Exact Relations between Triplet Probabilities and Pair Correlations inABBinary Alloys and Ising Spin-½ Systems

Abstract

The probabilities for triplet occupation in an $\mathrm{AB}$ binary alloy (or spin one-half Ising magnet) are found to be exactly expressible as linear combinations of the three pair correlations if the configurational energy of the system possesses a certain symmetry. The required symmetry is that the energy be invariant when all $A$ atoms are replaced by $B$ atoms and vice versa (or all spins are flipped). Systems having only pairwise or even particle interactions satisfy this requirement. Roberts's values for the pair correlations in CuAu at various temperatures are used to calculate the probabilities of several triplet configurations. The results are somewhat paradoxical and can probably be attributed to the lack of a size-effect correction in Roberts's data. Equations for the triplet probabilities in alloy compositions other than 50-50 are also given; but these require a fourth parameter, the triplet correlation, which is not yet available experimentally.