Despite intensive studies in the past decades, the local structure of disordered matter remains widely unknown. We show the results of a coherent x-ray scattering study revealing higher-order correlations in dense colloidal hard-sphere systems in the vicinity of their crystallization and glass transition. With increasing volume fraction, we observe a strong increase in correlations at both medium-range and next-neighbor distances in the supercooled state, both invisible to conventional scattering techniques. Next-neighbor correlations are indicative of ordered precursor clusters preceding crystallization. Furthermore, the increase in such correlations is accompanied by a marked slowing down of the dynamics, proving experimentally a direct relation between orientational order and sample dynamics in a soft matter system. In contrast, correlations continuously increase for nonequilibrated, glassy samples, suggesting that orientational order is reached before the sample slows down to reach (quasi-)equilibrium.
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