Calculation geometrical 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... 

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.

Figure 12.6 Calculated absorption spectra of aluminum spheres, randomly oriented ellipsoids (geometrical factors 0.01, 0.3, and 0.69), and a continuous distribution of ellipsoidal shapes (CDE). Below this is the real part of the Drude dielectric function.

Figure 12.7 Calculated extinction cross section per unit volume of a silicon carbide ellipsoid with geometrical factors 0.1, 0.3, and 0.6. Cext - Cabs for sufficiently small absorbing particles.

Silver crystallizes in the face-centered cubic (fee) form, (a) Make a sketch of the three basal faces of silver with the Miller indices [i.e., (100), (110), and (111)] and calculate the atom densities on these faces in atoms per cm2. The interatomic distance of Ag-Ag is equal to 0.2889 nm. (b) If only geometric factors are responsible for differences in the adsorption, what is the sequence of the surface concentration of adsorbed species on the individual planes (Bockris)... 

Early attempts to establish the existence or otherwise of a geometric factor were based upon the assumption that the surfaces of metal particles consisted of extensive arrays of atoms arranged in well-defined low index planes the optimum metal—metal distances for the strain-free adsorption of the reactant hydrocarbon were calculated [84,157]. As noted in Sect. 4.2 (p. 50) such an approach led to the conclusion that only certain crystal planes should be active in alkene and alkyne hydrogenation... 

To calculate the effective diffusivity in the region of molecular flow, the estimated value of D must be multiplied by the geometric factor e/x which is descriptive of the heterogeneous nature of the porous medium through which diffusion occurs. 

Kinetic data, whether they are obtained classically from isothermal decompn studies or by DSC, can be used to calculate the critical temp at which any size of an expl can self-heat to expln. The heat-balance problem has been examined by Frank-Kamenetskii (Ref 1) and by Zinn and Mader (Ref 4). The resulting relationship between kinetic and geometric factors is as follows. ... 

There are (n+1) unknowns in this equation where n is the number of reflections contributing at radius r on the film. The intensities, I (r,4> ), in this equation are equal to the background subtracted optical densities at the centers of the reflections. These intensities, once calculated, must be corrected for geometric factors in the same way as intensities measured by conventional procedures. 

Each data point was calculated from data falling at a different radius about the center of the diffraction pattern. The intensities, I(R), have not been corrected for geometric factors. The positions, 0, are plotted relative to the position expected for the layer line assuming 49 units in three turns. 

The maximum velocity at the axis of the contactor, Wj(0), is a function of the geometric factors and operating conditions. The experimental results have been fitted to an empirical equation for calculation of the interstitial velocity at the contactor axis in jet spouted beds. The fitting has a... 

Empirical correlations proposed in this paper have been proven to be valid for calculating the interstitial velocity at any position of the contactor. These equations takes into account, as well as the geometric factors of the contactor the operating variables such as particle size, particle density and particle shape. 

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