# On Coherency-Induced Ordering in Substitutional Alloys: I. Analytical

Source: [On Coherency-Induced Ordering in Substitutional Alloys: I. Analytical](<https://www.sota2.com/research/paper/68fa1ea17a2b558e2932399f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:28:16.665Z

Authors: Dean J. Lee, Jong K. Lee

Published: 1999-11-17T16:23:40.000Z

## Abstract

As pointed out by Linus Pauling in his classic work on the relationship between crystal packing and ionic radius ratio, a difference in atomic size can be accommodated more readily by an ordered structure than by a disordered one. Because of mathematical complexity, however, very few works have been reported for substitutional alloys. In this work, coherency-induced ordering in substitutional alloys is examined through a simple model based on a two-dimensional square lattice. Within the assumption of nearest neighbor interactions on a square lattice, both modified Bragg-Williams and Onsager approaches show that coherency strain arising due to atomic mismatch can exert profound effects on order-disorder transitions in substitutional alloys. If the alloy system is elastically homogeneous and Vegard's law is obeyed, the order-disorder transition is of a second-order kinetics. If the atomic mismatches significantly deviate from Vegard's law, however, the transition may become a first-order kinetics, as the configurational free energy surface is composed of double wells. At the transition of a first-order kinetics, the lattice parameter can either increase or decrease upon heating, i.e., the lattice parameter of an ordered state can be less or greater than that of a disordered state. The results of Onsager's approach are independently confirmed with those of the Discrete Atom Method, a Monte Carlo technique predicated upon the combination of statistical mechanics and linear elasticity.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9911267>)

[PDF](<https://arxiv.org/pdf/cond-mat/9911267.pdf>)