Ideal solution phase diagrams

Figure 17 Idealized, theoretical phase diagram for a binary surfactant/water system (Li is a solution of micelles, L2 is a solution of reversed micelles).

Equations diagrams (2a) and (b) allow calculation of such as those illustrated in Figs. ideal solution phase lb through g. The... 

Figure 12.9 Accessing the co-crystal region by extrapolation of the individual solubilities in a highly non-ideal ternary phase diagram. The co-crystal domain is reached by adding A to a saturated solution of B in S (solid arrow), but not by adding B to a saturated solution of A in S (dotted arrow).

Ideal and real solid solutions, phase diagrams... 

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).

Replacing —(S — S ) by —and integrating Eq. (1.13) gives the final expression for an ideal binary phase diagram of a solid solution system A-B. This equation is also indicated as the van Laar equation for a two-component system A-B [3]. 

It can be seen in Fig. 1.5 that the higher the heats of fusion the broader the width between the liquidus and solidus lines of an ideal system. Furthermore, the difference between the heats of fusion determines the asymmetric shape of the phase diagram. In Section 1.3.1 the consequences of the shape of the solid solution phase diagrams on the segregation behavior in normal freezing growth processes will be discussed. 

It is essentially a phase diagram which consists of a family of isotherms that relate the equilibrium pressure of hydrogen to the H content of the metal. Initially the isotherm ascends steeply as hydrogen dissolves in the metal to form a solid solution, which by convention is designated as the a phase. At low concentrations the behaviour is ideal and the isotherm obeys Sievert s Law, i.e.,... 

Figure 8.14 Relationship between the (p. v) and (/. x) (vapor + liquid) phase diagrams for an ideal solution.

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... 

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.

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Figure 4.4 Phase diagram for the system Si-Ge at 1 bar. The solid lines represent experimental observations [2] while the dotted and dashed lines represent calculations assuming that the solid and liquid solutions are ideal with ACp -f 0 and ACp = 0, respectively.

In this particular case of ideal solutions the phase diagram is defined solely by the temperature and enthalpy of fusion of the two components. 

Positive deviations from ideal behaviour for the solid solution give rise to a miscibility gap in the solid state at low temperatures, as evident in Figures 4.10(a)-(c). Combined with an ideal liquid or negative deviation from ideal behaviour in the liquid state, simple eutectic systems result, as exemplified in Figures 4.10(a) and (b). Positive deviation from ideal behaviour in both solutions may result in a phase diagram like that shown in Figure 4.10(c). 

Negative deviation from ideal behaviour in the solid state stabilizes the solid solution. 2so1 = -10 kJ mol-1, combined with an ideal liquid or a liquid which shows positive deviation from ideality, gives rise to a maximum in the liquidus temperature for intermediate compositions see Figures 4.10(h) and (i). Finally, negative and close to equal deviations from ideality in the liquid and solid states produces a phase diagram with a shallow minimum or maximum for the liquidus temperature, as shown in Figure 4.10(g). 

In Chapter 13 we discussed briefly the solid-liquid equilibrium diagram of a feldspar. Feldspar is an ideal, solid solution of albite (NaAlSiaOg) and anorthite (CaAlSi20g) in the solid state as well as an ideal, liquid solution of the same components in the molten state. The relationships that we have developed in this chapter permit us to interpret the feldspar phase diagram (Figure 13.4) in a quantitative way. 

The use of an ideal-solution model meant that there were a number of instances where calculated and experimental results were quantitatively at variance. However, the approach very successfully predicted the general form of most of the phase diagrams, for example whether they were peritectic or eutectic, and accounted for the appearance of intermediate phases in systems such as Cr-Rh. That the approach could do this using such simple and internally self-consistent models is a demonstration of the inherent power of CALPHAD methods. The importance of this first step therefore cannot be overestimated, although its significance was not... 

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