Free energy, equilibrium phase diagrams

This finding is illustrated on a free energy vs. composition diagram in Fig. C.6. The free-energy curve for the (3 phase is a vertical line at AT = 1, because the (3 phase has been assumed to be pure component B. Note especially that the change in fj>2 with P (or r) causes a change in the equilibrium solubility of component B in a. 

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

If the phase separation is possible, the free energy of phase separation is negative and characterized by a deep minimum. Because of this the unknown variables of the equation, which are necessary for constructing phase diagrams, may be found by minimization of the fimction Agpg. This term, as distinct from the free energy of mixing, allows in the closed form the condition of the phase equilibrium (bimodal equation) to be recorded for... 

Based on the standard Gibbs free energy of the various oxides, three triple points can be calculated WO2.72. WO2.9, WO2 at about 600°C, W02,9, WO3, WO2 at about 270°C, and WO2, WO2.72, W at 1480°C. Using this data, a phase diagram can be constructed. The stability of the various oxides is shown in Fig. 8.2 with respect to the partial pressures of H2O and H2, and temperature. Because aU of these compositions are equilibrium compositions, any of them can be produced simply by annealing W or WO3 at the given partial pressure ratio and temperature. 

Let us call the melt phase a and the solid phase with complete immiscibility of components y. P is constant and fluids are absent. The Gibbs free energy relationships at the various T for the two phases at equilibrium are those shown in figure 7.2, with T decreasing downward from Ty to Tg. The G-X relationships observed at the various T are then translated into a T-X stability diagram in the lower part of the figure. 

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