Step profile

Figure 4-164 shows a steel body core bit with a long-taper, stepped profile fitted with impregnated natural diamond blocks as the primary cutting elements. The bit has no inner cone. Since there is no specific code for the natural diamond/steel body combination, the letter O (other) is used as the cutter type/ body material code. The profile code 3 is used to describe the long outer taper with little or no inner cone depth. The hydraulic design code 5 indicates a fixed... 

FIGURE 4 An example of a pump step profile as part of the compositional accuracy test for reservoirs A and B. Reservoir A contains I % methanol/water and reservoir B contains solvent A with 0.5% acetone added. Courtesy of PerkinElmer LAS, Shelton, CT. 

The composition profile is approximated by a step profile, with a uniform composition xf in the surface layer (0bulk phase x, at z>L. It is assumed that the total amount of liquid can be divided into two parts with the first constituting the homogeneous bulk phase (mole numbers in it n° = til -I- 2) and the remainder standing under the influence of the forces emanating from the solid surface causing adsorption (mole numbers, referred to unit mass of adsorbent, = n, -i- 2 the superscript a referring to adsorption) [17]. Simple mass balance considerations lead to the following expressions [12] ... 

So far, we tacitly assumed that the upper and lower terraces next to the step are below their roughening transition temperature. By fixing the boundary heights of the terraces, away from the step, at, say, level 0 for the lower and level 1 (in units of the lattice spacing) for the upper terrace, one can study the time evolution of the step width w, defined, for instance, as the second moment of the gradient of the step profile also above roughening. Then one obtains s =1/4 for terrace diffusion and 1/2 for evaporation kinetics, as predicted by the continuum description of Mullins and confirmed by our Monte Carlo simulations. 

As time goes on, below roughening, the steps will meander due to formation of kinks, with only rather few adatoms on the terraces. To overcome possible ambiguities in locating the step position, one may calculate the step profile z x, f) = [Hy h x, y, where the brackets, [ ], denote an average over several realizations, to smoothen the profiles (alternatively, one may increase M in a single realization). 

In the ID limit, Eqs. (7) and (8) and related equations have been used to analyze the relaxation of non-equilibrium step profile - and in a variety of other application We will not review this work here, but instead turn directly to two cases where characteristic 2D step patterns and step bunching are found as a result of the competition between the step repulsions and a driving force favoring step bunching. Perhaps the simplest application arises as a result of surface reconstmction. 

Fig. 19. The XPS step profiling of imide-siloxanes segmented copolymers [119]...

Assuming the parabolic profile and that L is short enough that the density varies linearly around z=h, Milner [55] showed that this equation can be transformed into a modified Bessel equation and solved analytically for v=l/2. In Fig. 4, his results for the velocity profile for a brush with a parabolic and step profile are... 

Hence, similar to the previous example, the range below 20 = 15° was excluded from further refinement. It is certainly worthwhile to note that this exclusion eliminates 400 points ( 9 %) from the profile, which contains more than 4,600 data points total, but it leaves out only 3 ( 0.3 %) of about 1000 possible Bragg reflections. As far as the structural model is of concern, such truncation of the experimental data is indeed valid, and is often employed in structure determination from powder diffraction. With this modification, followed by several least squares minimization steps, profile residuals decrease but Rb is slightly increased. 

Figure 6.7 Natural vegetation, for which stem density changes over depth, can be represented by a simpler canopy with a step distribution in frontal area density, a(z). This step distribution is generates a step profile of longitudinal velocity, (u).

Figure 6.11 Thickness of electrodeposited CdTe layers determined by step-profiling and mass analysis vs. charge turnover obtained from integration over the deposition current (Ernst, 2001).

All calculations from the measured diffraction efficiency to other numbers characterizing the material require the knowledge of either the sample thickness or the angular dependence of the diffraction efficiency. We chose the latter method since angle-dependent measurements can be performed easily in our set-up. The thickness values calculated from the holographic data were compared with independent measurements performed with a step profiler. The results always agreed within a few percent. To calculate n we inserted the optically determined thickness, since it corresponds exactly to the location of the hologram. 

Fig. 18. Dependence of the step time constant on deposition temperature for various bath compositions determined by a step profile analysis according to the Avrami law (Eq. 37).

This two-step profile of the potential across the interphase is also characteristic for certain types of modified electrodes in which the metal surface is coated with a film, whose thickness significantly exceeds the atomic scale. Such systems represent a much more complicated type of electrified interfaces, since the distribution of charged species depends crucially on the specific properties of the film. In most cases of sufficiently thick films, the profile of the Galvani potential across the interphase possesses a plateau inside the bulk film separating two potential drops at its interfaces with the electrode and the solution [16]. 

It is well known that both hydrophilic and highly hydrophobic fumed silica are efficient rheological additives for unsaturated polyesters. In more polar systems such as vinyl esters, however, only highly hydrophobic fumed silica is suitable. This observation is illustrated by the viscosity step profile of Wacker HDK N20 and H18 in Palatal P4 (UP) and in Atlac 590 (VE), respectively, depicted in Fig. 2. 

Fig. 2. Relative viscosity in a shear rate step profile at D =1 s, 10 s and 100 s, each 120 s, respectively, of four resin systems Wacker HDK N20 and HDK HI 8 in Palatal P4 (UP resin) and in Atlac 590 (VE resin) 35 wt% styrene 3 wt% fumed silica.

The step profile reveals that N20 and H18 dispersed in Palatal P4 exhibit an almost identical rheological behavior, whereas the apparent relative viscosities of N20 and H18 dispersed in Atlac 590 at low and moderate shear rates are distinctly different. To explain this behavior it is necessary to consider the polarity, functional groups, and chain length of the resins but also the surface properties of the fumed silica. All parameters together will influence the nature and strength of the colloidal forces, which govern the rheology of the mixtures. 

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