Temperature-composition phase diagrams solid-liquid

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.

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-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).

As noted above, lipids exist in a number of intermediate physical states or mesomorphs between the crystalline solid and the isotropic liquid. The stability of these phases depend on temperature and composition and each lipids pattern of dependency is conveniently described in the form of an isobaric temperature-composition phase diagram. Over the past few years two new and related methods of collecting mesomorphic phase information which are less time-consuming and more efficient... 

The thermal analysis of a number of normal alkanes was studied by Mazee (23). In the case of a binary mixture in which the components are completely miscible both in the liquid and solid states, the curves in Figure 10.12 were obtained. Curve a) is the temperature-composition phase diagram, while... 

If the system point is in a two-phase area of the phase diagram, we draw a horizontal tie line of constant temperature (on a temperature-composition phase diagram) or constant pressure (on a pressure-composition phase diagram). The lever rule applies. The position of the point at each end of the tie line, at the boundary of the two-phase area, gives the value of the composition variable of one of the phases and also the physical state of this phase either the state of an adjacent one-phase area, or the state of a phase of fixed composition when the boundary is a vertical line. Thus, a boundary that separates a two-phase area for phases a and P from a one-phase area for phase a is a curve that describes the composition of phase a as a funetion of T or p when it is in equilibrium with phase p. The curve is called a solidus, liquidus, or vaporus depending on whether phase a is a solid, liquid, or gas. 

Temperature-composition phase diagrams such as this are often mapped out experimentally by observing the cooling curve (temperature as a function of time) along isopleths of various compositions. This procedure is thermal analysis. A break in the slope of a cooling curve at a particular temperature indicates the system point has moved from a one-phase liquid area to a two-phase area of liquid and solid. A temperature halt indicates the temperature is either the freezing point of the liquid to form a solid of the same composition, or else a eutectic temperature. 

Figure 6.6 The Solid-Liquid Temperature-Composition Phase Diagram of Silicon and Germanium. Since both the solid and liquid phases are nearly ideal solutions, this diagram resembles the liquid-vapor phase diagram of an ideal liquid solution. From C. D. Thurmond, J. Phys. Chem., 57, 827 (1953).

Figure 6.17 Solid-Liquid Temperature-Composition Phase Diagram of Gold and Copper. From M. Hansen, The Constitution of Binary Alloys, McGraw-Hill, New York, 1958, p. 199.

Figure 6.18 shows the solid-liquid temperature-composition phase diagram of silver and copper at 1.00 atm. There are two one-phase regions of limited solid solubility, labeled a and /3. A tie line in the area between the a and P regions represents two coexisting saturated solid solutions, one that is mostly silver and one that is mostly copper. The tie line at 779°C connects the points representing the two solid phases and one liquid phase that can be at equilibrium with the two solid phases. The point representing this liquid phase is called the eutectic point. If a liquid that has the same composition as the eutectic is cooled, two solid phases will freeze out when it reaches the eutectic temperature, with compositions represented by the ends of the tie line. 

Figure 6.20 Solid-Liquid Temperature-Composition Phase Diagram of p-Xylene and Bromobenzene. From M. L. McGlashan, Chemical Thermodynamics, Academic Press, New York, 1979, p. 268.

Sometimes two substances form sohd-state compounds. Figure 6.21 shows the sohd-liquid temperature-composition phase diagram of aniline (A) and phenol (P), which exhibit a compound C6H5NH2 CeHsOH (abbreviated by AP) in the solid state. Such a compound has a crystal lattice containing both substances in a stoichiometric ratio. This crystal lattice is different from the crystal lattice of either A or P and A, and the three solids. A, P, and AP are almost completely insoluble in each other. The compound... 

Figure 6.21 Solid-Liquid Temperature-Composition Phase Diagram of Aniline and Phenol.

Rgure 6.22 solid-liquid temperature-composition Phase Diagram of Copper and Lanthanum. From R. E. Dickerson, Molecular Thermodynamics, W. A. Benjamin, inc.. New York, 1969, p.379. 

Sketch the solid-liquid temperature-composition phase diagram of CuCl (copper(I) chloride) and FeCl3 (iron(ni)... 

