Scanning theory

The Z-scan theory has been described by different authors. In the thin sample limit the Z-scan measurement is described either through Fresnel integration or through a Gaussian decomposition procedure [3,6]. 

With the reference block method the distance law of a model reflector is established experimentally prior to each ultrasonic test. The reference reflectors, mostly bore holes, are drilled into the reference block at different distances, e.g. ASME block. Prior to the test, the reference reflectors are scanned, and their maximised echo amplitudes are marked on the screen of the flaw detector. Finally all amplitude points are connected by a curve. This Distance Amplitude Curve (DAC) serves as the registration level and exactly shows the amplitude-over-distance behaviour" of the reference reflector for the probe in use. Also the individual characteristics of the material are automatically considered. However, this curve may only be applied for defect evaluation, in case the reference block and the test object are made of the same material and have undergone the same heat treatment. As with the DGS-Method, the value of any defect evaluation does not consider the shape and orientation of the defect. The reference block method is safe and easy to apply, and the operator need not to have a deep understanding about the theory of distance laws. 

Tersoff J 1993 Theory of scanning tunnelling microscopy Scanning Tunnelling Microscopy and Spectroscopy ed D A Bonnell (Weinheim VCH) ch 3... 

Selzer Y and Manler D 2000 Scanning electrochemical microscopy. Theory of the feedback mode for hemispherical ultramicroelectrodes steady-state and transient behavior Anal. Chem. 72 2383... 

R. Wiesendanger and H. J. Guntherodt, Scanning TunnelingMicroscopy III Theory of STM and Eelated S canning Probe Methods, Springer Series in Suface... 

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

All of the available levels of theory appear in the table of results. For example, a scan run at the MP2 level will also include the Flartree-Fock energies at each point. 

Scanning Tunneling Microscopy and Spectroscopy Theory, Techniques and Applications" ( D.A. Bonnell ed.),... 

Bonnell, D., Scanning Probe Microscopy and Spectroscopy Theory, Techniques, and Applications, 2nd ed., Wiley-VCH, New York, 2000. 

Theories and simulation of the operation of AFM in liquid have been attempted [102-104], In principle, molecular dynamics or NEMD may be a suitable method to mimic the operation of a scanning tip. The time scale, however, precludes simulating a long-enough scan to see a complete atom. Most studies, therefore, were made with equilibrium conditions and a fixed position of the AFM tip. Explicit consideration of electrolytes and electrostatic effects has not been modeled. 

Ritz G, Schmid M, Varga P, Borg A, Ronning M. 1997. Pt(lOO) quasihexagonal reconstruction A comparison between scanning tunneling microscopy data and effective medium theory simulation calculations. Phys Rev B 56 10518-10525. 

Fernandez JL, White JM, Sun YM, Tang WJ, Henkelman G, Bard AJ. 2006. Characterization and theory of electrocatalysts based on scanning electrochemical microscopy screening methods. Langmuir 22 10426-10431. 

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