Nonlinear Detection of Ultrasonic Vibrations in an Atomic Force Microscope

Kolosov, Oleg; Yamanaka, Kazushi

doi:10.1143/jjap.32.l1095

Cited by 300 publications

(199 citation statements)

References 7 publications

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“…Although beating and mixing are two intrinsically different effects that are classified by the type of mixer and their Fourier analyses, we will fully counterintuitively demonstrate that beating even dominates mixing, if the mixer is of higher order than quadratic! To illustrate the importance of beating in heterodyne measurements, we use the example of heterodyne force microscopy (HFM) [8][9][10] , as it represents a model system with a highly nonlinear mixing element (much higher order than quadratic). HFM enables the non-destructive imaging below a surface with nanometre resolution using an atomic force microscope [11][12][13][14][15][16][17][18][19] .…”

Section: Resultsmentioning

confidence: 99%

Beating beats mixing in heterodyne detection schemes

Verbiest

Rost

2015

Nat Commun

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Heterodyne detection schemes are widely used to detect and analyse high-frequency signals, which are unmeasurable with conventional techniques. It is the general conception that the heterodyne signal is generated only by mixing and that beating can be fully neglected, as it is a linear effect that, therefore, cannot produce a heterodyne signal. Deriving a general analytical theory, we show, in contrast, that both beating and mixing are crucial to explain the heterodyne signal generation. Beating even dominates the heterodyne signal, if the nonlinearity of the mixing element (mixer) is of higher order than quadratic. The specific characteristic of the mixer determines its sensitivity for beating. We confirm our results with both a full numerical simulation and an experiment using heterodyne force microscopy, which represents a model system with a highly non-quadratic mixer. As quadratic mixers are the exception, many results of previously reported heterodyne measurements may need to be reconsidered.

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Section: Resultsmentioning

confidence: 99%

Beating beats mixing in heterodyne detection schemes

Verbiest

Rost

2015

Nat Commun

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“…12, 13,14 A chapter on its own deserves subsurface imaging through the detection of the elastic properties of materials. Ultrasonic Force Microscopy (UFM) is a technique invented by Kolosov and Yamanaka,15 resulting from an adaption of Atomic Force Microscopy (AFM) working in Contact Mode (CM). It was initially proposed and developed in order to overcome the limits of Force Modulation Microscopy (FMM).…”

Section: Introductionmentioning

confidence: 99%

Subsurface imaging of two-dimensional materials at the nanoscale

et al. 2017

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Scanning probe Microscopy (SPM) represents a powerful tool that, in the past thirty years, has allowed one to investigate material surfaces in unprecedented ways at the nanoscale level. However, SPM has shown very little power of depth penetration, whereas several nanotechnology applications would require it. Subsurface imaging has been achieved only in a few cases, when subsurface features influence the physical properties of the surface, such as the electronic states or the heat transfer. Ultrasonic Force Microscopy (UFM), an adaption of the Atomic Force Microscopy (AFM) contact mode, can dynamically measure the stiffness of the elastic contact between the probing tip and the sample surface. In particular, UFM has proven highly sensitive to the near-surface elastic field in non-homogeneous samples.In this paper, we present an investigation of two-dimensional (2D) materials, namely flakes of graphite and molybdenum disulphide placed on structured polymeric substrates.We show that UFM can non-destructively distinguish suspended and supported areas and localize defects, such as buckling or delamination of adjacent monolayers, generated by residual stress. Specifically, UFM can probe small variations in the local indentation induced by the mechanical interaction between tip and sample. Therefore, any change in the elastic modulus within the volume perturbed by the applied load or the flexural bending of the suspended areas can be detected and imaged. Such a power of investigation is very promising in order to investigate the buried interfaces of nanostructured 2D materials such as in graphene-based devices.

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“…Because it is difficult to characterize the tip directly, approaches that eliminate the need for such information have been developed. UFM methods for obtaining quantitative elastic-property information were investigated extensively using an approach called differential UFM [KOL93,DIN00]. With this method, the cantilever response was measured for two different applied forces.…”

Section: Measurements and Analysismentioning

confidence: 99%

Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Turner¹

2005

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ObjectivesThe purpose of this project was to develop a fundamental understanding of the interaction of an ultrasonic wave with complex media, with specific emphases on recrystallization and sintering of metals. A combined analytical, numerical, and experimental research program was implemented. Theoretical models of elastic wave propagation through these complex materials were developed using stochastic wave field techniques. The numerical simulations focused on finite element wave propagation solutions through complex media. The experimental efforts were focused on corroboration of the models developed and on the development of new experimental techniques. The analytical and numerical research allows the experimental results to be interpreted quantitatively. Alteration in Collaborative ArrangementIn fall 2002, the Ames Lab partner, Dr. James C. Foley, announced that he was leaving for another position at Los Alamos National Laboratory. Dr. R. Bruce Thompson has served as the primary contact for this collaboration since Dr. Foley departed. Accomplishments (Recrystallization)Analytical Modeling. Expressions for the ultrasonic attenuation in media with arbitrary texture have been developed using stochastic wave propagation theory. Initial attempts at deriving simple expressions for the attenuation were unsuccessful. Therefore, a modified technique was developed that relies slightly more on numerical calculations. The method is based on a generalized function of a single scalar variable σ that characterizes the state of texture. In this case the weighting function for the individual grains is given by ( ) with θ as the grain orientation angle. Thus, when σ → 0 all grains are aligned and the material is transversely isotropic at the macroscale. As σ → ∞, all grains are randomly oriented and the material is isotropic at the macroscale.In terms of attenuation, the covariance of the microstructure is the primary quantity needed for the calculation of attenuation. It is defined by in which both Eqs. (2) and (3) include the grain orientation distribution function F such that and are dependent on σ. Example results using Eq. (2) are shown in Fig. 1 for both the average elastic properties as well as quasilongitudinal slowness surfaces in terms of σ. The transition from transversely isotropy to complete isotropy is captured well using the grain orientation distribution function. Example results for attenuation are shown in Fig. 2. Again, the transition from transverse isotropy to complete isotropy is shown. Of particular note is the peak observed in the SH attenuation when σ is about 0.5. Such information may be useful for process monitoring. (a) (b)Progress was also made in the study of multiple scattering in slab geometries. These results have applications associated with heterogeneous bonding and interface layers. Two example results are shown in Fig. 3. The layer is insonified by a plane longitudinal wave. One question in the multiple scattering regime is associated with the applicability of the diffusion li...

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Nonlinear Detection of Ultrasonic Vibrations in an Atomic Force Microscope

Cited by 300 publications

References 7 publications

Beating beats mixing in heterodyne detection schemes

Beating beats mixing in heterodyne detection schemes

Subsurface imaging of two-dimensional materials at the nanoscale

Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

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