AFM

In 1986, Gerd Binnig and Heinrich Rohrer shared the Nobel Prize in Physics “for their design of the scanning tunnelling microscope”. World of possibility. The AFM has inspired a variety of other scanning probe techniques.


Atomic force microscopy Getting a feeling for the nanoworld
Nature Nanotechnology News and Views (01 Aug 2007)

Nanomedicine Elastic clues in cancer detection
Nature Nanotechnology News and Views (01 Dec 2007)

AFMs can, however, image the topography of a surface much faster than they can map forces, and instruments that are capable of video-rate imaging will soon be available1, 2, 3. Although methods such as pulsed-force-mode AFM4 now permit much faster force measurements, we cannot even begin to dream of mapping mechanical forces with nanoindentation at this rate. However, we can try to gain similar information about mechanical forces from dynamic AFM and the other high-speed techniques that are used for imaging. In the amplitude modulation or 'tapping' mode of dynamic AFM, the tip is attached to a long cantilever that oscillates (with an amplitude of a few nanometres) at or near the resonance frequency of the cantilever. During each cycle the tip gently touches the surface, in effect performing a full nanoindentation cycle.

STARK R. Atomic force microscopy: Getting a feeling for the nanoworld, Nature Nanotechnology 2, 461-462 (2007)

Yamanaka, K., Ogiso, H. & Kolosov, O. Ultrasonic force microscopy for nanometer resolution subsurface imaging. Appl. Phys. Lett. 64, 178–180

Maivald, P.et al. 1991, Using force modulation to image surface elasticities with the atomic force microscope. Nanotechnology 2, 103

Ge, S.et al. 2000, Shear modulation force microscopy study of near surface glass transition temperatures. Phys. Rev. Lett. 85, 2340–2343Dinelli, F., Buenviaje, C. &

Overney, R. M. Glass transition measurements on heterogeneous surfaces. Thin Solid Films 396, 138–144 (2001).

Experimental and theoretical investigations of processes at surfaces have developed by measuring and analysing forces and properties of surfaces, films and interfacial phenomena in nanostructures. Microscopes such as scanning tunnelling with the sharp tip instead of lenses entered the nanoworld since 1981. In Scanning Tunnelling Microscope STM wavefunctions of electrons on the tip were overlapped by the ones of atoms of the surface. An atomic difference of distance between the tip and the surface changes the tunnelling current exponentially. The initial introduction to Scanning Tunnelling Microscopy entitled “Tunnelling through a controllable vacuum gap”, was published in Applied Physics Letters, in January 1982. (1) Atomic Force Microscopy AFM detects chemical interaction forces by measuring repulsion of atoms between the tip apex of microscope and a conductive surface vertically. AFM experiments initiated by scientists in IBM and Stanford in 1986 involve analysis of surface, topography, bonding, resistance, corrosion, friction, lubricant-film thickness, and mechanical properties at nanoscale.


Binnig, G., Rohrer, H., Gerber, Ch. & Weibel, E. App. Phys. Lett. 40, 178–180 (1982).
-Gerber Christoph et al, How the Doors to the Nanoworld Were Opened, Nature Nanotechnology, VOL 1 | OCTOBER 2006
Hill
-Sugimoto Y et al, Complex Patterning by Vertical Interchange Atom Manipulation Using Atomic Force Microscopy, Science, 17 Oct 2008, vol 322, no 5900, pp 413 - 417
- Bhushan, B. (ed.), 1997 Micro/nanotribology and its applications (proceedings of the NATO Advanced Study Institute on Micro/Nanotribology and its Applications, held in Sesimbra, Portugal, June 16-28 1996), NATO ASI Series, Series E: Applied Sciences, vol. 330, Dordrecht; London, Kluwer Academic.

Nanotribology: to predict level of wearing and friction of devices on atomic scale, engineers from several disciplines such as mechanical, materials, and chemical engineers have conducted various tests on machine components.


Christoph Gerber How the doors to the nanoworld were opened, Nature
nature nanotechnology | VOL 1 | OCTOBER 2006 | www.nature.com/naturenanotechnology

History of AFM: in 1986, Gerd Binnig and Heinrich Rohrer shared the Nobel Prize in Physics “for their design of the scanning tunnelling microscope”.

World of possibility. The AFM (centre) has inspired a variety of other scanning probe techniques.

Originally the AFM was used to image the topography of surfaces, but by modifying the tip it is possible to measure other quantities (for example, electric and magnetic properties, chemical potentials, friction and so on), and also to perform various types of spectroscopy and analysis.

Binnig, G., Quate, C. F. & Gerber, Ch. Phys. Rev. Lett. 56, 930–933 (1986). (most quoted AFM paper 4700)


The Planck constant (denoted h), also called Planck's constant, is a physical constant used to describe the sizes of quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory. The Planck constant is the proportionality constant between energy (E) of a photon and the frequency of its associated electromagnetic wave (ν). This relation between the energy and frequency is called the Planck relation.

A closely related constant is the reduced Planck constant, denoted ħ ("h-bar"), which is equal to the Planck constant divided by (or reduced by) 2π. It is used when frequency is expressed in terms of radians per second instead of cycles per second. The expression of a frequency in radians per second is often called angular frequency (ω), where ω = 2πν.


The de Broglie relations
The first de Broglie equation relates the wavelength λ to the particle momentum as

where is Planck's constant, is the particle's rest mass, is the particle's velocity, is the Lorentz factor, and is the speed of light in a vacuum.
The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency, it follows that short wavelengths are more energetic than long wavelengths. The second de Broglie equation relates the frequency of the wave associated to a particle to the total energy of the particle such that

where is the frequency and is the total energy. The two equations are often written as


where is momentum, is the reduced Planck's constant (also known as Dirac's constant, pronounced "h-bar"), is the wavenumber, and is the angular frequency.
See the article on group velocity for detail on the argument and derivation of the de Broglie relations. Group velocity (equal to the electron's speed) should not be confused with phase velocity (equal to the product of the electron's frequency multiplied by its wavelength).
Matter wave phase
In quantum mechanics, particles also behave as waves with complex phases. By the de Broglie hypothesis, we see that
.
Using relativistic relations for energy and momentum, we have

where E is the total energy of the particle (i.e. rest energy plus kinetic energy in kinematic sense), p the momentum, γ the Lorentz factor, c the speed of light, and β the velocity as a fraction of c. The variable v can either be taken to be the velocity of the particle or the group velocity of the corresponding matter wave. See the article on group velocity for more detail. Since the particle velocity v < c for a massive particle according to special relativity, phase velocity of matter waves always exceed c, i.e.
,
and as we can see, it approaches c when the particle velocity is in the relativistic range. The superluminal phase velocity does not violate special relativity, for it doesn't carry any information. See the article on signal velocity for detail.


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