Thermodynamic Properties of Binary Solid Solutions on the Basis of the Nearest Neighbor Approximation

An approximate method of computing the partition function of a binary solid solution is formulated. If the only constraints are on the mean energy and mean composition, it is shown that no metastable phase is predicted. The partition function is shown to be obtainable from the largest eigenvalue of a quadratic form and the condition for a phase transition is shown to be related to the degeneracy of the largest eigenvalue. The physical interpretation of the eigenfunction is shown to be related to the probability of surface configuration, while the square of the eigenfunction is related to the probability of a configuration on the interior of the crystal. Some simple examples are discussed which are related to the effect of coordination number on phase transitions.