Statistical Theory of Binary Alloys. I

Abstract

The number of arrangements of atoms A and B on the lattice points, which have a given number of pairs of nearest neighbours of type AA, is given by the idea of probability. In consequence, the free energy formulae are written down explicitly.
It is shown:-
(1) The superlattice problems of the various lattice types and at arbitrary concentrations can be treated by the application of one simple and general method.
(2) The relation assumed as the basis of the “quasi-chemical method”(1) can be obtained as the result of a purely mathematical process.
(3) The results of Bethe, Bragg-Williams, and several other investigators can be derived from our free energy formulae