Phase diagrams binary isomorphous

In pure titanium, the crystal structure is dose-packed hexagonal (a) up to 882°C and body-centered cubic (p) to the melting point. The addition of alloying dements alters the a—p transformation temperature. Elements that raise the transformation temperature are called a-stabilizers those that depress the transformation temperature, p-stabilizers the latter are divided into p-isomorphous and p-eutectoid types. The p-isomorphous elements have limited a-solubility and increasing additions of these dements progressively depresses the transformation temperature. The p-eutectoid elements have restricted p-solubility and form intermetallic compounds by eutectoid decomposition of the p-phase. The binary phase diagram illustrating these three types of alloy... 

AC or BC, which melts at a higher temperature than either of the pure elements (except for the InSb-Sb case). The binary phase diagram consists of two simple eutectic systems on either side of the compound (e.g., the A-AC and the AC-C systems). The third binary phase diagram represents solid-liquid equilibrium between elements from the same group. In Figure 1 the A-B portion of the ternary phase diagram is depicted as being isomorphous... 

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.

The theory of crossover critical phenomena has been extended to binary mixtures. This extension is based on a principle of isomorphism of critical phenomena which states that the thermodynamic behavior of fluid mixtures is similar to that of one-component fluids provided that the mixtures are kept at a constant value of a hidden field variable C [80-82]. For mixtures with a simple phase diagram in which the critical points of the two components are connected by a continuous critical locus, this hidden field C may be taken as a function of the difference of the critical potentials of the two components [83-85]. Based on this principle crossover equations have been proposed for the thermodynamic properties of a variety of fluid mixtures near the vapor-liquid critical locus [68,69,79,86-89]. A systematic procedure for extending the application to fluids with more complex phase diagrams has been developed by Anisimov et al. [90-92]. This procedure also incorporates crossover between the one-component vapor-liquid critical limit and the liquid-liquid critical limit of incompressible liquid mixtures [90, 91, 93]. 

We will now set out to compute the free energies for the solid and liquid phases of an ideal isomorphous binary system and the resulting phase diagram using a very simple model. If we add the entropy of mixing (Equation 12.3) to the dhemical potentials of pure A and pure B solid and we can write the free energy of the solid as... 

A complete classification of smectic phases by texture is not always possible. It can happen that similar textures are observed with two liquid crystalline states separated by a phase transition.If so, an extremely useful and powerful tool for assessing the type of mesophase is the determination of the isobaric temperature-concentration diagrams of binary mixtures. According to Sackmann and Demus isomorphous liquid crystals are considered as equivalent and characterized by the same symbol. While uninterrupted miscibility establishes isomorphism, the converse is not necessarily true. Temperature-composition phase diagrams for liquid crystalline mixtures can be generated from thermal data or, because of the various optical features characteristic of each mesophase structure, from observations of microscopic textures of the mesophases between crossed polarizers. The latter method (also called the contact method allows great rapidity in the assessment of the phase diagram. 

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