Data plane

The roughness parameters depend on the curvature and size of the tip, as well as on the treatment of the captured surface data (plane fitting, flattening, etc.). Therefore, these parameters should not be considered as absolute roughness values. However, in the present study the same tip was used for all films and all captured surfaces were treated in the same way. Tables 15.1 and 15.2 display the roughness parameters calculated fi-om the respective AFM images of both surfaces (top and... 

Step 3 The heart of calculation in ALM is a fuzzy interpolation and curve fitting method which is entitled IDS (Ink Drop Sptread). The IDS searches fuzzily for continuous possible paths on data planes. Assume that each data point on each x-y plane is a light source with a cone or pyramid shape illumination pattern. Therefore, with increase of distance of each data point, the intensity of light source decreases and goes toward zero. Also the illuminated patterns of different data points on each x-y plane are combined and new bright areas are formed. The IDS is exerted to each data point (pixel) on the normalized and discretized x-y planes. The radius of the base of cone or pyramid shape illumination pattern in each x-y plane is related to the positions of data in it. The radius increases until the all of the domain of variable in x-y plane be illuminated Figures 2c and 2d show the created illumination pattern (IL values) after the combination of the illumination patterns of different points in xi-y and X2-y planes, respectively. Here, pyramid shape illumination pattern has been used. 

If the data plane was not left, i.e. the part was assessed and approved on the PC, the changes are of course directly done through alteration of the data on the PC. 

The first system called LiSSA has been developed for interpretation of data from eddy-current inspection of heat exchangers. The data that has to be interpreted consists of a complex impedance signal which can be absolute and/or differential and may be acquired in several frequencies. The interpretation of data is done on the basis of the plot of the signal in the impedance plane the type of defect and/or construction is inferred from the signal shape, the depth from the phase, and the volume is roughly proportional to the signal amplitude. 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

In this section, two illustrative numerical results, obtained by means of the described reconstruction algorithm, are presented. Input data are calculated in the frequency range of 26 to 38 GHz using matrix formulas [8], describing the reflection of a normally incident plane wave from the multilayered half-space. 

Fig. 5. shows six ultrasonic reflection tomograms. Three of these are from the Plexiglas specimen (shown left) and three are from the AlSi-alloy (shown right). The tomograms are reconstructed from reflection data measured across the plane (b), (c) and (e), respectively. The dark regions indicate high reflectivity and represent specimen interfaces and discontinuities. 

Fig. 5. Reflection tomograms in Plexiglas and A/Si-alloy cylinders, respectively, reconstructed from data measured across plane (d), (e) and (f). High reflectivity is indicated by dark regions.

Using the theorem that the sufficiency condition for mathematical correctness in 3D-reconstruction is fulfilled if all planes intersecting the object have to intersect the source-trajectory at least in one point [8], it is possible to generalise Feldkamp s method. Using projection data measured after changing the sotuce-trajectory from circular to spiral focus orbit it is possible to reconstruct the sample volume in a better way with the Wang algorithm [9]. 

A two-dimensional slice may be taken either parallel to one of the principal co-ordinate planes (X-Y, X-Z and Y-Z) selected from a menu, or in any arbitrary orientation defined on screen by the user. Once a slice through the data has been taken, and displayed on the screen, a number of tools are available to assist the operator with making measurements of indications. These tools allow measurement of distance between two points, calculation of 6dB or maximum amplitude length of a flaw, plotting of a 6dB contour, and textual aimotation of the view. Figure 11 shows 6dB sizing and annotation applied to a lack of fusion example. 

A more elaborate theoretical approach develops the concept of surface molecular orbitals and proceeds to evaluate various overlap integrals [119]. Calculations for hydrogen on Pt( 111) planes were consistent with flash desorption and LEED data. In general, the greatly increased availability of LEED structures for chemisorbed films has allowed correspondingly detailed theoretical interpretations, as, for example, of the commonly observed (C2 x 2) structure [120] (note also Ref. 121). 

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... 

