Quantitative Metrics for Assessing Positional and Orientational Order in Colloidal Crystals

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.