Udo D. Schwarz

A GENERALIZED ANALYTICAL MODEL FOR THE ELASTIC DEFORMATION OF AN ADHESIVE CONTACT BETWEEN A SPHERE AND A FLAT SURFACE

A new method to calculate the elastic deformation of a sphere on a flat surface is presented. The model considers the influence of short-range as well as long-range attractive forces both inside and outside the actual contact area. In contrast to earlier models, this theory describes the nature of these deformations in the intermediate regime between the so-called JKR and DMT limits by simple analytic expressions. Equations for the calculation of the contact radius, the deformation, and the pressure distribution are given. In all equations, the critical force that might vary between the limiting values found in the DMT and the JKR model acts as transition parameter.

Noncontact atomic force microscopy

No other method has opened the door to progress in nanoscience and nanotechnology as much as the introduction of scanning probe methods did in the 1980s, since they offer a way to visualize the nanoworld. For maximum impact, however, the ability to image and manipulate individual atoms is the key. Initially, scanning tunneling microscopy was the only scanning-probe-based method that was able to achieve this resolution. Atomic force microscopy (AFM), on the other hand, was quickly developed into a versatile tool with applications ranging from materials characterization in ultrahigh vacuum and nanofabrication under ambient conditions, to biological studies in liquids, but its resolution was limited to the nanometer scale. The reason for this restriction resulted from the fact that the resolution in probe microscopy scales with the sharpness of the tip. In conventional AFM operational modes, a tip that is located at the end of a leaf spring (the so-called cantilever) is either dragged over the surface in permanent contact or gently taps the surface while vibrating, and, whichever mode is used, tips quickly blunt through either permanent or intermittent contact. Maintaining the atomic sharpness of an initially atomically sharp tip requires that the tip never touches the surface. But how can the tip know that the surface is there if it is not allowed to touch? This problem was solved in the 1990s through the realization that the attractive forces acting on the tip when it is in close proximity to the sample affect the resonance frequency of the cantilever even though it is not in actual contact with the surface. Noncontact atomic force microscopy (NC-AFM) makes use of this effect by tracking the shift of the cantilever resonance frequency due to the force field of the surface without ever establishing physical contact between the tip and sample. Much to the astonishment of many, changes induced by individual atoms turned out to induce frequency shifts that are large enough to be detected, and thus atomic-scale imaging with AFM became a reality. Since the beginnings, almost two decades ago, NC-AFM has evolved into a powerful method that is able not just to image surfaces, but also to quantify tip–sample forces and interaction potentials as well as to manipulate individual atoms on conductors, semiconductors, and insulators alike. For the community to keep track of the rapid development in the field, a series of annual international conferences, starting in Osaka, Japan in 1998, has been established. The most recent conference from this series was held in Lindau, Germany, from September 18–22, 2011. Once again, substantial progress was presented; NC-AFM is now able to quantitatively map three-dimensional force fields of surfaces with atomic resolution in ultrahigh vacuum as well as in liquids, and methodological developments add more information to the measurements, for example, through the driving of higher cantilever harmonics or the recording of tunneling currents. For this Thematic Series of the Beilstein Journal of Nanotechnology, many of the presenters from the Lindau conference agreed to submit contributions in order to assemble a series that showcases the present state of the art in the field. I would like to thank all authors who have contributed their excellent original work to this series, all referees whose promptly provided reports have provided valuable suggestions for further improvements while keeping the publication times short, and the entire NC-AFM community for supporting the open access policy of the Beilstein Journal of Nanotechnology. Udo D. Schwarz New Haven, February 2012

Three-dimensional imaging of short-range chemical forces with picometre resolution

Chemical forces on surfaces have a central role in numerous scientific and technological fields, including catalysis, thin film growth and tribology. Many applications require knowledge of the strength of these forces as a function of position in three dimensions, but until now such information has only been available from theory. Here, we demonstrate an approach based on atomic force microscopy that can obtain this data, and we use this approach to image the three-dimensional surface force field of graphite. We show force maps with picometre and piconewton resolution that allow a detailed characterization of the interaction between the surface and the tip of the microscope in three dimensions. In these maps, the positions of all atoms are identified, and differences between atoms at inequivalent sites are quantified. The results suggest that the excellent lubrication properties of graphite may be due to a significant localization of the lateral forces.

Quantitative analysis of lateral force microscopy experiments

The analysis of lateral force microscopy experiments is discussed with emphasis on calibration issues and the statistical treatment of the original data in order to obtain reliable quantitative results. This includes an extensive discussion about the statistical and systematical errors which have to be considered if experimental results obtained under different experimental conditions (such as different cantilevers, samples, humidities, with or without lubricant, etc.) have to be compared. The proposed data analysis procedure is exemplified using data acquired on germanium sulfide and highly oriented pyrolytic graphite.

