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.