2. Experimental setups and materials

The contact mechanical methods described in this chapter all rely on atomic force microscopy. The results presented below were obtained with two different instruments operated in different environments, i.e., ambient air and ultrahigh vacuum. Measurements in ambient air were performed using an XE-100 AFM manufactured by Park Systems, Republic of Korea. Measurements in ultrahigh vacuum were performed with a VT-AFM manufactured by Omicron Nano-Technology GmbH, Germany. Figure 1 shows the respective schematics for each experimental setup. In both cases, a microfabricated cantilever with a sharp tip at its end is used to probe interaction forces with a sample surface. Depending on the physical properties of the tip and of the sample surface, various interaction forces can be probed: van der Waals, electrostatic, magnetic, and short-range forces [16]. In both experimental setups, such forces are measured using an optical beam deflection system. Thereby, a laser beam is reflected at the end of the cantilever onto a photodiode that yields an output voltage in proportion to the cantilever deflection. Typically, a four-segment photodiode is used. This enables to measure both normal and lateral forces according to.

Experimental Studies of Nanometer-Scaled Single-Asperity Contacts with Metal Surfaces http://dx.doi.org/10.5772/intechopen.72990 29

$$F\_n = \mathbb{C}\_n \text{SV}\_{AB} \text{ and } F\_l = \frac{\mathfrak{Z}}{2} \mathbb{C}\_l \frac{h}{L} \text{SV}\_{\mathbb{C}D} \tag{1}$$

where S is the sensitivity of the photodiode, which we assume to be isotropic; VAB and VCD are the sum voltages for the photodiode segments indicated in the subscripts; Cn and Cl are, respectively, the bending and torsion stiffnesses of the cantilever; h is the tip height; and L is the cantilever length.

metals has been observed to be governed by the dragging of nanoscale metallic junction giving rise to atomic stick-slip [3, 4]. The effects of surface-assembled monolayer (SAM) and oxidation on the nanotribology of Au(111) have been investigated and compared to the sliding friction behavior of an Au(111) surface [5]. It was shown that the formation of an Au neck at the Au (111)/tip interface determines the nanotribology of gold. Further, the authors have shown how the formation of such a neck can be suppressed by SAM and how the friction response of a gold surface can be switched by applying an electrochemical potential. In Refs. [6, 7], friction between Au islands and graphite was studied. AF<sup>2</sup>=<sup>3</sup> <sup>n</sup> dependence of the friction force on gold islands measured in ambient conditions was observed, where Fn is the normal force [6]. These contrasts with results in Refs. [3, 4], where almost no frictional energy dissipation was measured. In this load regime also, the authors recently showed how the shear strength of such junctions can be tuned by changing the metallurgical affinity between the contact materials [7]. Also, nanoscale wear experiments by AFM demonstrated the determinant role of plastic deformation mechanisms [8, 9]. AFM indentation has proven to be a capable experimental method to resolve the atomistic mechanisms of plastic deformation [10–14]. For example, this method has been applied to study single dislocation activation in KBr(100) single crystals [10], Cu(100) [11], and Au(111) [12–14]. There, atomistic plasticity events were observed in the shape of pop-ins, with lengths in the range of 1 Å. More recently, AFM indentation has been combined with noncontact AFM to quantitatively determine the hardness and the fundamental mechanisms of plastic deformation of Au(111) [14], and Pt(111), and Pt-based metallic glass

In this chapter, we describe three experimental methods based on atomic force microscopy and corresponding methods for statistical data analysis to determine the hardness and the mechanisms

The contact mechanical methods described in this chapter all rely on atomic force microscopy. The results presented below were obtained with two different instruments operated in different environments, i.e., ambient air and ultrahigh vacuum. Measurements in ambient air were performed using an XE-100 AFM manufactured by Park Systems, Republic of Korea. Measurements in ultrahigh vacuum were performed with a VT-AFM manufactured by Omicron Nano-Technology GmbH, Germany. Figure 1 shows the respective schematics for each experimental setup. In both cases, a microfabricated cantilever with a sharp tip at its end is used to probe interaction forces with a sample surface. Depending on the physical properties of the tip and of the sample surface, various interaction forces can be probed: van der Waals, electrostatic, magnetic, and short-range forces [16]. In both experimental setups, such forces are measured using an optical beam deflection system. Thereby, a laser beam is reflected at the end of the cantilever onto a photodiode that yields an output voltage in proportion to the cantilever deflection. Typically, a four-segment photodiode is used. This enables to measure both normal

surfaces [15].

