Calculations and Discussion

Let us accomplish the calculations for the model Si-Ni-Pt system (for detailed experimental investigations, see [13-15]). For a successful analysis we must fix the diffusivities in the intermediate phases and, the boundary equilibrium concentrations on the phase diagram, and the 

It should be noted once again that in our analysis, the diffusion characteristics of the intermediate ternary y-phase are described using the interdiffusion coefficient D for Ni and Pt species at their own sublattices in the y phase, while the diffusion characteristics of the phase are expressed through the effective diffusivity D, when the real diffusion coefficient is normahzed to the concentration interval of /3 -phase existence. 

solving Equations 9.26-9.30, we get the constants for the moving j8-phase boundaries k and k, the concentrations nd CgSAfi — y interphase boundary in both phases, the respective concentration nd the coefficient S, which describes the change of diffusivity for the jS-phase due to alloying. The results of the calculations depending on the interrelation between diffusivities of intermediate phases are presented in Table 9.1. Here, the following set of main parameters have been used. 

as the interdiffusion coefficient in the ternary y phase diminishes, it becomes possible to observe the growth suppression of the binary intermediate phase. Further, the magnitudes of boundary concentrations at the (f-y interphase boundary correspond to the conode, which shifts along the phase diagram toward c , and the respective value of Cg determines the concentration interval of the phase, which allows one to find that the effective diffusivity of the phase is less than the maximal one by 1/8, where 

the important physical factor is the effect of the slow pushing out of the third component by the moving phase boundary because of its low solubihty in the neighboring phase and with respect to the low diffusivity in the parent ternary phase. 

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As we have seen, unless the pressure is considerably larger than 1 bar, T is very nearly 1. Except for special circumstances, we will assume it is unity in future calculations and discussions of activity in solution, and we will drop the designation of (1 bar) pressure for the standard state pressure. That is,/f(l bar) will be set equal to / (/>), the vapor fugacity at a pressure p, and both will be designated as/f, so that equation (6.100) can be written as... 

In some articles cited the data are presented so that they can apply to only one step. In such cases our calculations and discussion focus on that step. 

In Section 2 we briefly present the theoretical framework and schemes of the hybrid method used to compute the electronic states of clusters and the algorithm used for structure optimizations. Section 3 is devoted to the presentation and discussion of our results and a comparison with the DIM computations of Tutein and Mayne The emission lines originating from Na(3p)Ar excited states are also calculated and discussed. 

The main purpose of this section is consideration of the FIR spectra due to the second dipole-moment component, p(f). However, for comparison with the experimental spectra [17, 42, 51] we should also calculate the effect of a total dipole moment ptot. In Refs. 6 and 8 the modified hybrid model44 was used, where reorientation of the dipoles in the rectangular potential well was considered. In this section the effect of the p(f) electric moment will be found for the hat-curved, potential, which is more adequate than the rectangular potential pertinent to the hybrid model. In Section VI.B we present the formula for the spectral function of the hat-curved model modified by taking into account the p(f) term (derivation of the relevant formula is given in Section VI.E). The results of the calculations and discussion are presented, respectively, in Sections VI.C and VI.D. 

In this paper we present a comprehensive first-principles study of the structural, electronic and optical properties of undoped and doped Si nanosystems. The aim is to investigate, in a systematic way, their structural, electronic and stability properties as a function of dimensionality and size, as well as pointing out the main changes induced by the nanostructure excitation. A comparison between the results obtained using different Density Functional Theory based methods will be presented. We will report results concerning two-dimensional, one-dimensional and zero-dimensional systems. In particular the absorption and emission spectra and the effects induced by the creation of an electron-hole pair are calculated and discussed in detail, including many-body effects. 

With the help of these relations, the alignment tensor s/2q(J = 3/2 iia) was calculated and discussed in detail in Section 4.6.1.3, using numerical values for the radial dipole integrals Res2p and Red 2p and the relative phase A. 

Trace Metal Availability for the Model Cell - Calculation and Discussion. 

Calculations have been carried out on the following systems Fe(porph) (O2) and Fe(Pc)(02) the reaction between rf-Oi and ethylene in a Mo complex Fe(por-ph) (NH3)(02) The last calculation disagrees with a previous ab initio calculation in suggesting a Fe " Of configuration for the groundstate this disagreement is attributed to a different choice of basis functions. Boca has published a review of his calculations, and discusses other calculations and crystal structure data . ... 

In a lengthy theoretical paper, Rondan and Houk considered the available data, described ab initio calculations and discussed earlier explanations concerning the stereochemical aspects of the ring openings of substituted cyclobutenes.These authors came to the following conclusions. The stereochemistry of the thermal electrocyclic conrotatory ring opening of 3- and 4-substituted cyclobutenes is controlled by... 

The temperature of the upper plate is l, and that of the lower is 0 < L- Calculate and discuss the pattern of the temperature profile (0 2), under the assumption that the viscous dissipation cannot be neglected. 

Richer et al. (1982) present thermodynamic data for silica species equivalent to a quartz solubility of 6 ppm at 25°C, which corresponds to a concentration of 1 O " mol/kg. The same solubility is supported by Fournier, who gives log (quartz) = 0.41 - 1309/T(K) (see Nordstrom et al. 1990). We will assume a quartz solubility value of 6 ppm at 25°C in future calculations and discussions. 

The distribution of spot sample compositions of a certain size, taken from a randomly mixed batch of A and B, can be calculated theoretically. The methods of calculation are standard statistical techniques, and several papers have shown how various aspects of these basic ideas can be applied to solids mixing. Most of the calculations and discussion center around three distributions binomial, normal, and Poisson. 

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