Solid solution phase relationships

Phase Relationship between the Solid and Liquid. A phase relationship may involve a number of crystalline forms from which materials can be separated. When a solid material is precipitated as a result of the solution becoming supersaturated, crystallization occurs. Crystallization may be achieved by... 

Oxysalt bonded cements are formed by acid-base reactions between a metal oxide in powdered solid form and aqueous solutions of metal chloride or sulphate. These reactions typically give rise to non-homo-geneous materials containing a number of phases, some of which are crystalline and have been well-characterized by the technique of X-ray diffraction. The structures of the components of these cements and the phase relationships which exist between them are complex. However, as will be described in the succeeding parts of this chapter, in many cases there is enough knowledge about these cements to enable their properties and limitations to be generally understood. 

Two situations are found in leaching. In the first, the solvent available is more than sufficient to solubilize all the solute, and, at equilibrium, all the solute is in solution. There are, then, two phases, the solid and the solution. The number of components is 3, and F = 3. The variables are temperature, pressure, and concentration of the solution. All are independently variable. In the second case, the solvent available is insufficient to solubilize all the solute, and the excess solute remains as a solid phase at equilibrium. Then the number of phases is 3, and F = 2. The variables are pressure, temperature and concentration of the saturated solution. If the pressure is fixed, the concentration depends on the temperature. This relationship is the ordinary solubility curve. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Fig. 2. Relationship between catalyst temperature and reaction time for reaction catalyzed by Ni/Al203(—) and Ni-MgO solid solutions (—) temperature (K) of the gas phase (a) 1019 (b) 899 (c) 809 (d) 625. The reaction was carried out in a fixed-bed reactor (a quartz tube of 2 mm inside diameter) at atmospheric pressure. Before reaction, the feed gas was allowed to flow through the catalyst undergoing heating of the reactor from room temperature to 1073 K at a rate of 25 K min-1 to ignite the reaction, and then the reactant gas temperature was decreased to the selected value. Reaction conditions pressure, 1 atm catalyst mass, 0.04 g feed gas molar ratio, CH4/O2 = 2/1 GHSV, 90,000 mL (g catalyst)-1 h-1) (25).

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. 

Henry s Law constant (i.e., H, see Sect. 2.1.3) expresses the equilibrium relationship between solution concentration of a PCB isomer and air concentration. This H constant is a major factor used in estimating the loss of PCBs from solid and water phases. Several workers measured H constants for various PCB isomers [411,412]. Burkhard et al. [52] estimated H by calculating the ratio of the vapor pressure of the pure compound to its aqueous solubility (Eq. 13, Sect. 2.1.3). Henry s Law constant is temperature dependent and must be corrected for environmental conditions. The data and estimates presented in Table 7 are for 25 °C. Nicholson et al. [413] outlined procedures for adjusting the constants for temperature effects. 

In Chapter 13 we discussed briefly the solid-liquid equilibrium diagram of a feldspar. Feldspar is an ideal, solid solution of albite (NaAlSiaOg) and anorthite (CaAlSi20g) in the solid state as well as an ideal, liquid solution of the same components in the molten state. The relationships that we have developed in this chapter permit us to interpret the feldspar phase diagram (Figure 13.4) in a quantitative way. 

The second type of transformation, the reconstructive transformation involves dis-solution/reprecipitation the initial phase breaks down completely (dissolves) and the new phase precipitates from solution (for a review see Blesa Matijevic, 1989). There is, therefore, no structural relationship between the precursor and the product. In contrast to the solid-state transformation, the reconstructive process is... 

Foster, P.K. Welch, A.J.F. (1956) Metal-oxide solid solutions. Part 1. Lattice constant and phase relationships in ferrous oxide (wiistite) and in solid solutions of ferrous oxide and manganous oxide. Trans. Faraday Soc. 52 1626-1635... 

The fugacity coefficient of the solid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity in brackets in equation 2, is defined as the real solubility divided by the solubility in an ideal gas. The solubility in an ideal gas is simply the vapor pressure of the solid over the pressure. Enhancement factors of 104 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 1010. Solubility data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting in a fairly linear relationship (52). 

