Control of Nanoscale Ripple Formation on Ionic Crystals by Atomic Force Microscopy

Abstract

On the most fundamental level, nanoscale wear can be considered as a process of atom-by-atom removal during mechanical contact between surfaces. But at the same time, nanoscale wear processes are often accompanied by the formation of quasi-periodic surface structures, i.e., ripples, in a self-enhancing process driven by lateral force variations. Understanding and potentially controlling the complex mechanisms of ripple formation are interesting from a general tribological point of view, since our experiments bridge the gap between the early stages of atomic scale wear to the ensuing phenomena of abrasive wear on larger length scales. In this work, we have now analyzed this phenomenon by reciprocating single asperity scratching of an atomic force microscopy (AFM) tip across a flat surface of an ionic crystal under ultrahigh vacuum (UHV) conditions. In particular, the influence of dynamic scan parameters like sliding velocity $v_{x}$ and the vertical adjustment velocity for topography changes $v_{z}$ has been explored. Our experiments show that the sliding velocity $v_{x}$ does not influence friction, wear, and the resulting surface structure, with the latter confirming numerical simulations for ripple formation. However, the vertical velocity $v_{z}$ can be used as a direct control parameter for ripple formation, where low values of $v_{z}$ seem to enhance the elastic instabilities that drive the surface patterning.

Graphical Abstract

Appendices

Appendix

A: Vertical Velocity Calibration of the Piezo Scanner

In our AFM system (Omicron UHV VT-AFM), the normal force feedback is made available by the user-interface as a single integral-gain parameter whose magnitude can be changed between 0 and 100%, while no proportional gain is applied.

To quantify the vertical movement of the piezo scanner, we have started an AFM image without the tip being in contact with the sample. In addition, the usual signal of the photo-diode related to the bending of the cantilever was disconnected from the control unit and replaced by a sinusoidal input voltage (Fig. 8a). This configuration allows to monitor the vertical velocity of the piezo tube as a function of the feedback settings. Figure 8b, c then show the obtained piezo displacement as a function of time with feedback settings of 0.05% and 10% (please note that we have manually shifted the minima values of the piezo vertical displacement to 0).

As input, we have chosen relatively high voltages. In this case, the output voltage of the initial differential amplifier is mostly saturated throughout the oscillation cycle which results in a rectangular voltage input to the integrator. The integration of this input then leads to a linearly changing piezo displacement. From the slopes of the piezo displacement curves (red lines, Fig. 8a) we can determine the maximum velocity $v_{z}$ for vertical piezo movement for a given feedback setting.

In our experiments, $v_{z}$ has been found to scale linearly with the feedback setting values (Fig. 8d). Overall $v_{z}$ thus appears to be a good parameter to characterize the feedback operation since the vertical velocity range with which the integral controller can modify the piezo position is limited by $v_{z}$ and thus by the feedback value.

Fig. 8

Typical input voltage curve and the vertical velocity of the piezo displacement at different feedback settings. a A typical sinusoidal input signal with an amplitude of 1 V and frequency of 20 Hz was used as the input of the photo-diode. In order to keep the output of photo-diode a constant, the piezo tube retracts and extends. Since a high input voltage was used, the initial differential-amplifier mostly saturates and b and c show the linearly varying piezo displacement curves as a function of time with the feedback settings of 0.05% and 10%, respectively. The vertical velocity of the piezo scanner $v_{z}$ can be obtained by linear fits as illustrated by the red solid lines. d The value of $v_{z}$ increases linearly with increasing feedback settings (Color figure online)

B: Typical Curves Recorded Both for the Trace and Retrace Scan

Figure 9a–d show the trace (blue solid lines) and retrace (red dash lines) results obtained at $v_{z}$ = 51 nm/s while Fig. 9e–h show the similar results obtained at a larger $v_{z} = 5096$ nm/s. For both values of $v_{z}$ the data has been recorded after a prominent ripple structure had already been formed. The vertical black arrows clearly indicate correlations between lateral force, tip displacement ($z_{{\text {tip}}}$) and the differential of $z_{{\text {tip}}}$ for the backwards scan. Similar to the trace analysis in Fig. 3, the tip tends to remain at a given position on the surface (or is at least slowed down considerably) while the lateral force is already building up. Only once a sufficient lateral force is reached, the tip slides up to the top of the mound. When the tip is on the way down the mound, lateral force decreases in the beginning and reaches its minimum directly after the mound, then lateral force starts to increase again.

Fig. 9

Representative scan-lines with $v_{z}=51$ nm/s (left panels) and $v_{z}=5096$ nm/s (right panels) obtained after a prominent ripple structure had already been formed for a and e normal force, b and f lateral forces recorded during the trace (blue solid lines) and retrace scan (red dash lines). c and g z-Displacement of the AFM tip ($z_{{\text {tip}}}$) and d and h The calculated differential of $z_{{\text {tip}}}$. In addition, the vertical black dash lines indicate the correlation between the different channels for the retrace scan (Color figure online)

C: Ripples on KBr and NaCl

As specified in the data sheets, the initial radius of our diamond tips is approximately 10 nm. When using another one of these tips and after scanning 0.5 h on NaCl (001) surface, the adhesion force increased from approximately 0.7 nN to 1.4 nN and we estimate that the stable tip radius is $\sim$ 14 nm by considering the fact that the adhesion force scales linearly with the contact area. The observed periodicity of the ripples on KBr for this tip was found to be approximately 40 nm which is very close to the estimated tip diameter. In addition, we also did measurements on a NaCl surface and also for this material we found the periodicity of the ripples to be roughly 40 nm. This further corroborates concepts where the distance between ripples reflects the tip radius (see Fig. 10 for more details).

Fig. 10

Typical topography images together with the corresponding height cross sections along the center of the ripples on NaCl (001) (a and c) and KBr (001) (b and d) crystal surfaces. The periodic of ripples on two crystals are nearly the same

D: Phase Velocity

By following the maxima height of ripples in Fig. 2 over many scanning cycles, we can trace the position of individual ripples along the fast scan direction as a function of scan time as shown in Fig. 11. It appears evident that the ripples move from left to right during subsequent scans, and therefore, we can calculate their corresponding phase velocities by performing linear fits (solid black lines in Fig. 11). The estimated phase velocity is $-0.11 \pm 0.03$ nm/s for $v_{z}$ = 51 nm/s and is $-0.20 \pm 0.10$ nm/s for $v_{z}$ = 5096 nm/s. Please note the negative values indicate that the ripples move from right to left. Both values are four orders of magnitude lower than the scan velocity of $v_{x} = 1250$ nm/s. In the previous work done by Gnecco et al. [42], a slow phase velocity which is two orders of magnitude lower than the scan velocity for circular ripples on the polymer surface was also observed. Although we do not have a good understanding at this point, we assume that the phase velocity may depend on the tip shape and substrate material.

Fig. 11

Ripple position as a function of scan time. The data points were derived from Fig. 2 by tracing the maxima height of ripples