Large deviation from stoichiometry. I. Random arrangement of vacancies

5 Large deviation from stoichiometry. I. Random arrangement of vacancies 

Let us consider a crystal similar to that discussed in Sections 1,3.3 and 1.3.4, which, in this case, shows a larger deviation from stoichiometry. It is appropriate to assume that there are no interstitial atoms in this case, because the Frenkel type defect has a tendency to decrease deviation. Consider a crystal in which M occupies sites in N lattice points and X occupies sites in N lattice points. It is necessary to take the vacancy-vacancy interaction energy into consideration, because the concentration of vacancies is higher. The method of calculation of free energy (enthalpy) related to is shown in Fig. 1.12. The total free energy of the crystal may be written 

The sign of f S) is determined by the sign of the term, because the term (1 — 5) is always positive. The sign of / (5) is as follows  

The sign of the parameter p has to be minus, because we are intending to solve the equations in the condition 0. The parameter a corresponds to a reduced temperature. 

To examine the phase relation of this system deduced from eqn (1.94), let us consider the condition 3G( 5, a)/5(5 = 0  

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