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

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