Confined binary two-dimensional colloidal crystals: Monte Carlo simulation of crackformation

Abstract

Binary mixtures (A, B) of colloidal particles of different sizes in two dimensions may form crystalswith square lattice structure (the A-particles occupying the white sites and the B-particles theblack sites of a checkerboard). Confining such a system by two parallel ‘walls’ a distanceD apart, long-range order in the direction parallel to the walls is stabilized by‘corrugated walls’ that are commensurate with the lattice structure but destabilizedby structureless ‘hard walls’, even if there is no misfit between the strip widthD and the crystal lattice spacing. The crossover to quasi-one-dimensional behavior is studied by MonteCarlo simulations, analyzing Lindemann parameters and displacement correlation functions. WhenD is reduced and thus a misfit created, the stress in the crystal increases up to a criticalvalue, at which the stress jumps to much smaller values due to the formation of an (almostperiodic) crack pattern. These cracks typically have a width of several particlediameters, and are mostly disordered, although sometimes small domains withhexagonal order can be identified. At very large misfits, glass-like structures appear.We discuss various methods to characterize order and disorder in such systems.