Local Composition in a Binary Mixture on a One-Dimensional Ising Lattice

Abstract

Expressions for the local composition in a binary mixture of particles placed on an Ising lattice are given in one dimension (1D) as a function of the average composition and of the interchange energy. The particles are supposed to interact through pairwise interactions between nearest neighbors. The problem is solved by using the classic analogy with the Ising spin problem. The result for the first neighbor is in agreement with an expression obtained from quasi-chemical theory, which is known to be exact in 1D. The composition for more remote neighbors is also determined. Besides, a model proposed in the literature to calculate approximately the local composition for the first neighbor in any dimension is examined. The solution to the problem in 1D provides insight into the model and a different interpretation of the thermodynamic contributions involved in the method.

Local distributions of the 1D dilute Ising model

“…However, despite a long history, the local distributions of spins and non-magnetic interacting impurities in the 1D di-lute Ising model have not been described systematically as yet. The size distribution of clusters is of fundamental interest and has been studied intensively in the Ising or similar models [38][39][40][41][42][43][44][45][46][47][48][49][50] .…”