Thermodynamics, solid solutions

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

De Fontaine, D. (1979) Configurational thermodynamics of solid solutions, in Solid State Physics, eds. Ehrenreieh, H., Seitz, F. and Turnbull, D. (Aeademie Press, New York) p. 74. 

A common feature of all clathrates discussed so far is a host lattice, by itself thermodynamically unstable, which is stabilized by inclusion of the second component. The forces binding this component must be similar in nature to the intermolecular forces in liquids. It seems natural, therefore, to regard a clathrate compound as a solid solution of the second component in the (meta-stable) host lattice. 

Gold-copper, alloy (Au5Cu5, AuBCuB(S)), calculation of thermodynamic quantities, 136, 142 solid solution (CuAu), 129 Gold-lead, alloy (Au5Pb5), calculation of thermodynamic quantities, 136 Gold-nickel, alloy (Au5Ni8), calculation of thermodynamic quantities, 136, 142... 

Lead, excess entropy of solution of noble metals in, 133 Lead-thalium, solid solution, 126 Lead-tin, system, energy of solution, 143 solution, enthalpy of formation, 143 Lead-zinc, alloy (Pb8Zn2), calculation of thermodynamic quantities, 136 Legendre expansion in total ground state wave function of helium, 294 Lennard-Jones 6-12 potential, in analy-... 

In addition to this work on the / phase, both the thermodynamic and kinetic properties of the terminal solid-solution region, which extends to about 9 atom% lithium at 423 °C, were also investigated in detail [36]. 

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).

Stabilization of Ru based oxides by valve metal oxides has not been studied in such detail using photoelectron spectroscopy. The most common compositions, however, with relatively high valve metal content, are not in favor of formation of a solid solution. Studies of the phase formation in Ru/Ti mixed oxides has shown [49] that homogeneous solutions are formed for compositions with Ru < 2% or Ru > 98% (see Section 3.1.1). Therefore electrodes with other compositions are better described as physical mixtures and the electrochemical behaviour is most likely that of a linear superposition of the single components. It has to be considered, however, that the investigations performed by Triggs [49] concern thermodynamic equilibrium conditions. If, by means of the preparation procedure, thermodynamic equilibrium is... 

Fowle et al. (2000) have measured the sorption by a soil bacterium (B. subtilis) of uranyl in 0.1 M NaC104 at 25°C as a function of pH, time, and solid solute ratio, using a batch technique. The stoichiometiy and thermodynamic stability of the important uranyl-surface complexes indicated that uranyl formed two different surface complexes, one involving neutral phosphate functional groups, and another with deprotonated carboxyl functional groups, on the bacterial cell wall ... 

When in solid solution in the solid state, an impurity will alter the crystallinity by introducing impurity defects into the crystal lattice, thereby changing the thermodynamic and other physical properties of the solid, including the solubility and dissolution rate [2,37]. Prolonged equilibration of the solid state with the saturated solution, however, usually leads to recrystallization of the solute and to a consequent return of the crystallinity and the measured solubility of the solid state to that of the pure, highly crystalline solid. 

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-... 

The same requirement extends to the minerals considered in the calculation. Minerals in nature occur as solid solutions in which elements substitute for one another in the mineral s crystal structure, but thermodynamic datasets generally contain data for pure minerals of fixed composition. A special danger arises in considering the chemistry of trace metals. In nature, these would be likely to occur as ions substituted into the framework of common minerals or sorbed onto mineral or organic surfaces, but the chemical model would consider only the possibility that the species occur as dissolved species or as the minerals of these elements that are seldom observed in nature. 

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],...

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

Non-stoichiometry in solid solutions may also be handled by the compound energy model see for example a recent review by Hillert [16]. In this approach the end-member corresponding to vacancies is an empty sub-lattice and it may be argued that the model loses its physical significance. Nevertheless, this model represents a mathematically efficient description that is often incorporated in thermodynamic representations of phase diagrams. 

The use of energy minimization can be extended to solid solutions and highly non-stoichiometric compounds. In principle the method is simple we take a suitable thermodynamic average over the results of minimizations of different possible arrangements of the atoms. The overall procedure for a solution A0.5B0.5 is then as follows ... 

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