Binary and Ternary Systems

The addition of chemical reactions does not change this conclusion, because each chemical reaction a adds a new independent variable its extent of reaction, to each phase and at the same time adds the constraint for the corresponding chemical equilibrium A a = 0. Hence there is no net change in the number of independent variables. 

Let us compare the Gibbs phase rule and the Duhem equation the Gibbs phase rule specifies the total number of independent intensive variables regardless of the extensive variables in the system, while the Duhem equation specifies the total number of independent variables, intensive or extensive, in a closed system. 

BINARY LIQUID MIXTURES IN EQUILIBRIUM WITH THEIR VAPORS 

Consider a liquid mixture of two components, A and B, in equilibrium with their vapors. This system contains two phases and two components. The Gibbs phase rule tells us that such a system has two degrees of freedom. We may take these degrees of freedom to be the pressure and the mole fraction, xa, of component A. Thus, if we consider a system subjected to a constant pressure, for each value of the mole fraction xa there is a corresponding temperature at which the two phases are in equilibrium. For example, if the applied pressure is 0.5 bar, for the liquid to be in equilibrium with its vapor the temperature must be set at an appropriate value T. 

If the applied pressure is the atmospheric pressure, the temperature corresponds to the boiling point. In Fig. 7.5 curve I is the boiling point as a function of the mole fraction xa the boiling points of the two components A and B are Ta and Tq respectively. Curve II shows the composition of the vapor at each boiling temperature. If a mixture with composition corresponding to the 

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Cellulose Solvent. Although DMSO by itself does not dissolve cellulose, the following binary and ternary systems are cellulose solvents DMSO—methylamine, DMSO—sulfur trioxide, DMSO—carbon disulfide—amine, DMSO— ammonia—sodamide, DMSO—dinitrogen tetroxide,... 

In Part III heterogeneous equilibria involving clathrates are discussed from the experimental point of view. In particular a method is presented for the reversible investigation of the equilibrium between clathrate and gas, circumventing the hysteresis effects. The phase diagrams of a number of binary and ternary systems are considered in some detail, since controversial statements have appeared in the literature on this subject. 

The crystal structures of the borides of the rare earth metals (M g) are describedand phase equilibria in ternary and higher order systems containing rare earths and B, including information on structures, magnetic and electrical properties as well as low-T phase equilibria, are available. Phase equilibria and crystal structure in binary and ternary systems containing an actinide metal and B are... 

Tuning Structures and Properties in Lithium Binary and Ternary Systems... 

In the following, selected results will be presented on the conventional electrochemical synthesis of metal chalcogenide binary and ternary systems, conducted by employing variants of the methods outlined in the previous sections. A brief account of chemical bath deposition principles exemplified will be addressed at the end of this chapter, as being closely related to electrochemical deposition of thin films. 

Further specific information and recent results of the electrodeposition of Bi and Sb binary and ternary systems as well as of other thermoelectric materials can be found in the review of Xiao et al. [232],... 

Zeck S., and H. Knapp, "Vapor-Liquid and Vapor-Liquid-Liquid Phase Equilibria for Binary and Ternary Systems of Nitrogen, Ethane and Methanol Experiments and Data Reduction", Fluid Phase Equilibria, 25,303-322 (1986). 

Organic matter is also the essential component of natural soils and its association with microorganisms may influence the behavior and fate of toxic metals. A variety of batch complexation experiments were performed by Borrok et al. (2007) in single, binary and ternary systems for the three components natural organic matter (NOM), bacterium (B. subtilis) and metals (Pb, Cu, Cd, and Ni) to determine the significance of ternary complexation. They found that the formation of bacteria-metal-NOM complex is a rapid, fully-reversible chemical process. The stability of bacteria-metal-NOM complexes increases with the decrease of pH. All NOM fractions form ternary complexes to similar extents at circumneutral pH, but humic acid becomes the dominant NOM fraction in ternary complexes at low pH. The abundance of humic acid in ternary form is greatest with Ni or Cd systems and less with Pb and Cu systems. Their results suggest that... 

