Phase map

Figure 4. (a) Correlation image of centrally loaded square aluminium plate clamped along all four sides, (b) Raw phase map shearogram. (c) Image enhanced phase map. 

The application of interference techniques overcomes the limitations exerted by the large optical wavelengths. With commercial phase-measurement interference microscopes (PMIM), a surface resolution of the order of 0.6 nm can be achieved [33, 34]. In a microscope a laser beam is both reflected from the sample surface and from a semitransparent smooth reference surface (Fig. 3). The interference pattern is recorded on an area detector and modulated via the piezo-electric driven reference surface. The modulated interference pattern is fed into a computer to generate a two-dimensional phase map which is converted into a height level contour map of the sample surface. While the lateral resolution (typically of the... 

Figure 9. Phase reconstruction of image reported in Figure 6 using the reference of image reported in Figure 8. The phase map is shown in (a), which includes a laterally averaged line-scan of 15 pixels, (b) A surface map of the two particles shape is displayed. The surface plot has been heavily noise filtered through Gaussian smoothing to better display the particles shape.

Systems and materials. The reaction was carried out at several compositions in an ionic and in a nonionic system. The ionic system consisted of an emulsifier (49.6 wt % cetyltrimethyl ammonium bromide (CTAB)/50.4% n-butanol), hexadecane, and water. The nonionic emulsifier consisted of 65.7% polyoxyethylene (10) oleyl ether (Brij 96) and 34.4% n-butanol, again with hexadecane and water. In both systems, mlcroemulslon (pE) compositions used were obtained by diluting an initial 90 weight percent (%) emulsifler/10% oil mixture with varying amounts of water. Micro-emulsion samples thus obtained had final compositions of 30 to 80% water. Phase maps describing these systems have been published (10-11). 

SOLVE/RESOLVE is a program system that permits automation of all the steps between processed data and interpretation of phased maps. These include scaling of data measured at multiple wavelengths, location of anomalous scatterers. 

Based strictly on equilibrium considerations, bounds can be set on the stability of voids as a function of temperature and pressure. Although this type of phase map does not depict the time dependency of an actual process, it does provide a limiting scenario toward which the actual process would be heading at any point in the curing cycle. It is surprising that high void pressures are possible if sufficient moisture is present in the resin. 

The phase map shown in Figure IB represents the skin permeation enhancement activity of the formulations containing binary mixtures of lauryl sarcosinate and sorbitan monolaurate at different concentrations and compositions. The region of maximum activity lies in a very narrow range of compositions. For such a nonlinear activity-composition behavior, it is very important to probe the binary phase map at as fine a resolution as possible, thus increasing the experimentation volume. 

B) Activity phase map of a binary combination indicates highest skin permeabilization and light... 

Figure 2 (A) Design of a ternary formulation. (B) Activity phase map of a ternary combination of chemical penetration enhancers. Dark gray indicates highest skin permeabilization and light gray indicates lowest skin permeabilization.

It is impossible to represent a quaternary or higher order formulation as a 2-D phase map. 

I will return to this diagram near the end of the chapter, particularly to amplify the meaning of error removal, which is indicated by dashed horizontal lines in Fig. 7.1. For now, I will illustrate the bootstrapping technique for improving phases, map, and model with an analogy the method of successive approximations for solving a complicated algebraic equation. Most mathematics education emphasizes equations that can be solved analytically for specific variables. Many realistic problems defy such analytic solutions but are amenable to numerical methods. The method of successive approximations has much in common with the iterative process that extracts a protein model from diffraction data. 

Figure 1. Phase identification using Si/Al ratio images, a) silicon b) aluminum c) Si/Al ratio image d) Si/Al intensity profile e) selection of intensity cut-offs f) "semi-quantitative" phase map...

Figure 19.11 Phase maps f(x, y) of a 6x4/um region of a fatigued FeCap (108 cycles) after negative (left) and positive (right) poling and evolution map of the piezoelectric phase signal f(x, E) (central picture) under varying (triangular shape) electric field E of the horizontal line indicated by the horizontal arrows. PI, P2, LI and L2 are discussed in detail later.

Figure 19.12 Amplitude maps A(x, y) of the piezoelectric vibration corresponding to the respective phase maps of Figure 19.11.

When a substrate or inhibitor binds to a protein, it displaces water. As a result, electron density for ordered water is replaced by electron density for part of the ligand molecule. This means that there may be no appreciable peak in the difference map. In addition, because of somewhat incorrect phases, the substrate or inhibitor will appear in a difference map with reduced electron density, usually about half that of a well-phased map (half-weight AF map). Consequently, the practice has sometimes been to multiply coefficients. Often a map that combines the features of a difference map Fph Fp, enhanced by a factor of two, and of the native protein map Fp, is used. The coefficients of the Fourier synthesis are then ... 

Previous findings on the actual microemulsion are given in references (9 17) where the system s phase map vs.concentration in the temperature interval (-20°C + 80°C), viscosity measurements,dielectric analysis of liquid samples against both concentration and frequency, the thermally stimulated dielectric polarization release (TSD), electro-optical phenomena, light scattering, Raman spectroscopy and sound propagation investigations are reported. 

The phase diagrams were prepared at room temperature by the usual method, where a weighed aliquot of the surfactant/ cosurfactant mixture (E) was diluted with known amounts of water (W) and then titrated with oil (0) to turbid and clear endpoints. Alternatively, the dilution of E could be made with oil and titration with the water. Generally, fifteen to thirty titrations were sufficient to roughly outline the phase maps. Solubility limits were also determined by titration of the solvent with the solute (or solute solution) to a cloudy endpoint. 

As the pseudo-ternary phase map indicates, the sulfolane-containing system used in this work solubilizes the organophosphate TBP very effectively. From the 50Z point on the E-W axis, over 60% oil can be added while a clear fluid solution is maintained Even at 80% water it is possible to add nearly 20% oil before turbidity and subsequent phase separation occurs. It is not known whether a true microemulsion exists in this clear region. However this enhanced solubilization of TBP is not simply a co-solvent effect of the sulfolane and water. This was confirmed by determining the maximum solulbility (6.7%) of TBP in a 2 1 (w/w) mixture of sulfolane and water, respectively. 

Figure 1. Phase map of the Pentanol/CTAB/Water/Hexadecane System. The emulsifier (E) [40% CTAB, 60% Pentanol, w/w] plus water (W) plus Hexadecane oil (0) = 100% by weight. The clear single phase region is denoted by (I).

Figure 3. Phase map of the Sulfolane/CTAB/Water/CEES System.

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