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Bond orientational ordering in a metastable supercooled liquid: a shadow of crystallization and liquid–liquid transition

It is widely believed that a liquid state can be characterized by a single order parameter, density, and that a transition from a liquid to solid can be described by density ordering (translational ordering). For example, this type of theory has had great success in describing the phase behaviour of hard spheres. However, there are some features that cannot be captured by such theories. For example, hard spheres crystallize into either hcp or fcc structures, without a tendency of bcc ordering which is expected by the Alexander–McTague theory based on the Landau-type free energy of the density order parameter. We also found hcp-like bond orientational ordering in a metastable supercooled liquid, which promotes nucleation of hcp crystals. Furthermore, theories based on the single order parameter cannot explain water-like thermodynamic and kinetic anomalies of a liquid and liquid–liquid transition in a single-component liquid. Based on these facts, we argue that we need an additional order parameter to describe a liquid state. It is bond orientational order, which is induced by dense packing in hard spheres or by directional bonding in molecular and atomic liquids. Bond orientational order is intrinsically of local nature, unlike translational order which is of global nature. This feature plays a unique role in crystallization and quasicrystal formation. We also reveal that bond orientational ordering is a cause of dynamic heterogeneity near a glass transition and is linked to slow dynamics. In relation to this, we note that, for describing the structuring of a highly disordered liquid, we need a structural signature of low configurational entropy, which is more general than bond orientational order. Finally, the water-like anomaly and liquid–liquid transition can be explained by bond orientational ordering due to hydrogen or covalent bonding and its cooperativity, respectively. So we argue that bond orientational ordering is a key to the physical understanding of crystallization, quasicrystallization, glass transition, water-like anomaly and liquid–liquid transition. A unified description of these phenomena may be possible along this line.