Geometric factors

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

The conductivity is obtained from this by division by the geometric factor (A/l), givmg... 

It is of particular interest to be able to correlate solubility and partitioning with the molecular stmcture of the surfactant and solute. Likes dissolve like is a well-wom plirase that appears applicable, as we see in microemulsion fonnation where reverse micelles solubilize water and nonnal micelles solubilize hydrocarbons. Surfactant interactions, geometrical factors and solute loading produce limitations, however. There appear to be no universal models for solubilization that are readily available and that rest on molecular stmcture. Correlations of homologous solutes in various micellar solutions have been reviewed by Nagarajan [52]. Some examples of solubilization, such as for polycyclic aromatics in dodecyl sulphonate micelles, are driven by hydrophobic... 

Unless extremely high potentials are to be used, the intense electric fields must be formed by making the radius of curvature of the needle tip as small as possible. Field strength (F) is given by Equation 5.1 in which r is the radius of curvature and k is a geometrical factor for a sphere, k = 1, but for other shapes, k < 1. Thus, if V = 5000 V and r = 10 m, then, for a sphere, F = 5 x 10 V/m with a larger curvature of, say, Iff m (0.1 mm), a potential of 500,000 V would have to be applied to generate the same field. In practice, it is easier to produce and apply 5000 V rather than 500,000 V. 

In order to do this, we anticipate the form of the expression for Equation (10.31) will show that 1 /1q can be written as the product of two terms an optical-molecular factor we symbolize as and a geometrical factor 1 + cos where r is the distance from the scattering molecule and 0 is... 

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

The crystal stmeture and stoichiometry of these materials is determined from two contributions, geometric and electronic. The geometric factor is an empirical one (8) simple interstitial carbides, nitrides, borides, and hydrides are formed for small ratios of nonmetal to metal radii, eg, < 0.59. 

K. K , = geometrical factors, depending upon the more important parameters such as area of the grounding grid, its depth and conductor spacing and less important factors, such as diameter of the conductors and the thickness of the finishing surface by concrete or gravel. 

Neglecting unimportant geometric factors,the integrated X-ray intensity diffracted from a thin film is... 

Geometrical factors such as structure (aggregation) and porosity of the particles. 

The simplest type of solutions which exhibit non-randomness are those in which the non-randomness is attributable solely to geometric factors, i.e. it does not come from non-ideal energetic effects, which are assumed equal to zero. This is the model of an athermal solution, for which... 

To establish a criterion for any size room and outlet, the Ar number was adjusted using a geometrical factor. The modified Ar was defined as... 

The proportion factors related to the reaction constants, together with the geometrical factors of the reaction chamber, can be included in one coefficient G, gi ving... 

Table 1. The geometrical factor for some extreme case of ellipsoids.

The geometrical factor, like the filling factor, shifts the position of the resonance peak. When = 0 we have the case of an infinite cylinder (see Table 1). An infinite cylinder connects one side of the crystal to the other. Therefore, the electrons travel freely through the crystal. Actually, this is not the situation of metallic particles dispersed in an insulator any more. The situation corresponds... 

Fig. 9. Case of metallic particles with Crude parameters fitOp = 1 eV, hf = 0.01 eV, dispersed in an insulating matrix with parameters fiojp i = 2 eV, ftfi = 1 eV and fttO] = 5 eV, filling factor/ = 0.5 and geometrical factor N between 0 and 1.

Table 2. These parameters refer to the Maxwell-Garnett (Eq.(6)) and Bruggeman calculations with a filling factor f 0.6. N denotes the geometrical factor. All other values are in eV.

The geometric factor can be illustrated by considering the amount of sunlight (or radiative heat) received by Earth from the Sun. If you draw a huge sphere with a radius of 150 million km (93 million miles) around the sun that passes through Earth, the geometric factor for the Sun to Earth would he the ratio of the area on that sphere s surface blocked by Earth to the surface area of the sphere. Obviously, Earth receives only a tiny fraction of the total energy emitted from the Sun. 

Geometric Factors and Heterogeneities in Relation to Localized Attack... 

Basically there are two approaches to predicting the occurrence of erosion corrosion. Practical or experience based methods typified by Keller s approach for carbon steels in wet steam. Keller developed an equation that related the erosion corrosion rate as a function of temperature, steam quality, velocity and geometric factor. In recent years this approach has... 

Deposit uniformity The uniformity of a deposit is an important factor in its overall corrosion resistance and is a function of geometrical factors and the throwing power of the plating solution. A distinction is made here between macro-throwing power, which refers to distribution over relatively large-scale profiles, and micro-throwing power, which relates to smaller irregularities... 

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