

Figure 12

Distribution of the incline lengths for narrowed (left part) and widened (right part) screw dislocations. Dislocations with clearly visible plateau have been colored in lighter gray. Gaussians have been added to guide the eye.

Figure 13

Plateau height distribution for those widened dislocations that show a clear plateau (26 of the 38 widened dislocations).

Figure 14

Plateau width and partial-splitting width distributions for those widened dislocations that show a clear plateau (26 of the 38 widened dislocations).