Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays

TL;DR

This paper introduces a new understanding of nanoscale compositional patterning as coherent, single-phase ordering driven by uniformity constraints, supported by a superspace model and a simple lattice-gas simulation.

Contribution

It proposes a novel interpretation of nano-patterns as uniformity-driven orderings rather than phase segregation, using a superspace approach and a simple binary lattice-gas model.

Findings

Reproduces nano-chessboard and nano-diamond patterns with a simple model

Shows these patterns can be explained by occupational modulated structures

Demonstrates the role of modulation vectors in pattern formation

Abstract

We propose that systems exhibiting compositional patterning at the nanoscale, so far assumed to be due to some kind of ordered phase segregation, can be understood instead in terms of coherent, single phase ordering of minority motifs, caused by some constrained drive for uniformity. The essential features of this type of arrangements can be reproduced using a superspace construction typical of uniformity-driven orderings, which only requires the knowledge of the modulation vectors observed in the diffraction patterns. The idea is discussed in terms of a simple two dimensional lattice-gas model that simulates a binary system in which the dilution of the minority component is favored. This simple model already exhibits a hierarchy of arrangements similar to the experimentally observed nano-chessboard and nano-diamond patterns, which are described as occupational modulated structures with two independent modulation wave vectors and simple step-like occupation modulation functions.