Contact stiffness, response amplitude

Fig. 13.5. Quantitative measurements of contact stiffness by UFM (a) theoretical calculation of the UFM response on Si (1) and Ge (2) surface, using the engineering parameters ESi = 164 GPa, EGe = 121 GPa, surface energy in an ambient environment y = 1 N m-1, and the manufacturer s data for cantilever stiffness kc = 2.8 nN nm-1 and tip radius Rt = 10 nm (b) experimentally measured UFM response of a silicon surface (c) schematic illustration of the differential UFM approach to the measurement of contact stiffness (Kolosov and Yamanaka 1993), from the threshold amplitude values (ai and a2) for two different normal force values (Fi and P2), the contact stiffness Seff is given by Seff = (F2 — -Fi)/(a2 — ) (d) experimental stiffness measurements... 

To minimise the friction effect, it has been proposed to use smaller amplitudes and higher frequencies [122,137]. The so-called scanning local-acceleration microscopy (SLAM) is another modification of contact-mode SFM which was implemented by vibrating the sample at a frequency above the highest tip-sample resonance (region III in Fig. 13b). In this frequency range (around 1 MHz), the cantilever response to the sample excitations becomes independent of the cantilever stiffness and depends linearly on the contact stiffness and reciprocally on the cantilever mass m (Fig. 13b) ... 

Fig. 7 Development of fatigue cracks in an epoxy/glass contact under gross slip condition (1Hz, displacement amplitude 60 xm) (from [97]). White arrows indicate the occurrence of crack initiation and propagation at the edge of the contact under the action of tensile stresses. The lateral contact stiffness, K, is essentially a measurement of the elastic response of the epoxy substrate within the contact zone. Brittle crack propagation is associated to a drop in stiffness due to the additional accommodation of the imposed displacement provided by crack opening mechanisms...

Thin hexafluoropropylene (HFP) films were deposited applying different reactor conditions by a radio frequency plasma enhanced chemical vapor deposition process onto photolithographic masked silicon surfaces, (a) depicts the crosslink density calculated from ESCA experiments (28). (b) shows the normalized amplitude response. The difference between silicon and HFP response was measured from recorded images allowing for an accurate statistical averaging, and converted into the difference in contact stiffness ks. The SFM measurements were carried in a nitrogen atmosphere (humidity < 4 %) at room temperature. Scan speed was 50 jjm/s, applied lateral modulation amplitude 3.5 nm, and modulation frequency 13 kHz. No external load was applied to the cantilever. 

As discussed in Sect. 2.2.2, FMM images can lose the material contrast when the sample stiffness exceeds the stiffness of the cantilever. In addition, the net signal contains friction effects because of the cantilever bending and the sample indentation. Furthermore, in liquid samples, capillary forces dominate the response at low frequencies [ 127]. These drawbacks can be overcome by operating the microscope above the contact resonance frequencies. In the so-called con-tact-mode scanning local-acceleration microscope the cantilever oscillates at very low amplitudes of ca. 0.1 nm which still provides strong enough contrast with respect to the mechanical properties [122]. Since the response of the canti-... 

In the contact mode, there are static modes (de-modes), and dynamic modes (ac-modes). In the former, a cantilever-type spring bends in response to the force which acts on the probing tip until a static equilibrium is established [1]. In the dynamic mode, the lever oscillates close to its resonance frequency. A distance-dependence force shifts the resonance curve. Another technique is to modulate the position of the sample at a frequency below the cantilever resonance but above the feedback-response frequency and send the response signal to a lock-in amplifier to measure the signal s amplitude and phase [4]. The lock-in output is connected to the auxiliary data acquisition channels to form an image - this approach is popularly known as force modulation (FM-mode). FM-mode imaging or force cmve is an AFM technique that identifies and maps differences in surface stiffness or elasticity. 

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