28 Contact and Fracture Mechanics

governing wear and friction of metallic surfaces.

2. Experimental setups and materials

and lateral forces according to.

The setups illustrated in Figure 1 mostly differ in the arrangement of their piezoelectric scanners. For the measurements in UHV, a sample tube xyz-scanner was used to both scan the sample surface and control the height of the cantilever or the interaction force between tip and sample. In the setup used for measurements in ambient conditions, a linear xy nanopositioning stage was used to scan the sample surface, while a separate linear z-scanner was used to control the height of the cantilever or the interaction forces between tip and sample.

In this work, the cantilever stiffnesses were determined either according to the geometrical beam theory [17] or following the thermal noise analysis [18]. According to the geometrical beam theory, Cn <sup>¼</sup> Ewt<sup>3</sup> <sup>4</sup>L<sup>3</sup> and Cl <sup>¼</sup> Gwt<sup>3</sup> <sup>3</sup>h2L, where E is Young's modulus, G is the shear modulus, w is the width of the cantilever, and t its thickness. The length and the width of the cantilever can be measured by means of optical or electron microscopy. The thickness is usually determined from the first bending resonance frequency of the cantilever <sup>f</sup>0, with <sup>t</sup> <sup>¼</sup> <sup>2</sup> ffiffiffiffi <sup>12</sup> <sup>p</sup> <sup>π</sup> 1:8752 ffiffi r E q <sup>f</sup> <sup>0</sup>L<sup>2</sup> , where r is the mass density. Alternatively, the normal stiffness can be determined from the mean square

Figure 1. Experimental setups: instrumental setup used in (a) UHV and (b) ambient conditions; (c) TEM images of a typical diamond-coated Si single-crystalline AFM cantilever and its tip.

average of the thermal noise amplitude z<sup>2</sup> D E according to Cn <sup>¼</sup> kBT <sup>z</sup><sup>2</sup> h i, where kB is the Boltzmann constant and T the absolute temperature. The thermal noise vibrations of a cantilever beams can be recorded with the same optical beam deflection system as illustrated in Figure 1. The recorded signal consists in the superposition of all vibrational bending modes. It is important to note that the modes are not phase coherent. The identification of each mode is usually determined by fast Fourier transformation (FFT) of the time signal into a frequency spectrum (see Figure 2). In the case of the results shown in Figure 2, the power spectral density (PSD) function of the thermal noise amplitude was calculated by using the pburg function of the MATLAB software. The area below the spectra then corresponds to the mean square of the thermal noise.

Experimental records of the thermal noise are, however, limited by the bandwidth of the photoelectric detector. In our experimental setups, the bandwidth of the detector is 2 MHz. The detection of the thermal noise is, however, further limited by the electrical noise level of the photoelectric detector. This becomes critical for higher frequent modes and stiffer structure in which case the vibration amplitude may be below the noise level of the detector. In this project, the electrical noise background of the photodetector was measured independently by reflecting the laser beam onto the photoelectric detector from a smooth surface of a bulk sample of the same material as used to manufacture the measured microstructures. As shown in Figure 2(c), only the first two vibration modes of the cantilever can be identified. To account for the difficulty of analysis of higher vibration modes, the thermal noise analysis is usually restricted to the first mode. In this case, Eq. (1) can be multiplied by a weight factor:

$$\frac{3}{16} \alpha\_1^2 \left(\frac{\sin \alpha\_i + \sinh \alpha\_i}{\sin \alpha\_i \sinh \alpha\_i}\right)^2 \mathbb{C}\_n \left< \overline{z\_1^{\*2}} \right> = k\_B T \tag{2}$$

the signals shown in Figure 2 yield z<sup>∗</sup><sup>2</sup>

siders the lowest resonance mode:

oscillator.

