Phase diagrams boundary versions

For phase diagrams, a phase boundary is one end of a tie-line and, therefore, is dependent on the phase which exists at the other end of the tie-line. In a binary system, two independent measurements are therefore needed to define the tie-line in the case of a liquid/solid phase boundary this would be and Xg at temperature T. Ideally it would be desirable to have these two compositions as independent variables giving rise to two independent equations of error. The Lukas programme does this by making two equations but where the dependence of error on one of the measurements is weak. This is important if the two concentrations have different accuracies. For some types of experimental values newer versions of the Lukas programme offer different kinds of equations of error (Lukas and Fries 1992). 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

Each diagram is labeled with number (1, 2) followed by a type (a, b, c, d) of fluid phase behavior. Titles of boundary versions of the complete phase diagram contain two letters (ah, CD, Ibb, Idd etc.) or numbers (12a, 12c, 12d" etc.) according to the neighboring types, which transform one into another. 

Figure 1.13 Systematic classification of binary complete phase diagrams (p-T projections). Boundary versions of phase diagram are shown in frames (Reproduced by permission of the PCCP Owner Societies).

Versions (a) and (b) in Fig. 5 contain equivalent information. Stable structures appearing on the phase diagram form a convex hull in energy-composition coordinates. The slope of each section in the convex hull is either the boundary chemical potential, or the equilibrium chemical potential in which stable configurations can coexist. Therefore, we can choose the fitness of a structure to be its distance to the convex hull. The EA search... 

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