Multicomponent system ternary

More complicated phase diagrams for multicomponent systems (ternary and higher) can be found in the references at the end of the chapter. 

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

Studies on multicomponent systems have been mainly restricted to relatively simple ternary systems containing a solvent as component 1 and-solutes as components 2 and 3. For such a system, under zero-volume flow conditions (Eq. (3)), exact expressions for the fluxes of the components 2 and 3 may be written as independent quantities of the forces involved so that the linear laws to which the Onsager reciprocal relationship applies may be written as follows341 ... 

Knowledge of the expressions for the chemical potentials of each of the components allows theoretical prediction of the critical concentration boundaries of the phase diagram for ternary solutions of biopolymeri + biopolymer2 + solvent. According to Prigogine and Defay (1954), a sufficient condition for material stability of this multicomponent system in relation to phase separation at constant temperature and pressure is the following set of inequalities for all the components of the system ... 

There is, however, another statement of the necessary and sufficient condition of thermodynamic stability of the multicomponent system in relation to mutual diffusion and phase separation that is less stringent than equation (3.20) because it may be fulfilled not for every component of the multicomponent system. For example, in the case of the ternary system biopolymeri + biopolymer2 + solvent, it appears enough to fulfil only two of the inequalities (Prigogine and Defay, 1954)... 

In earlier chapters we examined systems with one or two types of diffusing chemical species. For binary solutions, a single interdiffusivity, D, suffices to describe composition evolution. In this chapter we treat diffusion in ternary and larger multicomponent systems that have two or more independent composition variables. Analysis of such diffusion is complex because multiple cross terms and particle-particle chemical interaction terms appear. The cross terms result in TV2 independent interdiffusivities for a solution with TV independent components. The increased complexity of multicomponent diffusion produces a wide variety of diffusional phenomena. 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

The usual choice of a reference state other than the pure components is the infinitely dilute solution for which the mole fractions of all solutes are infinitesimally small and the mole fraction of the solvent approaches unity that is, the values of the thermodynamic properties of the system in the reference state are the limiting values as the mole fractions of all the solutes approach zero. However, this is not the only choice, and care must be taken in defining a reference state for multicomponent systems other than binary systems. We use a ternary system for purposes of illustration (Fig. 8.1). If we choose the component A to be the solvent, we may define the reference state to be the infinitely dilute solution of both B and C in A. Such a reference state would be useful for all possible compositions of the ternary systems. In other cases it may be advantageous to take a solution of A and B of fixed... 

In multicomponent systems, compounds are frequently formed between components. The following phase diagrams are for ABC ternary system forming a binary compound AB which melts congruently, as it is stable at its melting point ... 

Recently a fairly inexpensive way of high-temperature experimentation has been found to investigate refractory sulfides and related multicomponent systems up to temperatures of nearly 2000 °C using resistance furnaces. These techniques are discussed below and applied to some sulfide systems, in particular of those metals which belong to the VI-B group. The binary systems chromium-sulfur, molybdenum-sulfur, tungsten-sulfur, as well as some other ternary and quaternary systems and their reactions are reviewed and completed within the limits of the new experimental procedure. 

Pressure-temperature diagrams offer a useful way to depict the phase behaviour of multicomponent systems in a very condensed form. Here, they will be used to classify the phase behaviour of systems carbon dioxide-water-polar solvent, when the solvent is completely miscible with water. Unfortunately, pressure-temperature data on ternary critical points of these systems are scarcely published. Efremova and Shvarts [6,7] reported on results for such systems with methanol and ethanol as polar solvent, Wendland et al. [2,3] investigated such systems with acetone and isopropanol and Adrian et al. [4] measured critical points and phase equilibria of carbon dioxide-water-propionic acid. In addition, this work reports on the system with 1-propanol. The results can be classified into two groups. In systems behaving as described by pattern I, no four-phase equilibria are observed, whereas systems showing four-phase equilibria are designated by pattern II (cf. Figure 3). 