ð∞ 0

R fð Þd<sup>f</sup> <sup>¼</sup> <sup>π</sup>A1<sup>f</sup> <sup>1</sup>Q<sup>1</sup>

harmonic oscillator (SHO):

1

Similarly, the first peak of the PSD function can be fitted with the response function for a simple

where f<sup>1</sup> and Q<sup>1</sup> are the resonance frequency and the quality factor of the first peak and A<sup>1</sup> gives the zero-frequency amplitude of the SHO response [19]. Integration of the SHO response function over all frequencies provides an estimate of the cantilever stiffness if one only con-

Figure 3 shows the first peak of the PSD function and corresponds to fitting curve using Eq. (4)

Atomic force microscopy imaging can either be performed in intermittent contact (tapping) or noncontact modes [20]. A detailed description of AFM operation in intermittent and noncontact modes is given elsewhere (see, e.g., Ref. [20]). In noncontact AFM an AFM cantilever is excited to its resonance frequency. The distance between tip and surface is kept in the range of a few

Figure 3. First peak of the PSD function shown in Figure 2 and fitted with the response function for a simple harmonic

4 1

<sup>þ</sup> f f <sup>1</sup> Q1

R fð Þ¼ <sup>A</sup>1<sup>f</sup>

f <sup>2</sup> � <sup>f</sup> 2 1 � �<sup>2</sup>

<sup>2</sup> <sup>¼</sup> <sup>z</sup><sup>∗</sup><sup>2</sup> 1 D E <sup>¼</sup> <sup>16</sup>kBT 3α<sup>2</sup> <sup>1</sup>Cn

for the same measurement data plotted in Figure 2; we obtain Cn = 0.814 N/m.

D E = 4.32 � <sup>10</sup>�<sup>21</sup> m2 at <sup>T</sup> = 293.15 K and Cn = 0.764 N/m.

Experimental Studies of Nanometer-Scaled Single-Asperity Contacts with Metal Surfaces

sinαisinhα<sup>i</sup> sinα<sup>i</sup> þ sinhα<sup>i</sup> � �<sup>2</sup>

� �<sup>2</sup> (3)

http://dx.doi.org/10.5772/intechopen.72990

(4)

31

where α<sup>1</sup> = 1.875 is the dimensionless wavenumber of the first bending vibration mode (see Ref. [18] for more details).

To determine the stiffness of the cantilever, it is thus of utmost importance to accurately calculate the mean square amplitude of the thermal noise vibrations. The fast Fourier transformation (FFT) methods, such as implemented in the pburg function, are usually applied to estimate the PSD function. Integrating the PSD function and using Eq. (2) to determine the cantilever stiffness from

Figure 2. (a and b) Recorded time-dependent amplitude signals, (c) power spectral density (PSD) function of the signal shown in (a and b) and after background electrical noise removal.

the signals shown in Figure 2 yield z<sup>∗</sup><sup>2</sup> 1 D E = 4.32 � <sup>10</sup>�<sup>21</sup> m2 at <sup>T</sup> = 293.15 K and Cn = 0.764 N/m. Similarly, the first peak of the PSD function can be fitted with the response function for a simple harmonic oscillator (SHO):

average of the thermal noise amplitude z<sup>2</sup>

30 Contact and Fracture Mechanics

D E

below the spectra then corresponds to the mean square of the thermal noise.

constant and T the absolute temperature. The thermal noise vibrations of a cantilever beams can be recorded with the same optical beam deflection system as illustrated in Figure 1. The recorded signal consists in the superposition of all vibrational bending modes. It is important to note that the modes are not phase coherent. The identification of each mode is usually determined by fast Fourier transformation (FFT) of the time signal into a frequency spectrum (see Figure 2). In the case of the results shown in Figure 2, the power spectral density (PSD) function of the thermal noise amplitude was calculated by using the pburg function of the MATLAB software. The area

Experimental records of the thermal noise are, however, limited by the bandwidth of the photoelectric detector. In our experimental setups, the bandwidth of the detector is 2 MHz. The detection of the thermal noise is, however, further limited by the electrical noise level of the photoelectric detector. This becomes critical for higher frequent modes and stiffer structure in which case the vibration amplitude may be below the noise level of the detector. In this project, the electrical noise background of the photodetector was measured independently by reflecting the laser beam onto the photoelectric detector from a smooth surface of a bulk sample of the same material as used to manufacture the measured microstructures. As shown in Figure 2(c), only the first two vibration modes of the cantilever can be identified. To account for the difficulty of analysis of higher vibration modes, the thermal noise analysis is usually

restricted to the first mode. In this case, Eq. (1) can be multiplied by a weight factor:

sinα<sup>i</sup> þ sinhα<sup>i</sup> sinαisinhα<sup>i</sup> � �<sup>2</sup>

where α<sup>1</sup> = 1.875 is the dimensionless wavenumber of the first bending vibration mode (see

