Contact Stiffness Measurements with an Atomic Force Microscope

Young’s modulus of phyllosilicate nanoscrolls measured by the AFM and by the in-situ TEM indentation

“…The advanced version of the bending-based test method of AFM was used with special algorithm to establish the nanobridge span length and to identify the boundary conditions of the nanobridge fixation [29]. If one end of the nanobridge rested on a protrusion and the other was in a depression, we used the results of [30] to correct the contribution to the deformation signal from an AFM probe sliding over an inclined object. The nanobridges, formed from nanoscrolls deposited on the gratings, were preliminarily studied in a Quanta 200 scanning electron microscope (FEI, USA).…”

“…Automatically, the deformation is determined by 85% of the contact part of the force curve and does not correspond to the setpoint force F SP , but to the actual force, which is the sum of F SP and F E . To eliminate the contribution from the AFM probe sliding on inclined sample areas into the signal D, we used a simplified version of the filter [30], which is reduced to multiplying the measured signal value by the square of the cosine of the angle θ between the vertical direction and the surface normal at the point of measurements. Such a correction does not affect the bending profile of horizontally located nanobridges, since it is equal to unity on them.…”

“…On a solid and flat sample, it is maximum and is considered equal to the cantilever stiffness. The amount of the signal reduction determines the stiffness of the probe-sample contact; see more details in [30]. In Fig.…”

Surface Tension and Shear Strain Contributions to the Mechanical Behavior of Individual Mg‐Ni‐Phyllosilicate Nanoscrolls

“…Figure 3 shows AFM images and bending profiles of (1) a horizontal nanobridge and (2) a rare case of a tilted nanobridge [80] having one end at the bottom of the trench. The corrected data (Figure 3e, profiles 1c and 2c in Figure 3f,g) was calculated using Equation (5) (Experimental Section),while the raw data (Figure 3d, profiles 1r and 2r in Figure 3f,g) was made by multiplying δ by 0.85 −1 (because Bruker algorithm treats only 85% of the contact part of the force curve, Figure 3b).…”

“…• The use of rigid Si/SiO 2 substrates with periodic trenches and a roughness of the horizontal sections of about 1 nm; • Taking account of AFM tip slipping when scanning a cylindrically-shaped nanobridge and testing strongly tilted particles (with one end situated in the trench) by using the correcting filter; [80] • Carrying out a comparative analysis of two deformation profiles with span lengths l determined based on topography (l t ) or deformation (l s ) signal data images; [81] • Determining boundary conditions using the original algorithm [81] for every nanobridge; • Testing double span nanobridges in order to check the reproducibility of the Young's modulus values; • Implementation of density functional theory (DFT) for the Young's modulus calculation.…”