Solid-liquid diagram

The more components in a system, the more complex are the phase equilibria and it is more difficult to represent phases graphically. Descriptions of multi-component solid-liquid diagrams and their uses have been given by Mullin 3, Findlay and Campbell , Ricci , Null(10) and Nyvlt 11 1 and techniques for predicting multi-component solid-liquid phase equilibria have been presented by Hormeyer et alS12 Kusik el al.(n), and Sander et al.(U). 

In practice, the presence of other aromatics signiheantiy affects the solid/liquid diagram of the mixture, but, as a first approximation, only the shape of the ME Iiquidus is modified Indeed as shown by the solubilit) cun es of the different isomers in the aromatic solution, considered to be ideal (Fig. 4.11), p-xylene is the compound that crystallizes first as the temperature is lowered... 

Construction of material balance lines on solid-liquid diagrams depends... 

A brief discussion of solid-liquid phase equihbrium is presented prior to discussing specific ciystaUizatiou methods. Figures 22-1 and 22-2 illustrate the phase diagrams for biuaiy solid-solution and eutec-... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

Figure 9.2. Constitutional supercooling in alloy solidification (a) phase diagram (b) solute-enriched layer ahead of the solid/liquid interface (c) condition for a stable interface (d) condition...

The recent book by Young [91Y02], Phase Diagrams of the Elements, presents an authoritative and comprehensive account of the influence of pressure on polymorphic and solid-liquid transitions. Both theoretical and experimental work are succinctly summarized. 

Crystallization-based separation of multi-component mixtures has widespread application. The technique consists of sequences of heating, cooling, evaporation, dilution, diluent addition and solid-liquid separation. Berry and Ng (1996, 1997), Cisternas and Rudd (1993), Dye and Ng (1995), Ng (1991) and Oyander etal. (1997) proposed various schemes based on the phase diagram. Cisternas (1999) presented an alternate network flow model for synthesizing crystallization-based separations for multi-component systems. The construction... 

Over the years, Pourbaix and his co-workers in the CEBELCOR Institute, founded under his direction, extended these diagrams by including lines for metastable compounds. Figure 7.66 illustrates such a presentation for the Fe-O system over the temperature range 830-2200 K. Pourbaix used these diagrams as a basis for a discussion of the stability of metallic iron (solid, liquid and vapour phases), the oxides of iron as a function of oxygen pressure and temperature from which he explained the protection of iron at high temperature by immunity and passivation. He also pointed out the... 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

In the CO2 phase diagram of Figure 8.1, we considered only (solid + liquid), (vapor + solid) and (vapor + liquid) equilibria. A (solid + solid) phase transition has not been observed in C(>,m but many substances do have one or more. Equilibrium can exist between the different solid phases I, II, III, etc., so that... 

Figure 8.21 gives the ideal solution prediction equation (8.36) of the effect of pressure on the (solid + liquid) phase diagram for. yiC6H6 + xj 1,4-C6H4(CH3)2. The curves for p — OA MPa are the same as those shown in Figure 8.20. As... 

Solid + Liquid Equilibria in Less Ideal Mixtures We should not be surprised to find that the near-ideal (solid + liquid) phase equilibria behavior shown in Figures 8.20 and 8.21 for (benzene + 1,4-dimethylbenzene) is unusual. Most systems show considerably larger deviations. For example, Figure 8.22 shows the phase diagram for. vin-C Hw +. The solid line is the fit of the... 

Figure 8.22 (Solid + liquid) phase diagram for. vin-CiaHut +. viCsHs. The circles are the experimental melting temperatures and the lines are the fit of the experimental results to equation (8.31). The dashed lines are the ideal solution predictions from equation (8.30).

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

In Fig. 8.8, we see that sulfur can exist in any of four phases two solid phases (rhombic and monoclinic sulfur), one liquid phase, and one vapor phase. There are three triple points in the diagram, where various combinations of these phases, such as monoclinic solid, liquid, and vapor or monoclinic solid, rhombic solid, and liquid, coexist. However, four phases in mutual equilibrium (such as the vapor, liquid, and rhombic and monoclinic solid forms of sulfur, all in mutual equilibrium) in a one-component system has never been observed, and thermodynamics can be used to prove that such a quadruple point cannot exist. 

Use the phase diagram for compound X below to answer these questions (a) Is X a solid, liquid, or gas at normal room temperatures (b) What is the normal melting point ol X ... 

The potential-pH diagram for the system selenium-water at 25 °C is given in Fig. 2.3. This diagram was construeted by using the homogeneous and heterogeneous (solid/liquid, gas/liquid) equilibria listed in the previous page, in which all of the above-referred dissolved substances of selenium (as well as solid Se) participate. 

Fig. 15. Schematic energy diagram of the n-type semiconductor electronic bands at the solid/liquid interface modulated by discontinuous metal coating ...

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