The effect of thermal agitation on atomic arrangement in alloys-III

Abstract

The various theoretical treatments of the atomic arrangement in alloys which have recently been given by different workers have been discussed in a paper by Professor W. L. Bragg and the writer in the last number of the 'Proceedings'. The purpose of this paper is in the first place to discuss further the relation between the free energy of the alloy and the quantities occurring in the earlier treatment of the problem by these authors and to give the detailed calculations of the equilibrium equations for a general case, first, from the standpoint of the Boltzmann distributions formula, and, secondly, from the principle of minimum free energy. The treatment recently given by Bethe differs essentially from previous treatment in that he assumes the energy associated with the atomic arrangement to be uniquely determined by the order of neighbours (σ) and not by the superlattice order S. By comparing the dependence of the entropy of the atomic arrangemet on σ with its dependence on S the quantitative relation of the two types of treatment may readily be seen. This is done in the present paper. It is further shown that an approximate treatment of the problem, assuming interaction only between nearest neighours, may be given by combining the formula of Bragg and Williams for superlattice order with an approximate formula of Bragg and Willaims for superlattice order with an approximate formula for "liquid" order.