The relationship between aluminous sepiolite and the magnesian form is not at all clear as yet. The question of whether or not aluminous sepiolite can be precipitated directly from solution should be posed since alumina concentration in alkaline solutions (pH 7-9) is assumed to be quite low. For the present, palygorskite should probably be considered as a phase produced through solid-solution equilibria due to its high alumina content. Possibly most sepiolites are produced in this way. Even the inonomineralic deposits in saline lakes or deep sea cores contain sepiolites with high alumina contents (Parry and Reeves, 1968 McLean, et al., 1972). 

Colloid Stability as a Function of pH, Ct, and S. The effects of pertinent solution variables (pH, Al(III) dosage Ct, Al(III) dosage relative to surface area concentration of the dispersed phase S upon the collision efficiency, have been determined experimentally for silica dispersions and hydrolyzed Al(III). However, one cannot draw any conclusion from the experimental results with respect to the direct relationship between conditions in the solution phase and those on the colloid surface. It has been indicated by Sommerauer, Sussman, and Stumm (17) that large concentration gradients may exist at the solid solution interface which could lead to reactions that are not predictable from known solution parameters. 

The Gibbs phase rule is the basis for organizing the models. In general, the number of independent variables (degrees of freedom) is equal to the number of variables minus the number of independent relationships. For each unique phase equilibria, we may write one independent relationship. In addition to this (with no other special stipulations), we may write one additional independent relationship to maintain electroneutrality. Table I summarizes the chemical constituents considered as variables in this study and by means of chemical reactions depicts independent relationships. (Throughout the paper, activity coefficients are calculated by the Debye-Hiickel relationship). Since there are no data available on pressure dependence, pressure is considered a constant at 1 atm. Sulfate and chloride are not considered variables because little specific data concerning their equilibria are available. Sulfate may be involved in a redox reaction with iron sulfides (e.g., hydrotroilite), and/or it may be in equilibrium with barite (BaS04) or some solid solution combinations. Chloride may reach no simple chemical equilibrium with respect to a phase. Therefore, these two ions are considered only to the... 

Solid-Solution Models. Compared with the liquid phase, very few direct experimental determinations of the thermochemical properties of compound-semiconductor solid solutions have been reported. Rather, procedures for calculating phase diagrams have relied on two methods for estimating solid-solution model parameters. The first method uses semiem-pirical relationships to describe the enthalpy of mixing on the basis of the known physical properties of the binary compounds (202,203). This approach does not provide an estimate for the excess entropy of mixing and thus... 

Considering all the facts discussed above, we are able to draw a diagram which shows the temperature-stable phase relationship of a binary system in which no solid solution forms. The completed equilibrium diagram or phase diagram may look like the following figure ... 

Figure 7.7 Phase relationships in the system Al2Si05-Mn2Si05 in pressure-temperature-composition space projected onto the P,Tplane (from Abs-Wurmbach et al., 1983 Langer, 1988). Note the large increase of the andalusite stability field (And) with increasing Mn3+ contents plotted as mole per cent theoretical MnjSiO end-member. Insets (a) and (b) show how the triple point at 500 °C and 3.8 kb for pure Al2Si05 increases with rising Mn3 content of andalusite. [Legend to Mn-Al solid-solutions (ss) Ky = kyanite Sill = sillimanite Bm=braunite Cor=corundum Vir=viridine Qu=quartz.]...

If the composition of hydrogen in this system were to be fixed at a lower concentration, such that there is but a single condensed phase comprised of the two components in equilibrium with hydrogen gas (i.e., a solid solution of metal and absorbed hydrogen gas, but no metal hydride), there will be two degrees of freedom (/ = 2). There is no fixed relationship between pressure and temperature at constant composition in such a system. Both temperature and hydrogen pressure may be varied, changing the absorption or desorption... 

Equilibrium partitioning and mass transfer relationships that control the fate of HOPs in CRM and in different phases in the environment were presented in this chapter. Partitioning relationships were derived from thermodynamic principles for air, liquid, and solid phases, and they were used to determine the driving force for mass transfer. Diffusion coefficients were examined and those in water were much greater than those in air. Mass transfer relationships were developed for both transport within phases, and transport between phases. Several analytical solutions for mass transfer were examined and applied to relevant problems using calculated diffusion coefficients or mass transfer rate constants obtained from the literature. The equations and approaches used in this chapter can be used to evaluate partitioning and transport of HOP in CRM and the environment. 

For any system, stability relationships between solution phase species and solid phases can be used to construct ps—pH diagrams representing... 

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