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

The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

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

nano Online ◽

10.1515/nano.bjneah.6.14 ◽

2016 ◽

Author(s):

Kfir Kuchuk ◽

Uri Sivan

Keyword(s):

Frequency Modulation ◽

Force Spectroscopy ◽

Harmonic Force ◽

Explicit Formulae ◽

Higher Harmonic

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Computational Development of Single- and Dual-Frequency Modulation Atomic Force Spectroscopy for Ambient Air Applications

Volume 6: ASME Power Transmission and Gearing Conference; 3rd International Conference on Micro- and Nanosystems; 11th International Conference on Advanced Vehicle and Tire Technologies ◽

10.1115/detc2009-86844 ◽

2009 ◽

Author(s):

Gaurav Chawla ◽

Santiago D. Solares

Keyword(s):

Frequency Modulation ◽

Force Spectroscopy ◽

Ambient Air ◽

Interaction Force ◽

Single Frequency ◽

Dual Frequency ◽

Rapid Acquisition ◽

Atomic Force ◽

Modulation Mode ◽

Force Curves

The ability of atomic force microscopy (AFM) to acquire tip-sample interaction force curves has allowed researchers to understand the mechanical behavior of numerous materials at the nanoscale. However, AFM force spectroscopy with the most commonly used techniques can be a slow process for non-uniform samples, as it often requires the measurement to be performed at one fixed surface point at a time. In this paper we present two dynamic AFM based spectroscopy methods, one requiring operation in single-frequency-modulation mode and another using dual-frequency-modulation, which could allow a more rapid acquisition of topography and tip-sample interaction force curves. Numerical simulation results are provided along with discussions on the benefits and limitations of both.

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Drive-amplitude-modulation atomic force microscopy: From vacuum to liquids

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.3.38 ◽

2012 ◽

Vol 3 ◽

pp. 336-344 ◽

Cited By ~ 22

Author(s):

Miriam Jaafar ◽

David Martínez-Martín ◽

Mariano Cuenca ◽

John Melcher ◽

Arvind Raman ◽

...

Keyword(s):

Atomic Force Microscopy ◽

Amplitude Modulation ◽

Frequency Modulation ◽

Driving Force ◽

Oscillation Amplitude ◽

Dynamic Mode ◽

Force Microscopy ◽

Atomic Force ◽

Modulation Mode ◽

Feedback Scheme

We introduce drive-amplitude-modulation atomic force microscopy as a dynamic mode with outstanding performance in all environments from vacuum to liquids. As with frequency modulation, the new mode follows a feedback scheme with two nested loops: The first keeps the cantilever oscillation amplitude constant by regulating the driving force, and the second uses the driving force as the feedback variable for topography. Additionally, a phase-locked loop can be used as a parallel feedback allowing separation of the conservative and nonconservative interactions. We describe the basis of this mode and present some examples of its performance in three different environments. Drive-amplutide modulation is a very stable, intuitive and easy to use mode that is free of the feedback instability associated with the noncontact-to-contact transition that occurs in the frequency-modulation mode.

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Dual frequency modulation with two cantilevers in series: a possible means to rapidly acquire tip–sample interaction force curves with dynamic AFM

Measurement Science and Technology ◽

10.1088/0957-0233/19/5/055502 ◽

2008 ◽

Vol 19 (5) ◽

pp. 055502 ◽

Cited By ~ 15

Author(s):

Santiago D Solares ◽

Gaurav Chawla

Keyword(s):

Frequency Modulation ◽

Interaction Force ◽

Dual Frequency ◽

In Series ◽

Force Curves

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Observation of Dislocation DisAppearance in Aluminum Thin Films and Consequences for Thin Film Properties

MRS Proceedings ◽

10.1557/proc-505-149 ◽

1997 ◽

Vol 505 ◽

Cited By ~ 15

Author(s):

P. Müllner ◽

E. Arzt

Keyword(s):

Thin Film ◽

Thin Films ◽

Short Range ◽

Dislocation Core ◽

Interaction Force ◽

High Temperature Strength ◽

Film Properties ◽

Aluminum Films ◽

Transmission Electron ◽

Diffusive Movement

ABSTRACTDislocation structures in Al-Cu thin films have been studied by transmission electron microscopy (TEM). We have observed that the contrast of interface dislocations disappears in the electron beam. We assume that the contrast dissolution is due to the spreading of the dislocation core at the crystalline/amorphous interface or due to a diffusive movement of the dislocation through the oxide. In any case, the relaxation is assumed to be controled by irradiation induced diffusion. As a consequence, the short range stresses and at least partly also the long range stresses of the dislocations relax. This relaxation changes the interaction force between dislocations and may thus significantly affect the mechanical properties of thin films. It is concluded that interaction between interface dislocations may not be responsible for the high temperature strength of aluminum films.

