Voids spherical

Mephisto is devoted to predict the ultrasonic scans (A,B or C-scans) for a priori knowledge of the piece and the defects within. In the present version Mephisto only deals with homogeneous isotropic materials. The piece under test can be planar, cylindrical or have a more complex geometry. The defects can be either planar (one or several facets), or volumetric (spherical voids, side drilled holes, flat or round bottom holes). 

For more complicated geometries, the computations become more and more involved as it is the case for the ordinary electromagnetic Casimir effect. However, Casimir calculations of a finite number of immersed nonoverlapping spherical voids or rods, i.e. spheres and cylinders in 3 dimensions or disks in 2 dimensions, are still doable. In fact, these calculations simplify because of Krein s trace formula (Krein, 2004 Beth and Uhlenbeck, 1937)... 

Consider now a spherical void (e = 1) in an otherwise homogeneous medium. Light is not absorbed by such a void, but it can influence the absorption of light in the surrounding medium. The condition for a resonance in the extinction efficiency of a small spherical void follows readily from (12.17) ... 

If / is small (a nearly solid bubble), the two roots are approximately e+= — and c = —2 these are the resonance conditions for a spherical void in a medium with dielectric function c and a solid sphere with dielectric function in free space, respectively. As / is increased + increases monotonically and decreases monotonically, where lim, += 0 and lim, = — oo. (Of course, when /= 1, the bubble bursts )... 

For a spherical void of diameter d, the surface tension T at the void composite interface is a function of the pressure inside the void Pv and the pressure surrounding the void P (Eq. 13.19)... 

A basic distinction is made between closed-cell systems, where spherical or roughly spherical voids (cells) are fully separated by matrix material, and open cell systems where there are interconnections between voids. 

As shown in Fig. 3a, the size of PS bead is approximately 100 nm, and dried PS beads show an aggregate form. However, the pore sizes of calcined P4 and P3 are approximately 50 nm. Calcination resulted in polymer-free metal oxide strucures, with spherical voids smaller than the PS bead diameter, by 50%. This contraction phenomenon is obviously related to the reorganizaiton of the surrounding walls during the calcination process as evidenced in Fig. 3c and Fig. 3d. The part of the wall retracts by the burning PS bead [11]. This thermal treatment causes the link of metal oxide in the structure (Fig. 3d), and it is also affected by the calcination temperature. 

This equation can be used to estimate the minimum size of inclusion that can be observed, provided this is not limited by the resolution of the microscope. As an example, consider a spherical void of diameter At in quartz imaged using the strongest reflection lOTl for which tg = 68.5 nm at 100 kV. If the minimum contrast A/o//o that can be detected is 10%, then At (min) = 0.1tg/2x = 1.1 nm. In practice, this figure is probably optimistically small. 

Positronium in condensed matter can exist only in the regions of a low electron density, in various kinds of free volume in defects of vacancy type, voids sometimes natural free spaces in a perfect crystal structure are sufficient to accommodate a Ps atom. The pick-off probability depends on overlapping the positronium wavefunction with wavefunctions of the surrounding electrons, thus the size of free volume in which o-Ps is trapped strongly influences its lifetime. The relation between the free volume size and o-Ps lifetime is widely used for determination of the sub-nanovoid distribution in polymers [3]. It is assumed that the Ps atom is trapped in a spherical void of a radius R the void represents a rectangular potential well. The depth of the well is related to the Ps work function, however, in the commonly used model [4] a simplified approach is applied the potential barrier is assumed infinite, but its radius is increased by AR. The value of AR is chosen to reproduce the overlap of the Ps wavefunction with the electron cloud outside R. Thus,... 

Fig.l Ortho-positronium lifetime r=l/(Apu+ t) as a function of the void radius a-cylindrical void (infinitely long), lowest state b- spherical void, lowest state c- cylindrical void, first excited state d- spherical void, first excited state. The penetration parameter AR is assumed 0.166 nm. 

For the present three-phase composites with aligned (spheroidal) PSZ particles and (spherical) voids in the Ni matrix, the mean-field model provides the following set of relations ... 

Ba2YCu307 superconductor the calculated porosities for the two samples are 12.9 percent and 32.6 percent, respectively. Assuming that this porosity is in spherical voids, Equations 8 and 9 can be solved in an iterative fashion to give B0 and G0, from which the other elastic moduli can be calculated from Equations 4-7. A similar analysis is performed for the theory of Ledbetter and Datta. The results are given in Table III. 

Holland et al. extended the possible oxide structures to include not only silica, mesoporous silica, titania, zirconia, a yttria stabilized zirconia, and alumina but also oxides of W, Fe, V, and Sb [21]. These latter transition metals formed less ordered structures, containing areas of non-porous material. Different dilutions of alkoxide in alcohol resulted in various inorganic loadings, and moderate control in the wall thickness and window sizes between spherical voids [21 ]. SEM images of a series of macroporous titania structures obtained with different alkoxide dilutions in ethanol are shown in Fig. 3. Gundiah and Rao have also prepared macroporous materials of ternary mixed oxides, PdTiOj and Pb(ZrTi)03 [22]. 

Suspensions of polymer spheres of various diameter and surface functionality were templated to produce monoHthic silica containing dispersed spherical voids [33]. The pH of the aqueous latex solution was decreased to 2 before the... 

Figure 22. Exterior surface with pat- Figure 23. Spherical void in the cross terned cracks in an improperly cooled section of a pressure-atomized sulfur sulfur coating coating...

In many of the cross sections of pressure-atomized coatings, spherical voids are common and occasionally have diameters that are a significant fraction of the total coating thickness. This causes a localized decrease in the effective coating thickness (Figure 23) and may reflect gas entrainment associated with the relatively large size of the pressure-atomized sulfur droplets. 

A clathrate is thus an inclusion compound which is a solid solution of the guest atoms or molecules in a metastable crystalline form characterized by isolated large spherical voids of the host species. These structural criteria differentiate clathrates from the other intercalation compounds subsequently described (see 16.3 and 16.4), in which the available voids exhibit a uni- or two-dimensional arrangement (tunnel and sheet structures). 

The aforesaid is confirmed by an electron micrograph of the surface of a synthesized sample. The image shows a (111) section of the outer layer of spherical voids, with a lattice of white regions corresponding to the section of the VO2 skeleton the gray regions inside this lattice represent the whole set of lower... 

Sumida T, Wada Y, Kitamura T, Yanagida S (2000) Electrochemical preparation of macroporous polypyrrole films with regular arrays of interconnected spherical voids. Chem Commun p 1613... 

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