Figure Bl.22.1. Reflection-absorption IR spectra (RAIRS) from palladium flat surfaces in the presence of a 1 X 10 Torr 1 1 NO CO mixture at 200 K. Data are shown here for tluee different surfaces, namely, for Pd (100) (bottom) and Pd(l 11) (middle) single crystals and for palladium particles (about 500 A m diameter) deposited on a 100 A diick Si02 film grown on top of a Mo(l 10) single crystal. These experiments illustrate how RAIRS titration experiments can be used for the identification of specific surface sites in supported catalysts. On Pd(lOO) CO and NO each adsorbs on twofold sites, as indicated by their stretching bands at about 1970 and 1670 cm, respectively. On Pd(l 11), on the other hand, the main IR peaks are seen around 1745 for NO (on-top adsorption) and about 1915 for CO (tlueefold coordination). Using those two spectra as references, the data from the supported Pd system can be analysed to obtain estimates of the relative fractions of (100) and (111) planes exposed in the metal particles [26].

The polarization dependence of the photon absorbance in metal surface systems also brings about the so-called surface selection rule, which states that only vibrational modes with dynamic moments having components perpendicular to the surface plane can be detected by RAIRS [22, 23 and 24]. This rule may in some instances limit the usefidness of the reflection tecluiique for adsorbate identification because of the reduction in the number of modes visible in the IR spectra, but more often becomes an advantage thanks to the simplification of the data. Furthenuore, the relative intensities of different vibrational modes can be used to estimate the orientation of the surface moieties. This has been particularly useful in the study of self-... 

Figure Bl.22.3. RAIRS data in the C-H stretching region from two different self-assembled monolayers, namely, from a monolayer of dioctadecyldisulfide (ODS) on gold (bottom), and from a monolayer of octadecyltrichlorosilane (OTS) on silicon (top). Although the RAIRS surface selection rules for non-metallic substrates are more complex than those which apply to metals, they can still be used to detemiine adsorption geometries. The spectra shown here were, in fact, analysed to yield the tilt (a) and twist (p) angles of the molecular chains in each case with respect to the surface plane (the resulting values are also given in the figure) [40].

Figure Bl.22.10. Carbon K-edge near-edge x-ray absorption (NEXAFS) speetra as a fiinotion of photon ineidenee angle from a submonolayer of vinyl moieties adsorbed on Ni(lOO) (prepared by dosing 0.2 1 of ethylene on that surfaee at 180 K). Several eleetronie transitions are identified in these speetra, to both the pi (284 and 286 eV) and the sigma (>292 eV) imoeeupied levels of the moleeule. The relative variations in the intensities of those peaks with ineidenee angle ean be easily eonverted into adsorption geometry data the vinyl plane was found in this ease to be at a tilt angle of about 65° from the surfaee [71], Similar geometrieal detenninations using NEXAFS have been earried out for a number of simple adsorbate systems over the past few deeades.

Figure C3.6.4 Single-handed chaotic attractor and next-amplitude map reconstmcted from experimental data for tire BZ reaction, (a) The reconstmcted attractor projected onto tire + x)) plane (see tire text for a...

We now examine how a next-amplitude-map was obtained from tire attractor shown in figure C3.6.4(a) [171. Consider tire plane in tliis space whose projection is tire dashed curve i.e. a plane ortliogonal to tire (X (tj + t)) plane. Then, for tire /ctli intersection of tire (continuous) trajectory witli tliis plane, tliere will be a data point X (ti + r), X (ti + 2r))on tire attractor tliat lies closest to tire intersection of tire continuous trajectory. A second discretization produces tire set Xt- = k = 1,2,., I This set is used in tire constmction... 

SONNIA can be employed for the classification and clustering of objects, the projection of data from high-dimensional spaces into two-dimensional planes, the perception of similarities, the modeling and prediction of complex relationships, and the subsequent visualization of the underlying data such as chemical structures or reactions which greatly facilitates the investigation of chemical data. 

The ordering in Figure 7.31 of the MOs in terms of energy follows the rules that decreased x character and increased number of nodal planes increase the energy, but some details rely on experimental data. 

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

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