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The scattering of neutrons by protons

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1935.0055 ◽

1935 ◽

Vol 149 (866) ◽

pp. 176-183 ◽

Cited By ~ 45

Keyword(s):

Short Range ◽

Wave Length ◽

Interaction Force ◽

Isotropic Scattering ◽

Fast Neutrons ◽

Exchange Force ◽

Centre Of Gravity ◽

Ordinary Type ◽

The Asymmetry ◽

Limits Of Error

1. The mass defects of the lightest nuclei, particularly the ratio between that of the diplon and the α -particle, make it very probable that the range of the interaction force between proton and neutron is very small, of the order of about 10- 13 cm. Therefore, in all experiments in which scattering of neutrons by protons has been observed, their wave-length is larger than the range of the interaction force. In these circumstances it is well known that the scattering intensity will be independent of angle for that co-ordinate system in which the centre of gravity is at rest. For much higher energies, of course, this will no longer be true and one will expect then an anisotropy in the scattered intensity. This effect will become appreciable for energies for which the wave-length is of the same order as the range of the forces. Exact measurements of the angular distribution of scattered fast neutrons would therefore afford a direct check of the assumption of a short range and an estimate of this range. The existing experiments show an isotropic scattering within the limits of error, but are not accurate enough to allow very definite conclusions. 2. The importance of such experiments is further increased by the fact that, as was pointed out by Wick, the sign of the asymmetry in the scattering depends on whether the interaction is of the ordinary type or an exchange force as proposed by Heisenberg and Majorana, and observations of the asymmetry could therefore decide this question.

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An experimental investigation of higher-harmonic wave forces on a vertical cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112000008533 ◽

2000 ◽

Vol 414 ◽

pp. 75-103 ◽

Cited By ~ 42

Author(s):

MORTEN HUSEBY ◽

JOHN GRUE

Keyword(s):

Wave Amplitude ◽

Harmonic Wave ◽

Small Scale ◽

Large Set ◽

Harmonic Force ◽

Incoming Wave ◽

Wave Tank ◽

Fully Nonlinear ◽

Cylinder Radius ◽

Higher Harmonic

First- and higher-harmonic wave loads on a vertical circular cylinder are investigated experimentally in a wave tank of small scale. The incoming waves are (periodic) Stokes waves with wave slope up to 0.24. A large set of waves which are long compared to the cylinder radius is calibrated. The first seven harmonic components of the measured horizontal force on the cylinder are analysed. The higher-harmonic forces are significantly smaller than the first-harmonic force for all wave parameters. The measurements are continued until the wave amplitude is comparable to the cylinder radius, where the second-, third- and fourth-harmonic forces become of comparable size. Comparison with existing perturbation and fully nonlinear models shows, with a few exceptions, an overall good agreement for small and moderate wave amplitude. A fully nonlinear model agrees with the experiments even up to the seventh-harmonic force for part of the amplitude range. For the large amplitudes the models mostly give conservative predictions. It is important that the distance from the wave maker to the cylinder is large in order to avoid parasitic effects in the incoming wave field. The limited width of the wave tank is not important to the results except when close to resonance.

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Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.3.27 ◽

2012 ◽

Vol 3 ◽

pp. 238-248 ◽

Cited By ~ 22

Author(s):

Joachim Welker ◽

Esther Illek ◽

Franz J Giessibl

Keyword(s):

Atomic Force Microscopy ◽

Frequency Shift ◽

Frequency Modulation ◽

Matrix Method ◽

Oscillation Amplitude ◽

Decay Length ◽

Amplitude Dependence ◽

Force Microscopy ◽

Atomic Force ◽

The Matrix

In frequency-modulation atomic force microscopy the direct observable is the frequency shift of an oscillating cantilever in a force field. This frequency shift is not a direct measure of the actual force, and thus, to obtain the force, deconvolution methods are necessary. Two prominent methods proposed by Sader and Jarvis (Sader–Jarvis method) and Giessibl (matrix method) are investigated with respect to the deconvolution quality. Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude. The matrix method exhibits spikelike features originating from a numerical artifact. By interpolation of the data, the spikelike features can be circumvented. The Sader–Jarvis method has a continuous amplitude dependence showing two minima and one maximum, which is an inherent property of the deconvolution algorithm. The optimal deconvolution depends on the ratio of the amplitude and the characteristic decay length of the force for the Sader–Jarvis method. However, the matrix method generally provides the higher deconvolution quality.

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