Area densities

When used for superresolution, the laser beam is incident on b, which hides the domains in s. During read-out, b is heated and the domains in s are copied to b. The optical system sees only the overlap area between the laser spot and the temperature profile which is lagging behind, so that the effective resolution is increased. Experimentally it is possible to double the linear read-out resolution, so that a four times higher area density of the domains can be achieved when the higher resolution is also exploited across the tracks. At a domain distance of 0.6 pm, corresponding to twice the optical cutoff frequency, a SNR of 42 dB has been reached (82). 

The information is qualitative in nature. The area density of dots suggests local concentration differences, but the count rate at each point, which is fundamental information required for quantitation, is lost. 

Fig. 4.14. Fluorescence intensity from layers buried in a thick substrate. The dependence of intensity on the glancing angle was calculated for layers of different thickness but with a constant analyte area density. Silicon was assumed as substrate and Mo-Ka X-rays as primary beam. Total reflection occurs in the region below 0.1°. Without total reflection, the dashed horizontal line would be valid throughout [4.21].

Brown [46] continued the contact mechanics work on elastomers and interfacial chains in his studies on the effect of interfacial chains on friction. In these studies. Brown used a crosslinked PDMS spherical cap in contact with a layer of PDMS-PS block copolymer. The thickness, and hence the area density, of the PDMS-PS layer was varied. The thickness was varied from 1.2 nm (X = 0.007 chains per nm-) to 9.2 nm (X = 0.055 chains per nm-). It was found that the PDMS layer thickness was less than about 2.4 nm, the frictional force between the PDMS network and the flat surface layer was high, and it was also higher than the frictional force between the PDMS network and bare PS. When the PDMS layer thicknesses was 5.6 nm and above, the frictional force decreased dramatically well below the friction between PDMS and PS. Based on these data Brown [46] concluded that ... 

An example of a distributor design is shown in Figure 10. Hole density is low at the top of the pipe and is increased lower on the pipe. The maximum open area density of about 10% assures reasonable bubble formation in this design. The average veloeity out of the top row of holes starts at about 40 m/s and increases as the pressure rises and total flow increases. Total areas of holes plus bottom slot should be equal to at least two times the cross sectional area of the inlet pipe. 

In some specific cases one would like to convert the chemisorption data into an averaged particle size. In that case, the number of surface atoms per unit surface area (density of surface atoms) is an essential parameter. Since this number depends on the type of the crystallographic plane, (see Table 3.7), one also needs information on the types of crystallographic planes exposed to the gas phase. This is also important for another reason the adsorption stoichiometry may depend on the crystallographic plane. 

Particularly for thin Mossbauer absorbers with a low concentration of the resonance nuclide and high mass absorption, it may be problematic to apply the recommendation for sample preparation (f 0.2), because the resulting electronic absorption may be prohibitively high. In such a case, it may pay well to optimize the absorber thickness, i.e., the area density f. To this end, following the approach of Long et al. [33], we adopt the general expression ... 

Fig. 3.13 Signal-to-noise ratio of Mossbauer spectra as a function of the area density l of the sample for thin absorbers ( < 1) and negligible nonresonant background, A b A oo...

While the shell-and-tube heat exchanger is the most commonly used in the process industries, it has the disadvantages that the flow is not truly countercurrent, which limits the minimum temperature difference that can be accommodated, and the area density is relatively low. Commonly used alternatives for shell-and-tube heat exchangers are ... 

Figure 36. The scaled distributions of mean, P(H/Y ) (a), and Gaussian, P(K/Y]2) (b), curvatures scaled with the inteface area density, computed at several time intervals of the spindal decomposition of a symmetric blend. There is no scaling at the late times because the amplitude of the thermal undulations does not depend on the average growth of the domains, and therefore the scaled curvature distributions functions broaden with rescaled time.

Figure 42. (a) The droplet surface area density, S, as a function of droplet... 

In their works,51"54 the self-similar fractal dimension dF>ss of the two-dimensional distribution of the pits was determined by the analysis of the digitized SEM images using the perimeter-area method. The value of dF>ss increased with increasing solution temperature,51 and it was inversely proportional to the pit shape parameter and the pit growth rate parameter.53 Keeping in mind that dr>ss is inversely proportional to the increment of the pit area density, these results can be accounted for in terms of the fact that the increment of the pit area density is more decelerated with rising solution temperature. 

So, we can see that linear dependence of the number of ionizations on the area density of the atoms (corresponding to a complicated dependence on the atomic fractions) translates into a simple linear dependence on the mass fraction for a thin layer. 

Fig. 3 Surface-reactivity of the molybdenum hexacarbonyl complex as a function of the area density of - OH groups on an alumina surface...

Fe, and trace species such as V, Ni, and Zn. Detection limits range from about 20 to 200 ng/cm area density on each filter, corresponding to about 0.2 to 2 yg/filter. Typical uncertainties in the mass determination of a particular element were 15-20% or 2 yg/filter, whichever was larger. 

Thomason, L. W L. R. Poole, and T. Deshler, A Global Climatology of Stratospheric Aerosol Surface Area Density Deduced from Stratospheric Aerosol and Gas Experiment II Measurements 1984-1994, J. Geophys. Res., 102, 8967-8976 (1997). 

The rapid growth of interest in powders and their surface properties in many diverse industries prompted the writing of this book for those who have the need to make meaningful measurements without the benefit of years of experience. It is intended as an introduction to some of the elementary theory and experimental methods used to study the surface area, porosity and density of powders. It may be found useful by those with little or no training in solid surfaces who have the need to quickly learn the rudiments of surface area, density and pore-size measurements. 

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