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Fig. 6.4 Panel (a) Topographic image of a gold nano-cluster deposited on a freshly cleaved HOPG graphite (the blue plane is a 10-nm cut-off introduced for graphical reason). The measured height is in agreement with the nominal diameter of the deposited clusters while the shape strongly depends on tip dimensions. The corresponding energy dissipation signal is shown in panel (d). Panel (b): The tip oscillation amplitude A0 is increased at the beginning of the scan (bottom) by increasing the piezo amplitude oscillations (the amplitude set point is held fixed along the whole scan). As a consequence the energy dissipation signal increases [panel (e)], and the particle detachment is induced. After few scan lines A0 is reduced to the optimized value for imaging and the particle movement is stopped, the scan continues as a normal image acquisition. In panels (c) and (f) the same procedure is repeated while scanning the image from the top. The topographic images which correspond to panels (a)-(c), correctly do not reveal the variation of tip oscillation amplitude while the simultaneous acquisition of the phase shift signal, transformed into energy dissipation per cycle by (6.2), makes evident the energy dissipated into the substrate by the tip-cantilever system [panels (d)-(f)]

image, is increased at the beginning of the scan (bottom) to induce particle detachment and suddenly reduced to the optimized value for imaging to stop the particle movement. In panel (c) we repeat the same procedure scanning the image from the top. Correctly, the topographic images which correspond to panels (a-c) do not reveal the variation of driver oscillation amplitude because the amplitude set-point is kept fixed, while the simultaneous acquisition of the phase shift signal makes evident the effect of increasing the piezo oscillation amplitude. In particular, the use of the phase shift signal in AM-AFM mode allows to control and to evaluate the energy released to the substrate by the tip-cantilever system. The dissipated energy per cycle corresponds to phase variations through the relation [26,27]:

where Ad is the oscillation amplitude of the piezo and A is the oscillation amplitude of the tip near the surface, usually called amplitude set-point. Q is the quality factor of the resonance curve, k is the elastic constant of the cantilever and < is the phase shift between the external driving oscillation and the tip response. It is useful to replace the piezo oscillation amplitude Ad with A0, the tip oscillation amplitude far from the surface, because this parameter can be easily measured and calibrated during the experiment and it linearly depends on Ad at the resonance (A0 = Q Ad/:

Panels (d-f) of Fig. 6.4 represent the signal Etip corresponding to the topographic images presented on panels (a-c) and reconstructed from the phase data by (6.2).

The analysis of these images puts in evidence the typical effect that characterizes the interaction between the AFM oscillating tip and loosely bonded nano-objects. On one hand, a large tip oscillation amplitude, obtained by increasing the forcing oscillator amplitude Ad, produces an increase of energy dissipation during tipsubstrate interaction and, above a given threshold, it induces the detachment of nano-clusters. On the other hand, above the threshold, a smooth and controlled movement of the nano-cluster is usually obtained most likely as a result of many subsequent detachments and small movements.

In both cases the overall dynamical behavior of these nano-objects seems to be remarkably similar to that of macroscopic systems subjected to an external mechanical excitation. First to begin a cluster movement, a given threshold force should be applied, then the object moves but the displacement is damped by sliding friction. In our experimental conditions clusters may be repeatedly tapped and eventually detached and moved by the tip which continuously oscillates and scans over the surface. So the combination of these small displacements with AFM tip movements generates a visible track that we will call trajectory in the following. According to this model, dynamic cluster manipulation can help understanding nanoscale tribol-ogy effects both for what concern the static as well as the sliding friction behavior. In the first case the energy dissipation signal can be conveniently used to characterize the onset of sliding, while in the other case the sliding distance or the overall trajectory behavior are the interesting parameters to possibly extract tribology information on kinetic friction.

Fig. 6.5 Schematic representation of shape and relative positions of the tip and cluster. The relevant dimension parameter is the effective radius R = R1 C R2. Panel (a): Rp > Rt[l— sin(y)], the cluster interacts with the conical part of the tip and we have: R1 = Rt[1 C sin(y)] tan(y) C Rt[1 — sin(y)]/[cos(y)], R2 = Rpcos(y). Panel (b) Rp < Rt[1 — sin(y)], the cluster interacts with the spherical part of the tip and we have: R1 = (^^/R1Rp)/(1 C Rp/Rt),R2 = (2pRR)/(1 C Rt/RP)

Fig. 6.5 Schematic representation of shape and relative positions of the tip and cluster. The relevant dimension parameter is the effective radius R = R1 C R2. Panel (a): Rp > Rt[l— sin(y)], the cluster interacts with the conical part of the tip and we have: R1 = Rt[1 C sin(y)] tan(y) C Rt[1 — sin(y)]/[cos(y)], R2 = Rpcos(y). Panel (b) Rp < Rt[1 — sin(y)], the cluster interacts with the spherical part of the tip and we have: R1 = (^^/R1Rp)/(1 C Rp/Rt),R2 = (2pRR)/(1 C Rt/RP)

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