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

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 arrangement 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 favoured. 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 wavevectors and simple step-like occupation modulation functions.

Frustrated Octahedral Tilting Distortion in the Incommensurately Modulated Li3xNd2/3–xTiO3 Perovskites

“…[001] ED patterns demonstrate the presence of satellite reflections positioned close to the basic spots and the 1/2⟨ hk 0⟩, h , k - odd positions (Figure ). The satellites can be indexed in a (3 + 2)-dimensional approach assuming the diffraction vector H = h a * + k b * + l c * + m q 1 + n q 2 , with the modulation vectors q 1 = α 1 a * + 1/2 b * and q 2 = 1/2 a * + β 2 b *, where both α 1 and β 2 are slightly smaller than 1/2 (as suggested in ref ). This indexation is also in agreement with the reciprocal lattice reconstruction performed by Garcia-Martin et al With this choice of the modulation vectors, no reflection conditions are observed from the ED patterns, which suggests Pmmm and P 4/ mmm space groups for the basic structure of the x = 0.05, 0.08 and x = 0.12, 0.14 materials, respectively.…”

Superspace crystallography: a key to the chemistry and properties

“…Association of the defects owing to intersite repulsive or attractive forces coupled with the lattice strain can lead to complex ordering patterns that are strikingly different from an averaged picture based on random distributions of defect species over the relevant sublattices. These patterns are often driven by a tendency to minimize the free energy of the system through adopting a so-called uniform ordering, where the ordered species or structure fragments are distributed as homogeneously as possible (Perez-Mato et al, 1999;Gonzá lez et al, 2011Gonzá lez et al, , 2012. Another source of structural complexity originates from co-existing competing distortion modes favouring a frustrated structure, where an incommensurately modulated state provides a reasonable compromise satisfying both distortions simultaneously.…”

Phase-Field Study of Exchange Coupling in Co-Pt Nonstandard Nanochessboards

“…The nanoarchitectonics of self-assembled nanostructures at the nanoscale has played a pivotal role in propelling the ongoing advancement of nanodevices in the current millennium. In particular, the intriguing quasiperiodic dual-phase chessboard-like nanostructure or nanochessboard appears to be a common phenomenon, as observed in various decomposing metal alloys [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. Among these metal alloys, the Co-Pt nanochessboard represents a quasi-periodic nanocomposite comprising a magnetically hard L1 0 phase and a magnetically soft L1 2 phase [ 9 , 10 , 11 , 12 , 13 , 14 ].…”