Frictional duality observed during nanoparticle sliding.

One of the most fundamental questions in tribology concerns the area dependence of friction at the nanoscale. Here, experiments are presented where the frictional resistance of nanoparticles is measured by pushing them with the tip of an atomic force microscope. We find two coexisting frictional states: While some particles show finite friction increasing linearly with the interface areas of up to 310 000 nm(2), other particles assume a state of frictionless sliding. The results further suggest a link between the degree of surface contamination and the occurrence of this duality.

Tip artefacts in scanning force microscopy

Since its invention in 1986, scanning force microscopy (SFM) has experienced great success as a characterization method for topography on small scales. In spite of the enormous potential of the method, it is limited by the quality of the tip used for probing the surface topography. Convolutions of non‐ideal tip shapes with the real topography and tip bending, flexing and jumping effects produce artefacts in the resulting images.

Wavelet Analysis of Solar Flare Hard X-Rays

We apply a multiresolution analysis to hard X-ray (HXR) time profiles f(t) of solar flares. This method is based on a wavelet transform (with triangle-shaped wavelets), which yields a dynamic decomposition of the power at different timescales T, the scalogram P(T, t). For stationary processes, time-averaged power coefficients, the scalegram S(T), can be calculated. We develop an algorithm to transform these (multiresolution) scalegrams S(T) into a standard distribution function of physical timescales, N(T). We analyze 647 solar flares observed with the Compton Gamma Ray Observatory (CGRO), recorded at energies ≥25 keV with a time resolution of 64 ms over 4 minutes in each flare. The main findings of our wavelet analysis are: 1. In strong flares, the shortest detected timescales are found in the range Tmin ≈ 0.1-0.7 s. These minimum timescales are found to correlate with the flare loop size r (measured from Yohkoh images in 46 flares), according to the relation Tmin(r) ≈ 0.5(r/109 cm) s. Moreover, these minimum timescales are subject to a cutoff, Tmin(ne) TDefl(ne), which corresponds to the electron collisional deflection time at the loss-cone site of the flare loops (inferred from energy-dependent time delays in CGRO data). 2. In smoothly varying flares, the shortest detected timescales are found in the range Tmin ≈ 0.5-5 s. Because these smoothly varying flares exhibit also large trap delays, the lack of detected fine structure is likely to be caused by the convolution with trapping times. 3. In weak flares, the shortest detected timescales cover a large range, Tmin ≈ 0.5-50 s, mostly affected by Poisson noise. 4. The scalegrams S(T) show a power-law behavior with slopes of βmax ≈ 1.5-3.2 (for strong flares) over the timescale range of [Tmin, Tpeak]. Dominant peaks in the timescale distribution N(T) are found in the range Tpeak ≈ 0.5-102 s, often coinciding with the upper cutoff of N(T). These observational results indicate that the fastest significant HXR time structures detected with wavelets (in strong flares) are related to physical parameters of propagation and collision processes. If the minimum timescale Tmin is associated with an Alfvenic crossing time through elementary acceleration cells, we obtain sizes of racc ≈ 75-750 km, which have a scale-invariant ratio racc/r ≈ 0.03 to flare loops and are consistent with cell sizes inferred from the frequency bandwidth of decimetric millisecond spikes.

Calculation of the frequency shift in dynamic force microscopy

Abstract A theoretical study of the quality and the range of validity of different numerical and analytical methods to calculate the frequency shift in dynamic force microscopy is presented. By comparison with exact results obtained by the numerical solution of the equation of motion, it is demonstrated that the commonly used interpretation of the frequency shift as a measure for the force gradient of the tip–sample interaction force is only valid for very small oscillation amplitudes and leads to misinterpretations in most practical cases. Perturbation theory, however, allows the derivation of useful analytic approximations.

A scanning force microscope with atomic resolution in ultrahigh vacuum and at low temperatures

We present a new design of a scanning force microscope (SFM) for operation at low temperatures in an ultrahigh vacuum (UHV) system. The SFM features an all-fiber interferometer detection mechanism and can be used for contact as well as for noncontact measurements. Cooling is performed in a UHV compatible liquid helium bath cryostat. The design allows in situ cantilever and sample exchange at room temperature; the subsequent transport of the microscope into the cryostat is done by a specially designed transfer mechanism. Atomic resolution images acquired at various temperatures down to 10 K in contact as well as in noncontact mode are shown to demonstrate the performance of the microscope.

The atomic force microscope used as a powerful tool for machining surfaces

Abstract Different methods of creating and imaging small structures with an atomic force microscope (AFM) are reported. We show indentations, lines and more complex patterns created with three different techniques. On polymer surfaces we are able to reproducibly create structures with typical sizes down to 50 nm. This work constitutes an example of using the AFM for controlled machining of the surface. We discuss applications of the described method in basic and technological research.