Thermodynamic properties of solid solutions

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

In application of this method to solubility data (8) in the KCl-KBr- O system at 25°C, it is found that equilibrium is in general not attained, though some mid-range compositions may be near equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. It is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be demonstrated that equilibrium has been attained. 

The models used to deseribe the thermodynamic properties of solid solutions are the same as for liquid solutions. The h5rpotheses upon which these models are founded can be easily applied - all the more because the h q)othesis of the pseudo-lattice used for liquid solutions now becomes perfectly appropriate, and is no longer a hypothesis, but simply corresponds to the crystalline lattice. 

The new assessment for the Si-C system was primarily based on experimental SiC solubility data in liquid solution given by Scace and Slack [34], Hall [35], Iguchi [36], Kleykamp and Schumacher [37], Oden and McCune [38], and Ottem [14], Solid solubility data given by Nozaki et al. [39], Bean [40], and Newman [41] were used to determine the properties of solid solution. The eutectic composition reported by Nozaki et al. [39] and Hall [35] and peritec-tic transformation temperature determined by Scace [34] and Kleykamp [37] were also used in the thermodynamic optimization. Thermodynamic description of the SiC compound was taken from an early assessment [42]. The... 

Electrochemical processes occur in batteries, fuel cells, electrolysis, electrolytic plating, and corrosion (generally an undesirable process). Electrochemical processes can be used to produce electricity, to recover metals from solution, and for the measurement of the thermodynamic properties of electrolyte solutions. The device used to study electrochemical reactions is an electrochemical cell, which consists of two electrodes (metallic conductors) in electrolytes that are usually liquids containing salts, but may be solids, as in solid-state batteries. The two electrodes may be in the same electrolyte, as shown in Fig. 14.6-la, or each electrode may be in a separate compartment wiffi its... 

In 1952 James and Martin [12] replaced the liquid mobile phase with a gas phase two new chromatographic techniques were developed gas-liquid and gas-solid chromatography. This led to an unprecedented development in the analytical and preparative separation of mixtures and then, from 1969 [13,14], it allowed the determination of structure and morphology of stationary phases especially polymers and, from 1971 [15], the determination of the thermodynamic properties of polymer solutions. 

We adapt the above theory to specify the thermodynamic properties of binary solutions, whether solid or liquid. The use of lattice theory to liquids may seem paradoxical however, in considering fluid properties, one must distinguish between convection involving motion of the center of mass, and internal reconfigurations. The surroundings of a representative molecule in the liquid phase, even in convection, are a distorted version of those that prevail in the solid. Hence, as a rock-bottom approximation, it is not a travesty to apply lattice theories to the present case. 

From (1.5.6) important thermodynamic properties of perfect solutions may be directly deduced e.g. Raoult s law for the vapour pressure, osmotic pressure, equilibrium between a liquid solution and a solid phase. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

Since the interplay of theory and experiment is central to nearly all the material covered in this chapter, it is appropriate to start by defining the various concepts and laws needed for a quantitative theoretical description of the thermodynamic properties of a dilute solid solution and of the various rate processes that occur when such a solution departs from equilibrium. This is the subject matter of Section II to follow. There Section 1 deals with equilibrium thermodynamics and develops expressions for the equilibrium concentrations of various hydrogen species and hydrogen-containing complexes in terms of the chemical potential of hy-... 

In experimental investigations of thermodynamic properties of solutions, it is common that one obtains the activity of only one of the components. This is in particular the case when one of the components constitutes nearly the complete vapour above a solid or liquid solution. A second example is when the activity of one of the components is measured by an electrochemical method. In these cases we can use the Gibbs-Duhem equation to find the activity of the second component. 

By examining the compositional dependence of the equilibrium constant, the provisional thermodynamic properties of the solid solutions can be determined. Activity coefficients for solid phase components may be derived from an application of the Gibbs-Duhem equation to the measured compositional dependence of the equilibrium constant in binary solid solutions (10). 

By examining the compositional dependence of the equilibrium constant, the thermodynamic properties of the solid solution can be determined if the final solution is either at equilibrium or stoichiometric saturation. That is, the provisional activities and activity coefficients will be valid if either equilibrium or stoichiometric saturation is attained in the solubility data. 

Most thermodynamic data for solid solutions derived from relatively low-temperature solubility (equilibration) studies have depended on the assumption that equilibrium was experimentally established. Thorstenson and Plummer (10) pointed out that if the experimental data are at equilibrium they are also at stoichiometric saturation. Therefore, through an application of the Gibbs-Duhem equation to the compositional dependence of the equilibrium constant, it is possible to determine independently if equilibrium has been established. No other compositional property of experimental solid solution-aqueous solution equilibria provides an independent test for equilibrium. If equilibrium is demonstrated, the thermodynamic properties of the solid solution are also... 

Cressey G, Schmid R., and Wood B. I (1978). Thermodynamic properties of almandine-grossular garnet solid solutions. Contrib. Mineral Petrol, 67 397-404. 

The basic question is how to perform extrapolations so as to obtain a consistent set of values, taking into account various complications such as the potential presence of mechanical instability. Additional complications arise for elements which have a magnetic component in their Gibbs energy, as this gives rise to a markedly non-linear contribution with temperature. This chapter will concern itself with various aspects of these problems and also how to estimate the thermodynamic properties of metastable solid solutions and compound phases, where similar problems arise when it is impossible to obtain data by experimental methods. 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

It has been known that adsorption kinetics and/or thermodynamics of proteins depend on the electric or electrochemical properties of solid supports on which the proteins are adsorbed. This has led us to elucidate the effects of electrode potential on the adsorption behavior of avidin on the electrode surface. For this purpose, the electrode potential of a Pt electrode was varied systematically in the range of -0.5-+2.0 V in an avidin solution (pH 7.4). Although the data was somewhat scattered, a general trend was observed that the adsorption of avidin is suppressed by the application of a positive potential (+1.0-+2.0 V). This may be originating from the fact that avidin is a basic protein and has net positive charges in the solution of neutral pH. In the potential range tested, no significant acceleration in the adsorption was induced. 

Thus AC and BC can be chosen as thermodynamic components of the solid solution whose chemical potentials are independent of the C to A + atom ratio. Relying on the relative insensitivity of the thermodynamic properties of condensed phases to the pressure P, we neglect this pressure dependence in... 

Adequacy of Thermodynamic Data. Data on several important aluminosilicates appear to be insufficient for a detailed discussion of all equilibria. Information on the influence of solid solutions or coprecipitated phases on thermodynamic properties appears to be rather limited, as is that for metastable non-stoichiometric oxides (e.g., of manganese) and surface complexes. 

The relative positions of the H20—02 boundary and the Mn2+—Mn02 boundaries for both 10"3 and 10"7M activities of aqueous Mn2+ indicate that for pH values greater than about 4, Reaction 58 is spontaneous. Similarly, the pure solid phases MnCOa and Mn(OH)2 are unstable with respect to oxidation to MnO >. Extensive interpretations of manganese chemistry in terms of the thermodynamic properties of the oxides and on other solid phases and solution species of manganese can be found in the recent literature (3,14, 24). 

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