Spinodal lines in regular ternary solutions

Although it is very difficult to calculate the coexistence curve in a ternary system, the spinodal curve can be calculated quite simply. If we know this curve we can then obtain a general idea of the nature of the phase diagram. We consider a system at constant T and p, but instead of emplopng equation (16.86) we make use of (16.72). In a 

If we regard as a function of a 2 and Xg, we find quite easily that 

Substituting into (16.72) we then obtain the following equation for the spinodal  

For example, if a= - 10, j8 = 0, y = 0, this equation is that of a closed curve inside the composition triangle. For these values of the coefficients, the immiscibility curve will therefore also consist of a closed ring inside the triangle. The existence of such closed miscibility gaps, which are observed for example with the Cu + Au + Ni system, can therefore be interpreted in terms of regular solution theory without introducing any specifically ternary factor. 

In this chapter we shall discuss the consequences of perturbing a system, which is initially in stable equilibrium, to a neighbouring nonequilibrium state. Since the initial equilibrium is supposed to be stable then the system will tend to return to an equilibrium state. For the moment we shall only concern ourselves with the way in which the thermodynamic variables change as the perturbed system moves back to equilibrium. The characteristics of the final equilibrium state, which is in general different from the initial state, will be discussed in the next chapter. 

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