Energy, configurational free, Gibbs

The Gibbs free energy G and the chemical potentials include contributions from the internal energy, vibrational free energy, and configurational entropy. Since most relevant stmctures will have a low surface free energy, we obtain from (5.4) that... 

In this respect it must be recalled11 that all thermodynamic properties deduced from the crude version and the refined version II depend on the function r)(T,p) while for the other two versions it is the function f(lT, v) which is needed. As the thermodynamic properties of mixtures are usually measured in such conditions that T and p are independent variables (often with p 0), it is obviously easier to work with models involving rj(T,p) rather than (T, v). We shall therefore limit ourselves from now on to the crude version and the refined version II. Their Gibbs configurational free energies are respectively 21... 

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).

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). 

For Landau free energy (m = 0, - the order parameter), Zt is a partition function of an extended system with additional variable . The integral denoted in square brackets in Eq. (3-12) is simply the configurational partition function of the system with a fixed value of -Z. The statistical definition of the Gibbs free energy function combined with Eq (12) results in the following expression ... 

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