To determine the stiffness of the cantilever, it is thus of utmost importance to accurately calculate the mean square amplitude of the thermal noise vibrations. The fast Fourier transformation (FFT) methods, such as implemented in the pburg function, are usually applied to estimate the PSD function. Integrating the PSD function and using Eq. (2) to determine the cantilever stiffness from

Figure 2. (a and b) Recorded time-dependent amplitude signals, (c) power spectral density (PSD) function of the signal

Cn z<sup>∗</sup><sup>2</sup> 1 D E

shown in (a and b) and after background electrical noise removal.

Ref. [18] for more details).

according to Cn <sup>¼</sup> kBT

<sup>z</sup><sup>2</sup> h i, where kB is the Boltzmann

¼ kBT (2)

$$R(f) = \frac{A\_1 f\_1^4}{\left(f^2 - f\_1^2\right)^2 + \left(\frac{f f\_1}{Q\_1}\right)^2} \tag{3}$$

where f<sup>1</sup> and Q<sup>1</sup> are the resonance frequency and the quality factor of the first peak and A<sup>1</sup> gives the zero-frequency amplitude of the SHO response [19]. Integration of the SHO response function over all frequencies provides an estimate of the cantilever stiffness if one only considers the lowest resonance mode:

$$\int\_0^\pi R(f)\,\mathrm{d}f = \frac{\pi A\_1 f\_1 Q\_1}{2} = \left< \overline{z\_1^{\*2}} \right> = \frac{16k\_B T}{3a\_1^2 C\_n} \left( \frac{\sin \alpha\_i \sinh \alpha\_i}{\sin \alpha\_i + \sinh \alpha\_i} \right)^2 \tag{4}$$

Figure 3 shows the first peak of the PSD function and corresponds to fitting curve using Eq. (4) for the same measurement data plotted in Figure 2; we obtain Cn = 0.814 N/m.

Atomic force microscopy imaging can either be performed in intermittent contact (tapping) or noncontact modes [20]. A detailed description of AFM operation in intermittent and noncontact modes is given elsewhere (see, e.g., Ref. [20]). In noncontact AFM an AFM cantilever is excited to its resonance frequency. The distance between tip and surface is kept in the range of a few

Figure 3. First peak of the PSD function shown in Figure 2 and fitted with the response function for a simple harmonic oscillator.

imaging, diamond-coated silicon single-crystalline cantilevers were used (type CDT-NCLR, manufactured by NanoSensors, Switzerland). For the cantilever used on Au(111), the bending stiffness was found to be Cn = 55 N/m. For AFM indentation of Pt(111) and Pt57.5Cu14.7Ni5.3P22.5 metallic glass, a single cantilever of the same type as on Au(111) was used, whose normal stiffness

Experimental Studies of Nanometer-Scaled Single-Asperity Contacts with Metal Surfaces

http://dx.doi.org/10.5772/intechopen.72990

33

Prior to the measurements on Au(111), the sensitivity S of the photodiode was calibrated by recording a force-distance curve on nanocrystalline diamond, consisting in an initial retraction of the z-scanner by 50 nm away from the sample surface and a subsequent series of approach and retraction by the same distance at a velocity of 0.3 μm/s. These parameters were set to avoid tip damages during contact between the diamond-coated tip and the nanocrystalline diamond sample. The sensitivity of the photodiode was then determined by fitting the repulsive part of the force-distance curve with a linear function. In contrast, before AFM indentation on Pt(111) and Pt57.5Cu14.7Ni5.3P22.5 metallic glass, the sensitivity of the photodiode is calibrated in the noncontact mode of AFM, according to Ref. [22]. Thereby, we considered a conversion factor for the vibration energy of the cantilever determined from the optically

AFM indentation measurements consisted in recording the cantilever deflection upon extension of the z-scanner of the AFM. Owing to the tilt angle of the cantilever about the sample surface, a tilt correction was applied by moving the lateral scanner by Z tan w during a vertical scanner extension Z, where w = 13 is the tilt angle [23]. In this work the extension length Z of the zscanner was varied from 10 to 160 nm in the case of Pt(111) and Pt57.5Cu14.7Ni5.3P22.5 metallic