M.M. Kalina, S.K. Berdongarova, G.A. Sadykova and A.B. Fasman, Physicochemical characteristics of Raney catalysts prepared from y-metallides of some binary and ternary systems, in Mater. Resp. Nauchno-Tekh. Konf. Molodykh Uch. Pererab. Nefti Neftekhim., 3rd, A. Abdukadyrov, Ed., Sredneaziat. Nauchno-Issled. Inst. Neftepererab. Prom-sti., Tashkent, USSR, 1976, pp. 100-101 (Chem. Abs. 189 204764z). 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

Vega and Funk (59) Prediction of solid-liquid equilibria in multicomponent salt systems based on parameters estimated from binary and ternary systems. 

Stein et al. (2005) observed also that, in binary and ternary systems, the homogeneity regions of different Laves phases are generally separated by two-phase fields which are very narrow and of difficult determination. 

Thermodynamic optimisation is probably the largest single area of reported work m die jotmial CALPHAD. It invariably concerns binary and ternary systems and can... 

The main areas of application for more generalised models have, until recently, been restricted to binary and ternary systems or limited to ideal industrial materials where only major elements were included. The key to general application of CALPHAD methods in multi-component systems is the development of sound, validated thermodynamic databases which can be accessed by the computing software and, until recently, there has been a dearth of such databases. 

A simple method for predicting limits for glass-forming ability (GFA) in metallic alloys was proposed by Saunders and Miodownik (1983). lliey utilised the To criterion to predict the limit to the glass-forming range (GFR) of a number of binary and ternary systems. The To criterion follows the premise diat, if cooling conditions... 

CALPHAD calculations were made for a number of binary systems including Au-Si, (Hf,Ti,Zr)-Be and Ni-Ti (Saunders and MiodoAvnik 1983) and a series of ternaries Hf-Ti-Be, Hf-Zr-Be and Hf-Ti-Be (Saunders et al. 1985). Figure 11.6 shows such a calculation for Ni-Ti. The results were encouraging in that they predicted with reasonable accuracy the limit to glass formation when the terminal solid solutions were considered. However, there was limited success when taking into account compoimd phases. To this end the approach was extended to include the kinetics of transformation more explicitly. Remarkably good results were then obtained for a wide variety of binary and ternary system and these are reported in Section 11.3.4. 

The VLB was also measured for binary and ternary systems of [ethanol + [C2Cilm][C2S04] and [ethanol + ethyl ferf-butyl ether + [C2Cilm][C2S04] at 101.3 kPa [151]. This ternary system does not exhibit a ternary azeotrope. The possibility of [C2Cilm][C2S04] use as a solvenf in liquid-liquid extraction or as an entrainer in extractive distillation for fhe separation of the mixture ethanol/ethyl fcrf-butyl ether was discussed [151]. 

Lecat (32) is responsible for most of the azeotropic data on binary and ternary systems. Recently, however, Horsley (25) has compiled extensive tables of azeotropic data, thus making the information more available. These experimental data may be supplemented by estimations of the azeotropic composition and behavior of unknown systems by several reasonably reliable methods. Graphical methods, based on curves developed from experimental data, have been proposed by Lecat (82), Mair et al. (.ffi), Horsley (26), Skol-... 

Urea, as a cosolvent, is at the other extreme. All the concentration dependences of the binary and ternary systems are quite regular. The excess volume (Figure 6) is positive, which is rarely observed for nonelectrolytes in water. With the exception of the heat capacities of Bu4NBr, all the parameters Beu are positive for volumes and heat capacities, and the sign of the transfer functions is always opposite what we would expect for the structural hydration contribution to V° and Cp°. 

During the 1940s, a large amount of solubility data was obtained by Francis (6, 7), who carried out measurements on hundreds of binary and ternary systems with liquid carbon dioxide just below its critical point. Francis (6, 7) found that liquid carbon dioxide is also an excellent solvent for organic materials and that many of the compounds studied were completely miscible. In 1955, Todd and Elgin (8) reported on phase equilibrium studies with supercritical ethylene and a number of... 

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