Binary systems experimental examples

The dilated van Laar model is readily generalized to the multicomponent case, as discussed in detail elsewhere (C3, C4). The important technical advantage of the generalization is that it permits good estimates to be made of multicomponent phase behavior using only experimental data obtained for binary systems. For example, Fig. 14 presents a comparison of calculated and observed -factors for the methane-propane-n-pentane system at conditions close to the critical.7... 

Owing to their numerous actual and potential applications, several ternary and complex systems of these metals, especially of aluminium, have been investigated a few examples of the systematics of Al-Me-X alloys are presented in 5.18 and in Fig. 5.41. Recent contributions to this subject have been given with the study of the systems R-Al-Cu (Riani et al. 2005, and references there in). These rare earth alloys, characterized by the formation of several intermediate phases, are interesting also as raw materials for the preparation of amorphous alloys. Regularities in the trends of their properties have been underlined. The experimental and calculated data relevant to the binary systems Al-Fe, Al-Ni and Fe-Ni have been examined and discussed in a paper concerning the assessment of the ternary Al-Fe-Ni system (Eleno et al. 2006). 

An example of an early paper on a binary system is the work of Spencer and Putland (1973) on Fe-V. This combined a review of the thermodynamics and phase diagram of the Fe-V system with new, selective experimental thermodynamic... 

This chapter has shown many examples of the use of CALPHAD methods, ranging from an unusual application in a binary system, through complex equilibrium calculations to calculations for 10-component alloy systems. In all cases the use of CALPHAD methods has enhanced the understanding of processes, clearly defined alloy behaviour and provided vital information for other models, etc. It is also clear that equilibrium calculations can be used in many different areas and under a surprising number of different conditions. For numerous reasons, modelling will never completely replace experimental measurement. However, die quantitative verification of the accuracy of CALPHAD calculations now means that they can be seriously considered as an information source which can be used as an alternative to experimental measurement in a number of areas and can also enhance interpretation of experimental results. 

Binary and ternary spectra. We will be concerned mainly with absorption of electromagnetic radiation by binary complexes of inert atoms and/or simple molecules. For such systems, high-quality measurements of collision-induced spectra exist, which will be reviewed in Chapter 3. Furthermore, a rigorous, theoretical description of binary systems and spectra is possible which lends itself readily to numerical calculations, Chapters 5 and 6. Measurements of binary spectra may be directly compared with the fundamental theory. Interesting experimental and theoretical studies of various aspects of ternary spectra are also possible. These are aimed, for example, at a distinction of the fairly well understood pairwise-additive dipole components and the less well understood irreducible three-body induced components. Induced spectra of bigger complexes, and of reactive systems, are also of interest and will be considered to some limited extent below. 

As a typical example from industrial practice we consider the simulation of a process with the reaction of methylphosphinic acid and butanol to methylphosphinic acid butyl ester and water, which was modeled by Gordana Hofmann-Jovic at InfraServ Knapsack [C28]. Because of the lack of experimental data for the binary systems with phosphorous compounds, COSMO-RS was used for the prediction of the binary activity coefficients. Then the results were fitted by an NRTL equation and the entire process was modeled by a commercial process simulator. The resulting phase diagrams were in close agreement with experimental measurements obtained later (Fig. 8.2). 

In the intermediate domain of values for the parameters, an exact solution requires the specific inspection of each configuration of the system. It is obvious that such an exact theoretical analysis is impossible, and that it is necessary to dispose of credible procedures for numerical simulation as probes to test the validity of the various inevitable approximations. We summarize, in Section IV.B.l below, the mean-field theories currently used for random binary alloys, and we establish the formalism for them in order to discuss better approximations to the experimental observations. In Section IV.B.2, we apply these theories to the physical systems of our interest 2D excitons in layered crystals, with examples of triplet excitons in the well-known binary system of an isotopically mixed crystal of naphthalene, currently denoted as Nds-Nha. After discussing the drawbacks of treating short-range coulombic excitons in the mean-field scheme at all concentrations (in contrast with the retarded interactions discussed in Section IV.A, which are perfectly adapted to the mean-field treatment), we propose a theory for treating all concentrations, in the scheme of the molecular CPA (MCPA) method using a cell... 

The number of two-polymer, multipolymer, and multimonomer systems reported in the scientific and patent literature continues to rise without an adequate nomenclature to describe the several materials. This chapter is divided into three parts. (1) A proposed nomenclature system which uses a short list of elements (polymers or polymer reaction products). These elements are reacted together in specific ways by binary operations which join the two polymers to form blends, grafts, blocks, crosslinked systems, or more complex combinations. (2) The relationship between the proposed nomenclature and the mathematics of ring theory (a form of the new math9 ) is discussed. (3) A few experimental examples now in the literature are mentioned to show how the new nomenclature scheme already has been used to discover new multipolymer systems. 

The applicability of this model for the calculation of the composition of terpolymers produced at low conversions was demonstrated for a number of three component systems (see, for example, [6, 132]). This statement follows from the good agreement of the values of the terpolymer composition determined experimentally with those calculated according to the Alfrey-Goldfinger equations [45] within the framework of the terminal model. All six parameters of this model are considered to be known from the preliminary analysis of the data on three binary systems selected from the given three monomers. 

The examples discussed in the previous sections Illustrate models for deriving Isotherms for binary systems. A variety of variants (e.g. mobile adsorbates), alternatives (e.g. models based on computer simulations) and extensions (e.g. multimolecular adsorption. Inclusion of surface heterogeneity, can be, and have been, proposed. The extensions usually require more parameters so that agreement with experiment is more readily obtained, but as long as various models are not compared against the evidence, discrimination is impossible. As there are numerous theoretical (e.g. distinction between molecules in the first and second layer) and experimental (presence of minor admixtures, tenaciously adsorbing on part of the surface) variables one tends to enter a domain of diminishing returns. On the other hand, there are detailed models for certain specific, well-defined situations. Here we shall review some approaches for the sake of illustration. 

The P-V Diagram for a Multicomponent System. For a relatively volatile multicomponent system, a gasoline for example, an isotherm on the P-V diagram is similar to its counterpart for a binary system (Figure 23). However, it is commonly found that at the dew point the break in the P-V isotherm is not very pronounced in multi-component systems. Consequently, for systems of this type, it may be very difficult to fix the dew point in this manner. This experimental difficulty can be overcome by using a windowed cell and observing the pressure and volume when traces of liquid appear in the system. 

Activity coefficients can be derived from databanks, correlation models, structure interpolation methods or a priori methods. Modem methods allow the calculation of multicomponent behaviour on the basis of binary systems. In this case, only binary data are needed. Very often, however, experimental data for the binary mixture that forms the reactants are unknown. As an example let us consider the equation ... 

The numbers of transfer units for each binary pair may be obtained as described in Section 12.1.5 or from experimental data and these binary numbers of transfer units used directly in the estimation of the matrices of numbers of transfer units for multicomponent systems as Example 12.2.3 demonstrates. 

The quantity Smcs is the number of detected MCs+ ions per sputtered M atom. For fixed experimental conditions this term includes all the factors, such as, for example, T, Af2, etc. For a binary system with components A and B, for example. In and Ga as shown in Figure 16, and with ca+cb = 1, the yield of component... 

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