Ideal systems mixed crystals

Classified removal of course material also can be used, as shown in Figure 16. In a crystallizer equipped with idealized classified-product removal, crystals above some size ate removed at a rate Z times the removal rate expected for a perfecdy mixed crystallizer, and crystals smaller than are not removed at all. Larger crystals can be removed selectively through the use of an elutriation leg, hydrocyclones, or screens. Using the analysis of classified-fines removal systems as a guide, it can be shown that the crystal population density within the crystallizer magma is given by the equations... 

In the case of non—eutectic systems, the solid phase shows nearly ideal mixing, so that the surfactant components distribute themselves between the micelle and the solid in about the same relative proportions (i.e., both the mixed micelle and mixed solid are approximately ideal). However, in the case of the eutectic type system, the crystal is extremely non-ideal (almost a single component), while the micelle has nearly ideal mixing. As seen in earlier calculations for ideal systems, even though the total surfactant monomer concentration is intermediate between that of the pure components, the monomer concentration of an individual component decreases as its total proportion in solution decreases. As the proportion of surfactant A decreases in solution (proportion of surfactant B increases) from pure A, there is a lower monomer concentration of A. Therefore, it requires a lower temperature or a higher added electrolyte level to precipitate it. At some... 

The premise of ideal solubility is that the system must be considered as a mixture of components that do not form mixed crystals (Wesdorp et al. 2005). If the assumption of ideality holds true, then the Hildebrand equation may predict the solubility behavior of a binary TAG mixture (Knoester et al. 1972) ... 

The phenomenon of critical mixing occurs not only in liquid solutions but also in solid solutions mixed crystals). The conditions of stability for a solid solution are identical with those discussed above for liquid solutions. In particular, a system is always stable with respect to phase separation if it is ideal (c/. chap. XV, 14), and it can only become unstable if the activity coefficients depart sufficiently from unity. ... 

Finally we give an example of a system (fig. 23.4) in which a series of mixed crystals is formed, but where the deviations from ideality are such that the sohdus and liquidus curves pass through a minimum... 

It describes the thermodyrranric equiUbrium between the concentrations of impurities X in the solid and y, in the solution. The thermodyrranric eqirilibriirm is orrly achieved at low crystal growth rates v 0. In case of systems without formation of mixed crystals this distribution coefficient should ideally be close to zero. In reahty, however, the crystallized solid will not possess a distribution coefficient of... 

In this section, we consider how the optical spectra of an impurity ion mixed-crystal system can be understood in terms of a lattice-dynamical model [6]. In particular, we consider the d manganese (IV) MnF ion doped in a CsjSiFg lattice. The sharp lines and detailed vibronic structure of the absorption and emission spectra of the A2g - Eg transition makes the Mn ion in cubic symmetry an ideal system for study [7]. 

In addition, these thin films have been important in studies of electron transfer, relevant for catalytic systems [64], molecular recognition [65], biomaterial interfaces [66], cell growth [67], crystallization [68], adhesion [69], and many other aspects [70]. SAMs provide ideal model systems, because fine control of surface functional group concentration is possible by preparing mixed SAM systems of two or more compounds, evenly distributed over the surface [71, 72], as two- or... 

If the rate of attachment is small, the system tends to be ideally mixed, and the crystallization rate then is reaction limited or interface controlled. Of course, intermediate situations can occur. In food processing and storage, most crystallization is reaction limited. However, in foods of high viscosity or with narrow pores through which the solute has to move, diffusion may be the limiting step. 

In Figure 1 a simplified process scheme of the antisolvent crystallization of sodium chloride is displayed. The process is divided into three steps the crystallization, the solid-liquid separation and the antisolvent recovery or liquid-liquid separation. In the first step sodium chloride is crystallized by mixing the feed brine with an antisolvent. The crystallization is carried out at temperatures below the liquid-liquid equilibrium line in the single liquid phase area (see Figure 2). In the second step the crystals are separated from their mother liquor, e.g. by filtration or in a centrifuge. In the third and final step the antisolvent is separated from the water phase at a temperature above the liquid-liquid equilibrium line in the two liquid phase area, in which the ternary amine-water-salt system splits up into an amine and an aqueous phase. The recovered antisolvent is recycled within the process and most ideally the water phase is reused for the dissolution of crude sodium chloride. In this paper the crystallization and the liquid-liquid separation steps will be treated. 

Figure 12.1 Gibbs free energy functions (left column) and phase diagrams (right column) for binary systems with different thermodynamic properties of the co-crystal former B. The free energy functions are plotted for the separate liquid phases of A and B ((A)iiq + (B)iiq) as the reference state (AG = 0). Relative to this, the 1 1 mixture of liquid A and B ((A + B)iiq) is stabilized by 2Rrin(0.5) as a result of the mixing entropy. The melting points of A and AB are fixed and indicated by open circles, whereas the variable melting point of B is indicated by a solid circle. The liquidus curves in the phase diagrams are calculated based on the assumption of ideal behavior (Equations (12.1) to (12.3)).

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