Solids, binary systems

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Because of the interest in its use in elevated-temperature molten salt electrolyte batteries, one of the first binary alloy systems studied in detail was the lithium-aluminium system. As shown in Fig. 1, the potential-composition behavior shows a long plateau between the lithium-saturated terminal solid solution and the intermediate P phase "LiAl", and a shorter one between the composition limits of the P and y phases, as well as composition-dependent values in the single-phase regions [35], This is as expected for a binary system with complete equilibrium. The potential of the first plateau varies linearly with temperature, as shown in Fig. 2. 

The binary system lead-thallium shows an unusual type of phase diagram. Fig. 1, taken from Hansen (1936), represents in the main the results obtained by Kumakow Pushin (1907) and by Lewkonja (1907). The liquidus curve in the wide solid-solution region has a maximum at about 63 atomic percent thallium. The nature of this maximum has not previously been made clear. 

Tittes K, Plieth W (2007) Electrochemical deposition of ternary and binary systems from an alkaline electrolyte—a demanding way for manufacturing p-doped bismuth and antimony teUurides for the use in thermoelectric elements. J Solid State Electrochem 11 155-164... 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

The dominant mechanism of purification for column crystallization of solid-solution systems is recrystallization. The rate of mass transfer resulting from recrystallization is related to the concentrations of the solid phase and free liquid which are in intimate contact. A model based on height-of-transfer-unit (HTU) concepts representing the composition profile in the purification section for the high-melting component of a binary solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 20-10. The column crystallizer was operated at total reflux. The solid line through the data was com-putecfby Powers et al. (op. cit., p. 364) by using an experimental HTU value of 3.3 cm. 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

The adsorption plateaus on this solid, determined with each of the surfactants (Table II) and the individual CMC values, were used to calculate the adsorption constants input in the model. Figure 3 compares the total adsorption (sulfonate + NP 30 EO) of the pseudo-binary system investigated as a function of the initial sulfonate fraction of the mixtures under two types of conditions (1) on the powder solid, batch testing with a solid/liquid ratio, S/L = 0.25 g/cc (2) in the porous medium made from the same solid, for which this solid ratio is much higher (S/L = 4.0 g/cc). 

Connors and Jozwiakowski have used diffuse reflectance spectroscopy to study the adsorption of spiropyrans onto pharmaceutically relevant solids [12]. The particular adsorbants studied were interesting in that the spectral characteristics of the binary system depended strongly on the amount of material bound. As an example of this behavior, selected reflectance spectra obtained for the adsorption of indolinonaphthospiropyran onto silica gel are shown in Fig. 1. At low concentrations, the pyran sorbant exhibited its main absorption band around 550 nm. As the degree of coverage was increased the 550 nm band was still observed, but a much more intense absorption band at 470 nm became prominent. This secondary effect is most likely due to the presence of pyran-pyran interactions, which become more important as the concentration of sorbant is increased. 

Equations (4.7) and (4.8) may be solved numerically or graphically. The latter approach is illustrated in Figure 4.2 by using the Gibbs energy curves for the liquid and solid solutions of the binary system Si-Ge as an example. The chemical potentials of the two components of the solutions are given by eqs. (3.79) and (3.80) as... 

Figure 4.2 Gibbs energy curves for the liquid and solid solution in the binary system Si-Ge at 1500 K. (a) A common tangent construction showing the compositions of the two phases in equilibrium, (b) Tangents at compositions that do not give two phases in equilibrium. Thermodynamic data are taken from reference [2],...

Let us consider a binary system for which both the liquid and solid solutions are assumed to be ideal or near ideal in a more formal way. It follows from their near-... 

The mathematical treatment can be further simplified in one particular case, that corresponding to Figure 4.10(a). As we saw in the previous section, in some binary systems the two terminal solid solution phases have very different physical properties and the solid solubility may be neglected for simplicity. If we assume no solid solubility (i.e. as =a =1) and in addition neglect the effect of the heat capacity difference between the solid and liquid components, eqs. (4.29) and (4.30) can be transformed to two equations describing the two liquidus branches ... 

Figure 4.10 (a)-(i) Phase diagrams of the hypothetical binary system A-B consisting of regular solid and liquid solution phases for selected combinations of Q q and Qs°l. The entropy of fusion of compounds A and B is 10 J K 1 mol-l while the melting temperatures are 800 and 1000 K. 

The binary systems we have discussed so far have mainly included phases that are solid or liquid solutions of the two components or end members constituting the binary system. Intermediate phases, which generally have a chemical composition corresponding to stoichiometric combinations of the end members of the system, are evidently formed in a large number of real systems. Intermediate phases are in most cases formed due to an enthalpic stabilization with respect to the end members. Here the chemical and physical properties of the components are different, and the new intermediate phases are formed due to the more optimal conditions for bonding found for some specific ratios of the components. The stability of a ternary compound like BaCC>3 from the binary ones (BaO and CC>2(g)) may for example be interpreted in terms of factors related to electron transfer between the two binary oxides see Chapter 7. Entropy-stabilized intermediate phases are also frequently reported, although they are far less common than enthalpy-stabilized phases. Entropy-stabilized phases are only stable above a certain temperature,... 

The terms on the right-hand side of the first line represent the difference between the molar free enthalpies of the solid and liquid solutions at composition X Mb. In addition, a standard result for binary systems (e.g., Swalin, 1962) states for G and n the following relationship... 

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