The Non-Random, Two Liquid Equation was used in an attempt to develop a method for predicting isobaric vapor-liquid equilibrium data for multicomponent systems of water and simple alcohols—i.e., ethanol, 1-propanol, 2-methyl-l-propanol (2-butanol), and 3-methyl-l-butanol (isoamyl alcohol). Methods were developed to obtain binary equilibrium data indirectly from boiling point measurements. The binary data were used in the Non-Random, Two Liquid Equation to predict vapor-liquid equilibrium data for the ternary mixtures, water-ethanol-l-propanol, water-ethanol-2-methyl-1-propanol, and water-ethanol-3-methyl-l-butanol. Equilibrium data for these systems are reported. 

The extension of the CNT to homogeneous nucleation in atmospheric, essentially multicomponent, systems have faced significant problems due to difficulties in determining the activity coefficients, surface tension and density of binary and ternary solutions. The BHN and THN theories have been experiences a number of modifications and updates. At the present time, the updated quasi-steady state BHN model [16] and kinetic quasi-imary nucleation theory [24,66], and classical THN theory [25,33] and kinetic THN model constrained by the experimental data... 

Multicomponent systems containing four or more components become difficult to display graphically. However, process-design calculations can often be made for the extraction of the component with the lowest partition ratio K and treated as a ternary system. The components with higher K values may be extracted more thoroughly from the raffinate than the solute chosen for design. Or computer calculations can be used to reduce the tedium of multicomponent, multistage calculations. 

New data are presented for the P-T traces of the four phase line representing the melting point depressions in two ternary systems. These data are valuable for testing and development of predictive models of melting point depressions in multicomponent systems. 

Aluminum, boron, carbon, iron, nitrogen, oxygen, phosphorus, sulfur and titanium are the common impurities in the SoG-Si feedstock. Arsenic and antimony are frequently used as doping agents. Transition metals (Co, Cu, Cr, Fe, Mn, Mo, Ni, V, W, and Zr), alkali and alkali-earth impurities (Li, Mg, and Na), as well as Bi, Ga, Ge, In, Pb, Sn, Te, and Zn may appear in the SoG-Si feedstock. A thermochemical database that covers these elements has recently been developed at SINTEF Materials and Chemistry, which has been designed for use within the composition space associated with the SoG-Si materials. All the binary and several critical ternary subsystems have been assessed and calculated results have been validated with the reliable experimental data in the literature. The database can be regarded as the state-of-art equilibrium relations in the Si-based multicomponent system. 

Since the concentrations of impurities in solar cell grade silicon are in the range from ppb to a few percent, it is not necessary to take ternary interaction parameters into account. The activity coefficient of impurity, i , in a n-tli multicomponent system is given by differentiating (13.3) ... 

The good correspondence of calculations with the complex concentration dependence of activities in the CaO-FeO-SiO2 system illustrates the fact that our equations properly take into account the kinds of ternary interaction terms known to exist in such systems. (8,9,21) This feature lends confidence in the use of our equations for predictions in multicomponent systems (containing only silica as an acid component) based solely upon the subsidiary binaries. If, as it appears, this is generally true, our method provides an important predictive capability. 

We can theoretically justify an asymmetric combining rule which, for cases in which silica is the only acid component, leads to a priori predictions for ternary systems based on data for the three subsidiary binaries. It appears likely that such predictions would be valid for multicomponent systems. 

In tills section, we examine the thermodynamics of systems which contain a mixture of species. First, we generalize the thermodynamic analysis of the previous section to multicomponent systems, deriving the Gibbs phase rule. Then we describe the general phase behavior of binary and ternary mixtures. 

The development of cosmetic microemulsion cleansers with alkyl polyglycosides (APG) was described by Forster et al. [4]. This class of non-ionic surfactants has excellent environmental and skin compatibility. Cosmetic cleanser multicomponent systems are required to have good foaming and cleansing performance. Figure 8.3 shows a pseudo-ternary phase diagram of a five-component formulation. It consists of water, the oil dioctyl cyclohexane (DOCH), the non-ionic surfactant C12/14-APG, the anionic surfactant fatty alcohol ether sulphate (FAES) and the co-surfactant sorbitan monolaurate (SML). The phase diagram... 

The general equation for component activity coefficients is derived from summing the binary interactions throughout a multicomponent system. For example, the activity coefficient for component three of a ternary mixture is given by... 

Not aU possible applications of mass transfer theory have been discussed, and multicomponent systems have been treated as pseudo binary or ternary systems. To delve deeper, the reader should consult specialized books, some of which are listed in the References section. 

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