Solid-liquid phase diagrams

Figure 4. Liquid—solid phase diagrams of EC/DMC, EC/ EMC, and PC/EC. (Reproduced with permission from ref 159 (Figure 9). Copyright 2000 The Electrochemical Society.)...

As an example of a liquid-solid phase diagram, we consider the salol-thymol system shown in Fig. 

Below is the vapor-liquid-solid phase diagram for 02 and N2 determined by experiment... 

FIGURE 1.6-1 Two limiting typea of binary liquid-solid phase diagram (a) both solid phases are pure ( ) solids are miscible in all proportions. 

Figure 123-1 The liquid-solid phase diagram for ethyl benzene-toluene mixtures.

Figure 12.4-2 is an example of the liquid-solid phase diagram for the copper-cobalt system. There we see that copper and cobalt are partially miscible in the solid phase, and that there is a region of temperature and composition in which solid cobalt is in equilibrium with molten copper-cobalt solutions. Above its melting point, cobalt is completely miscible with copper. 

K. Takaizumi, Liquid-solid phase diagram of PrOH/water and BuOH/water systems as studied by DSC, J. Solution Chem., 2000, 29, 377-388. 

A liquid-solid phase diagram established for blends of iPP/POE by means of DSC and LS is presented at the top left of Fig. 7.12, displaying four distinct regions isotropic (I), coexistence of crystal-isotropic (Ci +1), coexistence of crystal-crystal-isotropic (C1+C2 + I), and crystal-crystal (Ci + C2- -C3). Cj and C2 represent the a- and y-form crystals of iPP, respectively, while C3 is designated for POE crystals (31). The blend preparation is identical to the procedure conducted for sPP/POE blend specimens. These iPP/POE blends are found to be completely miscible in the melt state, showing little or no depression of the melting point with composition. 

Figure 7.22 (a) Liquid-solid phase diagram for the ePP/POE blends displaying isotropic (I), coexistence of isotropic-crystal (I + Ci), coexistence of isotropic-crystal (I + Ci + C2), and crystal-crystal (Cl + C2 + C3) regions (Ci and C2 correspond to crystals of a- and 7-phase of ePP, respectively, while C3 corresponds to POE), (b-f) Optical micrographs obtained displaying the dependence of crystallization temperature on crystalline morphologies of the 70/30 ePP/POE blend isothermally crystallized at various temperatures. 

Figure 9.29 One of the many isomorphisms that exist between vapor-liquid and liquid-solid phase diagrams for binary mixtures. (1(0) An isobaric Txy diagram with a minimum boiling-point azeotrope and a miscibility gap above an LLE situation (right) an isobaric Txx diagram with a minimum melting-point solutrope and a miscibility gap above an SSE situation.

Ding, M. S., Liquid-solid phase diagrams of ternary and quaternary organic carbonates, J. Electrochem. Soc. 2004, i5i, A731-A738. 

Figure 4.19 In a full calculation of a phase diagram one can include the liquid phase. An ideal solution produces a liquid-solid phase diagram as on the left side of the figure. As the bond energy difference from Equation 4.25 becomes more significant the solid tends to prefer to separate into two phases. This has consequenees for both the low-temperature behavior described by Equation 4.29 and Figure 4.18 and for the liquid-solid relations. The result is the middle figure. A further increase in the tendeney to phase separate leads to the behavior on the right and to a binary eutectic phase diagram as in Figure 4.8.

Fig. 2. Phase diagram for the AlCl -EtMeImCl molten salt ( ) liquid-solid phase transitions and (O) glass transitions. Adapted from Fannin et al. [33] by permission of the American Chemical Society, Inc.

We now look at the phase diagram for water in Figure 5.10. Ice melts at 0 °C if the pressure is p° (as represented by T and Pi respectively on the figure). If the pressure exerted on the ice increases to P2, then the freezing temperature decreases to 7). (The freezing temperature decreases in response to the negative slope of the liquid-solid phase boundary (see the inset to Figure 5.10), which is most unusual virtually all other substances show a positive slope of (lp/dT.)... 

The Clapeyron equation, Equation (5.1), yields a quantitative description of a phase boundary on a phase diagram. Equation (5.1) works quite well for the liquid-solid phase boundary, but if the equilibrium is boiling or sublimation - both of which involve a gaseous phase - then the Clapeyron equation is a poor predictor. 

For phase diagrams, a phase boundary is one end of a tie-line and, therefore, is dependent on the phase which exists at the other end of the tie-line. In a binary system, two independent measurements are therefore needed to define the tie-line in the case of a liquid/solid phase boundary this would be and Xg at temperature T. Ideally it would be desirable to have these two compositions as independent variables giving rise to two independent equations of error. The Lukas programme does this by making two equations but where the dependence of error on one of the measurements is weak. This is important if the two concentrations have different accuracies. For some types of experimental values newer versions of the Lukas programme offer different kinds of equations of error (Lukas and Fries 1992). 

To single out the peculiarities in the phase behavior of ionic fluids, it is convenient to consider first the behavior of nonionic (e.g., van der Waals-like) mixtures. We note, however, that the subsequent considerations ignore liquid-solid phase equilibria, which in real electrolyte solutions can lead to far more complex topologies of the phase diagrams than discussed here [150],... 

Figure 13 Liquid-liquid equilibria phase diagrams of ternary polymer solutions (Xin et at, 2008a). Open circles the simulated results dotted lines Flory-Huggins short-dot lines RFT solid lines this work.

FIGURE 11.13 Phase diagram plotted as particle density, >, versus salt concentralion for particle charge Z = 400 (a) particle diameter of 0.109 un, (b) particle diameter of 0.234 p.m, (c) particle diameter of 0.400 /am. The BCC—FCC phase boundaries are the same for the three cases, but the liquid-solid phases boundaries are pushed to lower densities as the particle size is increased. Taken from Shih et al. [48]. Reprinted by permission by El vier Science Publishing. 

Solid-liquid equilibrium phase diagrams play an important role in the design of industrial crystallization processes. The calculation of phase diagrams can be used to validate the activity coefficient model used for process simulation. 

A general III—V solid-liquid ternary phase diagram is depicted in Figure 1. The two III—V binary systems, A-C and B-C, show similar behavior. Each system forms an equimolar compound,... 

In a one-component, or unary, system, only one chemical component is required to describe the phase relationships, for example, iron (Fe), water (H2O) or methane (CH4). There are many one-component systems, including all of the pure elements and compounds. The phases that can exist in a one-component system are limited to vapour, liquid and solid. Phase diagrams for one-component systems are specified in terms of two variables, temperature, normally specified in degrees centigrade,... 

Figure 5. Isothermal solid-liquid equilibrium phase diagram for the solvent + lauric acid + myristic acid system, (ideal solution)...

Since pressure and density are often unimportant to descriptions of liquids and solids, binary liquid-liquid and solid-solid phase diagrams are often limited to plots of temperature vs. composition. Figure 8.20 shows such a Txx diagram computed from the Porter equation with the temperature dependence of A given by... 

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