Temperature-composition phase

Fig. 12. Pressure-swing distillation of a minimum boiling binary azeotrope, (a) Temperature—composition phase diagram showing the effect of pressure on...

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

Figure 1. Temperature-composition phase diagrams of n-butanol (C4E0) and n-butoxyethanol (C4E1), respectively, with water, (redrawn from data in refs. 4 and 5.)...

Figure 2. Temperature-composition phase diagram for a polymer solution. T = (T - 0)/0...

Figure 2.3 Free energy of mixing curves for solid and liquid phases at various temperatures (a-e) and resulting temperature-composition phase diagram for a completely soluble binary component system (f). From O. F. Devereux, Topics in Metallurgical Thermodynamics. Copyright 1983 by John Wiley Sons, hic. This material is used by permission of John Wiley Sons, Inc.

Fig. 23. Magnetic and crystallographic temperature-composition phase diagram of the Gd5(SixGe x)4 compounds (after Morellon et a). (2000)). FM, PM. AF label different magnetic phases (FM ferromagnetic, PM paramagnetic, AF antiferromagnetic). 0(1), M and 0(11) label different crystallographic structures (0(1) orthorhombic Gd Si4 structure, M monoclinic structure, 0(11) orthorhombic GdsGe4 structure). The solid line marks the first-order magnetostructural phase boundary.

The coherency strain energy introduces an additional barrier to spinodal decomposition, which causes a shift on the temperature-composition phase diagram of the chemical spinodal, defined by d2filom/dc% = 0, to the coherent spinodal, defined by... 

A temperature-composition phase diagram for a surfactant solution is a characteristic phase diagrarr that delineates the conditions under which crystalline surfactant, monomers, or micelles will exist. On the phase diagram shown in Figure 12.5 (Smirnova, 1995), L represents the liquid phase, S the solid phase, and )(the surfactant mole fraction. The critical micellar temperature, CMT, is deLned as the line between the crystalline and micellar phases. Micelle formation occurs at temperatures greater than the CMT. The critical micellar concentration, CMC, line separates the micellar and... 

Temperature has a major impact on micellization and micellar solubilization. As discussed in the section of temperature-composition phase diagram, change in micellar size due to changes ir... 

Many solutes do not crystallize from a freeze-concentrated aqueous solution. Modification of the temperature/composition phase diagram to illustrate this behavior was first suggested by MacKenzie (15) and termed a supplemented phase diagram, whereas other investigators have used the term... 

Although temperature-composition phase diagrams of many liquids are similar to the one for an ideal solution shown above, there are a number of important solutions which exhibit a marked deviation. 

Figure 9. Temperature-composition phase diagram of the system pentaethylene glycol ether (C12E5), water, and n-octane. The weight ratio of water to octane is fixed at 60 to 40. Diffusivities were measured in samples denoted by filled circles. Phase diagram determined by Kahlweit et al. Reprinted with permission from Kahlweit et al. [11],...

Figure 14. Predicted (Goldstein and Leibler [19]) temperature-composition phase...

Temperature-composition phase diagrams for mixtures of solids and the liquids in equilibrium with them are very important in metallurgy and electronics. Figure 4.8 shows a simplified phase diagram for two phases that have a limited solubility for each other. 

Figure 11.6. A temperature-composition phase diagram (bottom) is generated by a series of Gibbs energy curves for each phase at multiple temperatures. The top shows the Gibbs energy curves for the a solid solution and liquid phases at Ti (as a function of composition).

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

This paper describes the results of an experimental study of condensed phase equilibria in the system MoFe-UFo carried out by thermal analysis and x-ray diffraction analysis. A temperature-composition phase diagram is constructed from the temperatures of observed thermal arrests in MoFe-UFe mixtures, and the basis for the formation of this particular type of diagram is traced to the physical properties of the pure components. The solid-solubility relations indicated by the diagram are traced to the crystal structures of the pure solids. 

Fig. 1. Temperature-composition phase diagram of polypeptide solutions...

Temperature-composition phase diagram (ideal solution)... 

Progress may be displayed on a temperature-composition phase diagram. 

Fig. 2 Pressure-temperature phase projection and examples of pressure-composition and temperature-composition phase diagrams for a Type I binary mixture.

Fig. 6.4. Experimental temperature-composition phase diagrams for several representative binary systems (a) Cu-Au (adapted from Massalski (1990)), (b) Ti-Al (adapted from Asta et at. (1992)), (c) Si-Ge (adapted from Massalski (1990)), (d) Al-O (adapted from Massalski (1990)).

Ozolips V., Wolverton C. and Zunger A., Cu-Au, Ag-Au, Cu-Ag and Ni-Au intermetallics First-Principles Study of Temperature-Composition Phase Diagrams and Structures, Phys. 

Pioneering work by Bates, Lodge and co-workers [5-12] demonstrated that the addition of diblock copolymer (A-B) into the mixture of its corresponding homopolymer A and B drives self-assembly into varied structures including droplet-type microemulsions [8], bicontinuous micro emulsions [5, 6, 8, 10, 12], hexagonal phases [10, 11] and lamellar phases [5, 8, 12]. Figure 7.1 shows a typical temperature-composition phase diagram of symmetric polyethylene (PE)/polyethylenepropylene (PEP)/PE-PEP mixtures [5]. To... 

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