Gibbs free energy curves

Figure 2.3 Conformation of the minimum Gibbs free energy curve in the binary compositional field (modified from Connolly, 1992).

Linear regions (constant slope, hence constant potentials) define the composition interval over which a two-phase assemblage is stable. Because the minimum Gibbs free energy curve of the system is never convex, the chemical potential of any component will always increase with the increase of its molar proportion in the system. 

Figure 3.9 Conformation of Gibbs free energy curve in various types of binary mixtures. (A) Ideal mixture of components A and B. Standard state adopted is that of pure component at T and P of interest. (B) Regular mixture with complete configurational disorder kJ/mole for 500 < r(K) < 1500. (C) Simple mixture IF = 10 - 0.01 X r(K) (kJ/ mole). (D) Subregular mixture Aq = 10 — 0.01 X T (kJ/mole) = 5 — 0.01 X F (kJ/ mole). Adopting corresponding Margules notation, an equivalent interaction is obtained with IFba = 15 - 0.02 X r(kJ/mole) Bab = 5 (kJ/mole).

The energy of elastic strain modifies the Gibbs free energy curve of the mixture, and the general result is that, in the presence of elastic strain, both solvus and spinodal decomposition fields are translated, pressure and composition being equal, to a lower temperature, as shown in figure 3.16. 

Figure 5JO (A) Simplified Gibbs free energy curves for various polymorphs along enstatite-diopside join at T = 1300 °C. (B) Resulting solvus, spinodal field, and miscibility gap compared with experimental data of McCallister and Yund (1977) on pyroxene unmixing kinetics (part B from Ganguly and Saxena (1992). Reprinted with permission of Springer-Verlag, New York).

The intersections of the Gibbs free energy curves of the melt with those of the solid mixture of components 1 and 2 at the various T (both phases having com-... 

Figure 7.4 Gibbs free energy curves and phase stability relations for two binary mixtures with complete miscibility of components (types I, II, and III of Roozeboom, 1899).

Roozeboom type I is obtained whenever the Gibbs free energy curve of the melt initially touches that of the mixture in the condition of pure component. This takes place at the melting temperature of the more refractory component (T2 in... 

There are two possible geometrical configurations between a mixture with a saddle-shaped Gibbs free energy curve (indicative of unmixing) and a phase with a concave curve, indicating complete miscibility of components (figure 7.7). 

Figure 7J Gibbs free energy curves and T-X phase stability relations between a phase with complete miscibility of components (silicate melt L) and a binary solid mixture with partial miscibility of components (crystals ]8). 

Figure 7,8 Gibbs free energy curves and T-X phase relations for an intermediate compound (C), totally immiscible with pure components. Column 1 Gibbs free energy relations leading to formation of two eutectic minima separated by a thermal barrier. Column 2 energy relations of a peritectic reaction (incongruent melting). To facilitate interpretation of phase stability fields, pure crystals of components 1 and 2 coexisting with crystals C are labeled y and y", respectively, in T-X diagrams same notation identifies mechanical mixtures 2-C and C-1 in G-X plots.

Figure 6.1. Gibbs free energy curves for Ti (a) a, j9 and liquid segments corresponding to the stable regions of each phase (b) extrapolated extensions into metastable regions (c) characterisation from Kaufinan (1959a) using equation (6.2) and (d) addition of the G curves for u and f.c.c. structures (from Miodownik...

Figure 2.3 The basis of the Hammond postulate and Hammond effect. The Gibbs free energy curves for a substrate and product (heavy lines) intersect on the reaction coordinate at the position of the transition state. A change of structure in S, away from the seat of reaction, destabilizes it, displacing its energy curve (lighter line) higher. The point of intersection moves closer to the substrate.

FIGURE 3.15.3 Gibbs free energy curves for liquid and solid mixtures which result in a phase diagram with a maximum. 

As an alternative, it is obvious that the result (7.5.5) coincides with the mean field approach to describe the critical phenomena of fluids. It is evident that this model corresponds to the formation of Gibbs free energy curves such as shown in panel (c) of Fig. 7.5.2. It relates to the boundary at which a system executes a first order transition the minima correspond to the r]Q values given by Eq. (7.5.5). 

We used infinite-dilution activity coefficients of 10 and 20 to create Fig. 6. Both are greater than 9, so we should expect the Margules equations to predict liquid/liquid behavior. Water and toluene have infinite-dilution activity coefficients in the thousands. They really dislike each other and break into relatively pure phases. If we examine the total Gibbs free energy curve, we gain the impression that the curve is totally convex-upward however, there is a slight downward move at the extremes because of the infinite downward slope of the mixing term at the extreme compositions. The two liquid phases are almost, but not quite pure. 

Figure 2. Gibbs free energy curves for a hypothetical system of polymorphs A, B, and C. The systems are classified as monotropic (forms A and C, forms B and C) or enantiotropic (forms A and B) with a transition temperature, T,. Melting points, T , for the polymorphs are shown by the intersection of the curves for the crystalline and liquid states. Adapted from Rodriguez-Spong et al., (2004) according to the relationships developed by Shalaev and Zografi (2002).

Figure 7.4 A hypothetical Gibbs free energy curve as a function of the number of moles of acetone added to the water.

Figure A.2 Gibbs free energy curves of the liquid (L) and solid (s) phases of an ideal solid solution system between T, (low temperature) and Ts (high temperature).

It should be briefly mentioned that the construction of binary phase diagrams with invariant phase transformations requires three Gibbs free energy curves-two for the solid phases a and p, and one for the liquid phase, L. At equilibrium temperature a common tangent exists for g, g and The position of the... 

Figure A.3 Equilibrium phase diagram of an ideal solid solution, constructed from the Gibbs free energy curves shown in Figure A.2.

Figure A.4 Gibbs free energy curves for invariant phase transitions, showing an eutectic (a) and a peritectic (b) reaction between a liquid (L) and two solid phases (a and P).

Fig. 1. Gibbs free energy curves with respect to composition near a solid—liquid interface (schematically). C, and Cj points correspond to an equilibrium state at the interface, and chemical potentials of components in the phases (tangents to the curves at these points) are equal. Deviation of the actual liquid composition (C,) at the interface temperature T, ftom the equilibrium concentration C, generates a tendency to restore the equilibrium (C — Ci, C2) or a driving force (AG,) for nucleation.

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