Minimum Threshold for Incipient Plasticity in the Atomic-Scale Nanoindentation of Au(111)

The formation of the smallest permanent indentation in a Au(111) surface is studied by scanning tunneling microscopy and atomic force microscopy in ultrahigh vacuum. The 9.5 nm radius W(111) indenter was characterized in situ by field ion microscopy. Elastic and plastic indentations are identified both in the residual impression image and by features in their force-displacement curves such as the sink-in depth, pop-ins, and hysteresis energy. Plasticity is best identified quantitatively in the force-displacement curves by the sink-in depth. The minimum of plastic damage producible in the substrate is associated with an energy budget of $\sim 70\mathrm{eV}$.

Figure 1

(a) FIM image of the W(111) indenter (5.5 kV tip voltage); (b) ball model of a W(111) with a 9.5 nm radius and Au(111) substrate to scale; (c) Au(111) terrace before and (d) after a $5\times 5$ indentation array with 20 nm spacing between indents (20 pA, $-0.05\mathrm{V}$ sample bias). Bolded numbers indicate plastic sites; italicized numbers indicate elastic sites.

Figure 2

Force and current recorded during indentation at elastic sites, (a) and (b), and plastic sites, (c) and (d). Loading and unloading directions are indicated by arrows. Additional arrows in (c) and (d) point to pop-in discontinuities in the force.

Figure 3

(a) Hysteresis energy obtained by integrating force-displacement curves. (b) Cumulative pop-in force and displacement obtained by summing pop-in events in each curve. (c) Sink-in depth between loading and unloading curves at 10 nN. Elastic sites are indicated by additional circles.

Figure 4

Cumulative distribution of the force measured at the first pop-in and corresponding maximum shear stress calculated from the Hertz model.