Void shapes

Nelson et al. [34] determined from void shapes that the ratio 7100/7110 was 1.2, 0.98 and 1.14 for copper at 600°C, aluminum at 550°C, and molybdenum at 2000°C, respectively, and 1.03 for 7100/7111 for aluminum at 450°C. Metal tips in field emission studies (see Section VIII-2C) tend to take on an equilibrium faceting into shapes agreeing fairly well with calculations [133]. 

For soil systems contaminated with Na+, kinematic viscosity is not significantly affected, thus the components controlling water flow velocity are the hydraulic gradient (A< >/AX) and soil permeability (k). The latter component (k) is influenced by clay dispersion, migration, and clay swelling. These processes may cause considerable alteration to such soil matrix characteristics as porosity, pore-size distribution, tortuosity, and void shape. 

If, for example, the void shape is spherical, the fraction of the pore volume filled by adsorbate at a given value of rp on the adsorption branch of the isotherm is represented as... 

Figure 8.37 Complex void shapes have been modeled by a eircular eraek emanating from a spherical void. This allows the stress intensity factor to be calculated. For short cracks, the solution approaches that of a surface crack, while for long cracks that for a circular crack of radius (R+a).

Both macroporous and mesoporous silicon are similarly exploited to achieve various types of separation and/or seed layers by high-temperature anneal and formation of active layer by epitaxial growth or epitaxial free processing (Depauw et al. 2008, 2009 Brendel et al. 2010). Similar studies of void shape evolution and SON (silicon-on-nothing) structure formation from masked anisotropic reactive ion etching resulting in square arrays of holes during H2 anneal were shown in Sudoh... 

Sudoh K, Iwasaki H, Hiruta R, Kuribayashi H, Shimizu R (2009) Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si (001). J Appl Phys 105 083536... 

However, free spaces remain between plane netwoik particles, called interstices or voids. In (a)-type arrangement, the void shape is a square, defined by joining the centers of the four spheres from successive parallel strings, with the surface ... 

Here S is the total surface area of all the three grain boundaries in the absence of the void. Si, S2, and S3 are the areas of intersections of the void with the respective GBs. Interaction with the electric field is as described in the previous case if the void center shifts from the junction position (%o,yo) to a new position (Xc,yc) without a change in void shape the system energy change due to the work of the electric field may be expressed as... 

Hong JK, Xu G, Piao D, MadihaUy SV (2012) Analysis of void shape and size in the collector plate and polycaprolactone molecular weight on electrospun scaffold pore size. J Appl Polym Sd 128(3) 1583-1591. doi 10.1002/app.38326... 

There is little experimental data and only a small amount of theoretical analysis relevant to the behavior of coarse porosity. Two theoretical approaches will be described, one using the bulk creep properties of the fuel and one based on stress-directed diffusion. Also an empirical approach is outlined. The theoretical treatments assume spherical porosity and cannot cope with changes in void shape as deformation proceeds. 

We noted in Section VII-2B that, given the set of surface tension values for various crystal planes, the Wulff theorem allowed the construction of fhe equilibrium or minimum firee energy shape. This concept may be applied in reverse small crystals will gradually take on their equilibrium shape upon annealing near their melting point and likewise, small air pockets in a crystal will form equilibrium-shaped voids. The latter phenomenon offers the possible advantage that adventitious contamination of the solid-air interface is less likely. 

Press and blow operations are used to produce wide mouth and some narrow neck containers, including beer botties. The difference between the press and blow operation and the blow and blow operation is that the parison is pressed iato shape by a plunger that fills the complete void ia the parison. 

Specific gravity is the most critical of the characteristics in Table 3. It is governed by ash content of the material, is the primary deterrninant of bulk density, along with particle size and shape, and is related to specific heat and other thermal properties. Specific gravity governs the porosity or fractional void volume of the waste material, ie. 

DRI can be produced in pellet, lump, or briquette form. When produced in pellets or lumps, DRI retains the shape and form of the iron oxide material fed to the DR process. The removal of oxygen from the iron oxide during direct reduction leaves voids, giving the DRI a spongy appearance when viewed through a microscope. Thus, DRI in these forms tends to have lower apparent density, greater porosity, and more specific surface area than iron ore. In the hot briquetted form it is known as hot briquetted iron (HBI). Typical physical properties of DRI forms are shown in Table 1. 

The characteristics of a powder that determine its apparent density are rather complex, but some general statements with respect to powder variables and their effect on the density of the loose powder can be made. (/) The smaller the particles, the greater the specific surface area of the powder. This increases the friction between the particles and lowers the apparent density but enhances the rate of sintering. (2) Powders having very irregular-shaped particles are usually characterized by a lower apparent density than more regular or spherical ones. This is shown in Table 4 for three different types of copper powders having identical particle size distribution but different particle shape. These data illustrate the decisive influence of particle shape on apparent density. (J) In any mixture of coarse and fine powder particles, an optimum mixture results in maximum apparent density. This optimum mixture is reached when the fine particles fill the voids between the coarse particles. 

The manufacture of metal in powder form is a complex and highly engineered operation. It is dominated by the variables of the powder, namely those that are closely connected with an individual powder particle, those that refer to the mass of particles which form the powder, and those that refer to the voids in the particles themselves. In a mass of loosely piled powder, >60% of the volume consists of voids. The primary methods for the manufacture of metal powders are atomization, the reduction of metal oxides, and electrolytic deposition (15,16). Typical metal powder particle shapes are shown in Figure 5. 

Catalytic Properties. In zeoHtes, catalysis takes place preferentially within the intracrystaUine voids. Catalytic reactions are affected by aperture size and type of channel system, through which reactants and products must diffuse. Modification techniques include ion exchange, variation of Si/A1 ratio, hydrothermal dealumination or stabilization, which produces Lewis acidity, introduction of acidic groups such as bridging Si(OH)Al, which impart Briimsted acidity, and introducing dispersed metal phases such as noble metals. In addition, the zeoHte framework stmcture determines shape-selective effects. Several types have been demonstrated including reactant selectivity, product selectivity, and restricted transition-state selectivity (28). Nonshape-selective surface activity is observed on very small crystals, and it may be desirable to poison these sites selectively, eg, with bulky heterocycHc compounds unable to penetrate the channel apertures, or by surface sdation. 

A mixture of PhenoHc MicrobaUoons and resin binder has a putty-like consistency. It can be molded to shape, troweUed onto surfaces, or pressed into a core. Curing gives a high strength, low density (0.144 g/cm ) foam free of voids and dense areas, and without a brittle skin. Syntactic foams are used in widely diverse appHcations, including boat flotation aids stmctural parts in aircraft, submarines, and missiles stmctural cores for waU panels and ablative heat shields for reentry vehicles and rocket test engines. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

---