Sketch the solid-liquid and liquid-vapor temperature-composition phase diagram of titanium and uranium. The two substances form a nearly ideal liquid solution with a uranium boiling temperature of 1133°C and a titanium boiling temperature of 1660°C. The melting temperature of uranium is 770°C, and that of titanium is 882°C. There is a compound, TiUa, which melts at 890°C. The eutectic between the compound and uranium is at uranium mole fraction 0.95 and 720°C, and the eutectic between titanium and the compound is at uranium mole fraction 0.28 and 655°C. Label each area with the number of independent intensive variables. ... 

Figure 8.12 Temperature versus composition phase diagram and corresponding free-energy composition diagrams at various temperatures. In the two-phase region, a mixture of the solid and liquid solution is the lowest-energy configuration.

Make reasonable assumptions. By considering the state of the system and the nature of its components, we can introduce sensible approximations that may vastly simplify the analysis but do little harm to the accuracy of the calculation. A consideration of the state would include identification of the phases present (solid, liquid, gas), estimates for temperature and pressure, and rough estimates for the composition. (For example, is a mixture dominated by one component or are any components present in very small amounts ). In general, it is helpful to locate known state points on phase diagrams, or at least to find where a mixture temperature lies relative to the pure-component melting and critical temperatures. By nature of the components we mean the kinds of intermolecular forces, such as simple van der Waals interactions, hydro-... 

Figure 4.7a shows the temperature-concentration phase diagram for the system naphthalene-/ -naphthol, which forms a continuous series of solid solutions. The melting points of pure naphthalene and -naphthol are 80 and 120 °C, respectively. The upper curve is the liquidus or freezing point curve, the lower the solidus or melting point curve. Any system represented by a point above the liquidus is completely molten, and any point below the solidus represents a completely solidified mass. A point within the area enclosed by the liquidus and solidus curves indicates an equilibrium mixture of liquid and solid solution. Point X, for instance, denotes a liquid of composition L in equilibrium with a solid solution of composition S, and point Y a liquid F in equilibrium with a solid S. ... 

Figure 13.2 shows two temperamre-composition phase diagrams with single eutectic points. The left-hand diagram is for the binary system of chloroform and carbon tetrachloride, two liquids that form nearly ideal mixmres. The solid phases are pure crystals, as in Fig. 13.1. The right-hand diagram is for the silver-copper system and involves solid phases that are solid solutions (substimtional alloys of variable composition). The area labeled s is a solid solution that is mostly silver, and s is a solid solution that is mostly copper. Tie lines in the two-phase areas do not end at a vertical line for a pure solid component as they do in the system shown in the left-hand diagram. The three phases that can coexist at the eutectic temperature of 1,052 K are the melt of the eutectic composition and the two solid solutions.

In Section 3.3.7.S, the equilibrium partitioning of a species between a liquid phase and a solid phase was briefly considered for three types of liquid-solid equilibria. The separation between two species i and j for such liquid-solid two-phase systems is briefly considered here. There are systems where three phases can be present for example, two immiscible solid phases and a saturated solution, as in the case of solid salt, ice and a saturated salt solution. Figure 4.1.10 shows a temperature vs. composition phase diagram where solid phase 1 coexists with solid phase 2 and a saturated liquid solution at the eutectic point E. Below the eutectic temperature T, immiscible pure solid phase 1 and 2 are present together. For these and more complex systems, the reader should refer to appropriate texts (Darken and Gurry, 1953 DeHoff, 1993). Separation between species i and j in simpler two-phase systems described in Figures 3.3.6A, where the solid phase is a homogeneous solution, will be determined now. 

Eutectic composition A composition that exhibits a local temperature minimum in the solid-liquid boundary in the phase diagram. 

The phase diagram describes the equilibrium constitution of the alloy - the one given by very slow cooling. In the last example all the liquid should have solidified at the point marked 2 on Fig. A 1.35, when all the solid has moved to the composition Xp = 80% and the temperature is 255°C. Rapid cooling prevents this the solid has not had time to move to a composition Xpp = 80%. Instead, it has an average composition about half-way between that of the first solid to appear (Xpp = 90%) and the last (Xpp = 80%), that is, an average composition of about Xpp = 85%. This "rapid cooling" solidus lies to... 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

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