Using Monte Carlo simulation techniques, we calculate the phase diagram for a square shouldersquare well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.

We carry out computer simulations of a simple, two-dimensional off-lattice model that exhibits inverse melting. The monodisperse system comprises core-softened disks interacting through a repulsive square shoulder located inside an attractive square well. By systematically varying the potential parameters, we increase the pressure range over which the liquid freezes to a crystal upon isobaric heating. The effect is largely controlled by the extent of the shoulder. Despite occurring in two dimensions, the melting transition is first order and to a liquid, rather than to a hexatic or quasicrystal phase. We also provide comment on a commonly employed correlation function used to determine the degree of translational ordering in a system.

We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial ac electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in turn form chains. We therefore approximate the system as composed of well-formed chains of dipolar hard spheres of a uniform length. The dipolar interaction between colloidal spheres gives rise to an effective interaction between the chains, which we treat as disks in a plane, that includes a short-range attraction and long-range repulsion. Hence, the system favors finite clustering over bulk phase separation, and indeed we observe at low temperature and density that the system does form a cluster phase. As the density increases, percolation is accompanied by a pressure anomaly. The percolated phase, despite being composed of connected, locally crystalline domains, does not bear the typical signatures of a hexatic phase. At very low densities, we find no indication of a "void phase" with a cellular structure seen recently in experiments.

Although there are numerous self-assembly techniques to prepare colloidal crystals, there is great variability in the methods used to characterize order and disorder in these materials. We assess different kinds of structural order from more than 70 two-dimensional microscopy images of colloidal crystals produced by many common methods, including spin-coating, dip-coating, convective assembly, electrophoretic assembly, and sedimentation. Our suite of analysis methods includes measures for both positional and orientational order. The benchmarks are two-dimensional lattices that we simulated with different degrees of controlled disorder. We find that translational measures are adequate for characterizing small deviations from perfect order, whereas orientational measures are more informative for polycrystalline and highly disordered crystals. Our analysis presents a unified strategy for comparing structural order among different colloidal crystals and establishes benchmarks for future studies.

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