Fictitious component

Use vapor pressure points for a fictitious component having the mixture molecular weight. This is better than calculating AHvap for individual components. Invariably, a light component or two will be near their critical points and give wild results, off by more than 100%. 

In geochemistry it is necessary to describe the composition of pyroxene by end-members that are compositionally simple and stoichiometrically well defined. It is also opportune to distinguish the various structural classes, because P-T stabihty and reactivity vary greatly with type of polymorph. This inevitably requires the formulation of fictitious components (i.e., components that have never been synthesized as pure phases in the structural form of interest, but that are present as members of pyroxene mixtures). For example, table 5.30 gives the list of pyroxene geochemical components proposed by Ganguly and Saxena (1987) (partly modified here). 

Based on the statistic thermodynamic treatment [156, 157], equilibria between the bulk phase and a monolayer thickness surface phase is assumed. Following the Koukkari and Pajarre [158] proposal, a fictitious species, Area, is introduced in the imaginary surface phase. The components of the surface phase are the fictitious components SiAm, AlAn, BAp, CAq, etc. The stoichiometric coefficients of the components in the surface phase can be determined by the molar surface area of the pure element. The chemical potentials of the components in surface phase are determined by the relation ... 

The molar surface areas and surface tensions of the metastable liquid B, C, O, and N have been estimated from the experimental values available in the literature using code written for this purpose. The chemical potential of the fictitious component, pArea, is equivalent to the surface tension of liquid melt, <7, with the unit, mN m 1. In this way, surface tension of a multicomponent melt can be directly determined using commercial thermodynamic software, ChemSheet, for example. 

Wei and Prater found that a new set of fictitious components, B, can be defined that have the important property of being uncoupled from each other. The quantities of B are represented by These components decay according to... 

Complex kinetic schemes cannot be handled easily, and, in general, a multidimensional search problem must be solved, which can be difficult in practice. This general problem has been considered for first-order reaction networks by Wei and Prater [13] in their now-classical treatment. As described in Ex. 1.4-1, their method defines fictitious components, B , that are special linear combinations of the real ones, Aj, such that the rate equations for their decay are uncoupled, and have solutions ... 

A first illustration of some of the features of the model presented above is performed in this section, on a fictitious component. 

If components other than oxides are used, it is advantageous to define fictitious components, for example the component F2—O (= fluorine-oxygen, with M = 2x 19—16 = 22) this can be used to replace a fluoride with an oxide and this hypothetical oxide component, for exart5)le Cap2 = CaO -H F2—O. This reduces the amount of data required... 

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. 

Using the equilibrium equations of the elasticity theory enables one to determine the stress tensor component (Tjj normal to the plane of translumination. The other stress components can be determined using additional measurements or additional information. We assume that there exists a temperature field T, the so-called fictitious temperature, which causes a stress field, equal to the residual stress pattern. In this paper we formulate the boundary-value problem for determining all components of the residual stresses from the results of the translumination of the specimen in a system of parallel planes. Theory of the fictitious temperature has been successfully used in the case of plane strain [2]. The aim of this paper is to show how this method can be applied in the general case. 

In integrated photoelasticity it is impossible to achieve a complete reconstruction of stresses in samples by only illuminating a system of parallel planes and using equilibrium equations of the elasticity theory. Theory of the fictitious temperature field allows one to formulate a boundary-value problem which permits to determine all components of the stress tensor field in some cases. If the stress gradient in the axial direction is smooth enough, then perturbation method can be used for the solution of the inverse problem. As an example, distribution of stresses in a bow tie type fiber preforms is shown in Fig. 2 [2]. 

If we use the symmetric convention for normalization,/ 0 is the fugacity of pure liquid / at the temperature of the mixture and at some specified pressure, usually taken to be the total pressure of the system. Equation (69) presents no problem for subcritical components, where the pure liquid can exist at the system temperature. However, for supercritical components in the symmetric convention,/,0 is a fictitious quantity which must be evaluated by some arbitrary extrapolation. 

Based on the above scheme and data concerning rates of individual reactions, fictitious experimental results for a batch reactor were generated in the form of initial and final concentrations for all components of the reaction mixture (see Table A-1). Identify the stoichiometry based on these data. The desired precision for 3 is 10 ... 

Compared to the traditional BOD and COD removal concept, which considers organic matter as degradable in a fictitious removal process, the concept described has moved to highlight biomass as being the real active component, depending on the nature and availability of organic substrates and electron acceptor. The heterotrophic biomass is, therefore, in terms of its activity, the central component of such a concept. 

For simplicity, we will use the fictitious chemical species as the subscripts whenever there is no risk of confusion. As shown above, this reaction can be rewritten in terms of two reacting scalars and thus two components for S. The closure problem, however, cannot be eliminated by any linear transformation of the scalar variables. 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

Table 5.37 lists the various terms of the lattice energy of some clinopyroxene components. Data refer to the C2/c spatial group. Components Mg2Si206 and Fe2Si20g, which crystallize in Pljlc, must thus be considered fictitious. ... 

W. Fickett in "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermole-cular Potentials , LosAlamosScientific-LabRept LA-2712(1962), pp 38-42, reports that pseudopotential theories are obtd by an approach completely different from perturbation theories. The problem of defining a system of detonation products consisting of both solid carbon in some form and a fluid mixt of the remaining product species has been formally rearranged to a single fictitious substance with an extremely complicated compn- temp-dependent potential function , called the pseudopotential. The fictitious substance corresponding to this potential is clearly non-conformal with the components of the mixt... 

The crucial bit of cleverness, then, is to take as a starting point a fictitious system of non-interacting electrons that have for their overall ground-state density the same density as some real system of interest where the electrons do interact (note that since the density determines the position and atomic numbers of the nuclei (see Eq. (8.2)), these quantities are necessarily identical in die non-interacting and in the real systems). Next, we divide the energy functional into specific components to facilitate further analysis, in particular... 

The Gibbs convention (Equation 17) states that we compare the real system with a fictitious one having the same total volume and total numbers of moles of all constituents as the real system. Under this convention the total moles of individual components 1 and 2 will differ between the real and the fictitious systems, but because the total of all moles of both components is the same, the surface excesses of each must sum to zero, and this is the meaning of Equation 20. 

When dealing with the electronic ground state T2, the advantage of the T-p isomorphism can be employed the I0 Ly, and Lz components of the (fictitious) orbital angular momentum (1=1) fulfill a relationship... 

The effective medium theory consists in considering the real medium, which is quite complex, as a fictitious model medium (the effective medium) of identical properties. Bruggeman [29] had proposed a relation linking the dielectric permittivity of the medium to the volumetric proportions of each component of the medium, including the air through the porosity of the powder mixture. This formula has been rearranged under a symmetrical form by Landauer (see Eq. (8), where e, is the permittivity of powder / at a dense state, em is the permittivity of the mixture and Pi the volumetric proportion of powder / ) and cited by Guillot [30] as one of the most powerful model. 

We choose the pure component to be the reference state for the compound, and therefore also the standard state. We choose the reference state of the M + species to be a fictitious system that contains only M + molecular entities and the reference state of A species to be a fictitious system containing only A molecular entities according to Equation (8.203). The symbols, p t and p% then represent the chemical potentials of the M+ and A species, respectively, in their standard state—the fictitious systems. However, the pure component is also a mixture of the two ions and, according to Equations (8.202) and (8.203), we have... 

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