Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• excitation of the first mode of a cantilever with measurements being performed at its harmonics [37]. Another method involved clever designs such as T-shaped cantilevers [38] and inner-paddled cantilevers [39] aiming at reducing the noise impact on force reconstruction. Bimodal AFM is another addition to the

A simple method for the determination of qPlus sensor spring constants

• John Melcher,
• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2015, 6, 1733–1742, doi:10.3762/bjnano.6.177

• of the spring constant of the sensor and complications from finite tip heights. Here we combine a numerical investigation of the force reconstruction with an experimental characterization of the flexural mechanics of the qPlus sensor. Numerical studies reveal significant errors in reconstructed force

• surface and the oscillating probe tip, and the spring constant k. The reconstructed tip–sample force is given by [17]: where Ω(z) = Δω(z)/ω0. The reconstruction requires that the z-separation between the tip and sample is varied while the frequency shift is monitored. Force reconstruction using other

• methods, such as the matrix method [15], also use the same input parameters. For a more in-depth comparison of force reconstruction methods see [18]. To extract meaningful forces from Equation 1, the input parameters must be calibrated. The accepted method for trustworthy calibrations is to establish an

Capillary and van der Waals interactions on CaF₂ crystals from amplitude modulation AFM force reconstruction profiles under ambient conditions

• Annalisa Calò,
• Oriol Vidal Robles,
• Sergio Santos and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2015, 6, 809–819, doi:10.3762/bjnano.6.84

• interactions; CaF2 wetting; force reconstruction; Introduction The study of the forces and energies released when a nanometric tip and a surface are progressively brought into contact has driven much of the recent investigation in atomic force microscopy (AFM) and has allowed for the mapping of materials

•  3d, here being don = 3 nm and doff = 5 nm) [14]. The jump in Ediss should correspond to the difference between the area of the approach and retraction force curves used in the simulation [27]. Notice that the force reconstruction process according to the Sader–Jarvis–Katan formalism recovers the

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• material properties [25][26][27] in obtaining the maximum force. Simulations can generate maps that provide the estimation of the peak forces for a large variety of conditions [27][28]. The range of applicability of the force reconstruction methods has also been verified by numerical simulations [29]. The

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

• Kfir Kuchuk and
• Uri Sivan

Beilstein J. Nanotechnol. 2015, 6, 149–156, doi:10.3762/bjnano.6.14

• scans must be performed at different heights. Additionally, higher harmonic amplitudes decrease rapidly with harmonic number, limiting the number of measurable harmonics and, hence, the accuracy of force reconstruction. Some methods to amplify the signals of higher harmonics have been exercised [6][20

• and Figure 2 demonstrate the accuracy of our formulae. Figure 1a,b confirms, in the small amplitude regime, the increased sensitivity to short range interaction of force reconstruction using higher harmonics compared with the Sader–Jarvis formula. As the oscillation amplitude grows smaller compared

• Supporting Information. Supporting Information File 12: Force reconstruction. Acknowledgements This work was supported by the Israeli Science Foundation under grants 1403/12 and I-Core 1902/12.

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

• Stanislav S. Borysov,
• Daniel Forchheimer and
• David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

• force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip–surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown

• , knowledge of the geometry of cantilever is not required to reconstruct the tip–surface force. The framework proposed harnesses a force reconstruction technique inspired by the Intermodulation AFM [27] (ImAFM), which was recently generalized to the multimodal case [28]. It is worth noting that the proposed

Polynomial force approximations and multifrequency atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

• polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip–surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high

• -resolution surface-property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximative force reconstruction, where the aim is to determine model parameters that best approximate the measured force spectrum. This approximative approach is not limited

• solutions can be obtained if the model is linear in the parameters [9][17][18][19]. Such a linear model of particular interest is the polynomial, as it constitutes a general expansion of the tip–surface force. Polynomial force reconstruction methods have been proposed theoretically and tested on simulated

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• motion. At a fixed probe height h above the surface, the two force quadratures FI and FQ give only qualitative insight into the interaction between the tip and the surface [13] and most quantitative force reconstruction methods are based on a measurement of FI and FQ at different h [14][15][16][17][18

• variety of force-reconstruction techniques [14][15][16][17][18][19]. Over the past decade, the dominate paradigm was to consider FI and FQ as functions of the static probe height h only, and only one oscillation amplitude A was considered at each probe height. FI and FQ are, however, functions of both h