Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation

Abstract

Colloidal photonic crystals, which show a complete band gap in the visible region, have numerous applications in fibre optics, energy storage and conversion, and optical wave guides. Intriguingly, two of the best examples of photonic crystals, the diamond and pyrochlore structure, can be self-assembled into the colloidal MgCu2 Laves phase crystal from a simple binary hard-sphere mixture. For these colloidal length scales thermal and gravitational energies are often comparable and therefore it is worthwhile to study the sedimentation phase behavior of these systems. For a multicomponent system this is possible through a theoretical construct known as a stacking diagram, which constitutes a set of all possible stacking sequences of phases in a sedimentation column, and uses as input the bulk phase diagram of the system in the chemical potential plane. We determine the stable phases for binary hard-sphere systems with varying diameter ratios using Monte Carlo simulations and analytical equations of state available in literature and calculate the corresponding stacking diagrams. We also discuss observations from event-driven Brownian dynamics simulations in relation to our theoretical stacking diagrams.

High antisite defect concentrations in hard-sphere colloidal Laves phases

“…Clearly, the commonly made assumption in the calculation of phase diagrams that the crystal composition is ideal is not valid here. To date, these types of defects have not been considered in any of the binary hard-sphere crystal studies, [3][4][5][6][7][8]31 nor in any colloidal binary phase diagram studies that we are aware of. While we have focused here only on the Laves phase and (5), but now taking f S L from cell theory.…”

“…Note that there is an extremely small Laves phase + fluid region at the tip of the green arrow in (a) that is not visible on either of the pressure scales displayed here, as the pressure range of the region is bDPs L 3 = 0.002. 31 FCC crystals, we like to stress that the assumption of ideal crystal composition has also been made for the calculation of phase diagrams of binary hard spheres which show regions of stability of e.g. NaZn 13 , AlB 2 .…”

“…Binary hard-sphere mixtures are perhaps the simplest possible model for studying binary crystal structures, and have been instrumental in understanding the phase behavior of colloidal systems. The equilibrium phase diagrams of binary hard-sphere mixtures for various size ratios have been extensively explored using simulations, [3][4][5][6][7][8]11,22,31 revealing a number of stable binary crystal structures. However, even for this classical colloidal system, antisite defects have not been considered.…”

Programmable self-assembly of diamond polymorphs from chromatic patchy particles

“…The mechanism of its formation is poorly understood. Conceptually, this approach is similar to an earlier proposed scenario of diamond manufacturing from a self-assembled Laves structure [38,39].…”

Superstructures of Multielement Colloidal Molecules: Efficient Pathways to Construct Reconfigurable Photonic and Phononic Crystals

“…Micro‐ and nanoscale colloidal building blocks provide an attractive platform for directed self‐assembly, a classic problem in soft matter research with the intention of facilitating spontaneous formation of desired structures . Over the past two decades, the scope of self‐assembly with colloidal particles has evolved from close‐packed structures and binary crystals, to more exotic, non‐close‐packed symmetries driven by different forms of anisotropy . These structures present complex and interesting collective behavior at different length scales, and provide the opportunity to carefully engineer functional metamaterials.…”