The plastic deformation of the three samples was analyzed based on nc AFM topographical images of the remaining indents and on the force-penetration curves. Typical topographical images of indented surfaces are shown for Au(111), Pt(111), and Pt57.5Cu14.7Ni5.3P22.5 metallic glass in Figure 5. For each indent, the projected area was determined by masking the area with threshold height values. This analysis was performed with the indentation analysis function of the software package Gwyddion [24]. It is, however, important to note that due to convolution effects with the shape of the tip, the size of indents imaged by nc AFM is underestimated (this effect is more pronounced for smaller indents). Also, in the case of Pt57.5Cu14.7Ni5.3P22.5 metallic glass, the prominence of the pileups makes an accurate determination of the projected area

The force-penetration (Fn – δ) curves were calculated from the recorded force-distance (Fn – Z) curves (see Figure 6). The principle of AFM indentation relies on the fact that the surface to be indented is softer than the AFM tip. In this case, an extension of the z-scanner leads, besides a deflection D of the cantilever, to a penetration of the AFM tip into the sample surface by the

Figure 6 shows a series of nc AFM images of Au(111), Pt(111), and Pt57.5Cu14.7Ni5.3P22.5 metallic glass surfaces after AFM indentation. In the case of Au(111), all indentations were performed with the same maximal load Fn = 7 μN and a same loading rate dFn/dt = 16 μN/s. For Pt(111) and Pt57.5Cu14.7Ni5.3P22.5 metallic glass surfaces, indentation is shown that was performed with varying maximum normal force values between Fn = 0.8 μN and Fn = 6 μN.

was found to be Cn = 46 N/m.

measured deflection [17].

glass and was set to Z = 150 nm for Au(111).

more difficult and less accurate.

penetration depth δ = Z D.

Figure 4. Topography images recorded by nc AFM on (a) Au(111), (b) Pt(111), and (c) Pt57.5Cu14.7Ni5.3P22.5 metallic glass surfaces.

nanometers. During scanning over a surface, changes in tip-sample distance due to sample topography result in changes in the amplitude and in a frequency shift of the cantilever resonance. To measure topography amplitude and/or frequency shift can be tracked by a feedback loop to keep the cantilever oscillation in resonance. Contact mode imaging relies on short-range interaction forces between the tip of a cantilever and the sample surface, the nature of which can be adhesive (attractive forces) or elastic (repulsive forces). During scanning, local changes in topography yield changes in the contact force between sample and surface. In this case, topography can be measured by tracking the normal contact force with a feedback loop to keep the contact force constant.

In this chapter, we present results obtained on single-crystalline metal and on metallic glass surfaces. An Au(111) polycrystalline thin film deposited on mica by physical vapor deposition was purchased by Phasis GmbH, Switzerland, and measured in ambient conditions (see Chapters III–V). Also, a Pt(111) surface and the surface of a Pt57.5Cu14.7Ni5.3P22.5 metallic glass were prepared for measurements in ultrahigh vacuum. The (111) surface of a platinum single crystal, purchased by MaTeck, Germany, was prepared by several cycles of Ar sputtering and annealing at 1000C. This resulted in the formation of 50–100 nm wide atomically flat terraces. A Pt57.5Cu14.7Ni5.3P22.5 metallic glass master alloy was prepared according to [21] and subsequently melt-spun. The amorphousness of the as-prepared metallic glass ribbons was confirmed by X-ray diffraction (XRD) with Cu Kα radiation and differential scanning calorimetry (DSC). To remove its native oxide layer, the surface of an as-prepared metallic glass ribbon was prepared by gentle Ar sputtering for 5 min with an energy of 1 keV.

All three sample surfaces were imaged by noncontact (nc) AFM to determine their respective RMS roughness Rq (see Figure 4). For atomically flat Au(111) and Pt(111), we found Rq = 0.407 nm and 0.372 nm, respectively, caused by atomic steps between terraces and adsorbates in the case of Au(111). For the Ar-sputtered Pt57.5Cu14.7Ni5.3P22.5 metallic glass, we found Rq = 0.375 nm.
