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

Abstract

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 indescribing the phase behaviour of hard spheres. However, there are some features thatcannot be captured by such theories. For example, hard spheres crystallize into either hcpor fcc structures, without a tendency of bcc ordering which is expected by theAlexander–McTague theory based on the Landau-type free energy of the density orderparameter. We also found hcp-like bond orientational ordering in a metastablesupercooled liquid, which promotes nucleation of hcp crystals. Furthermore, theoriesbased on the single order parameter cannot explain water-like thermodynamic andkinetic anomalies of a liquid and liquid–liquid transition in a single-componentliquid. Based on these facts, we argue that we need an additional order parameterto describe a liquid state. It is bond orientational order, which is induced bydense packing in hard spheres or by directional bonding in molecular and atomicliquids. Bond orientational order is intrinsically of local nature, unlike translationalorder which is of global nature. This feature plays a unique role in crystallizationand quasicrystal formation. We also reveal that bond orientational ordering isa cause of dynamic heterogeneity near a glass transition and is linked to slowdynamics. In relation to this, we note that, for describing the structuring of ahighly disordered liquid, we need a structural signature of low configurationalentropy, which is more general than bond orientational order. Finally, the water-likeanomaly and liquid–liquid transition can be explained by bond orientational orderingdue to hydrogen or covalent bonding and its cooperativity, respectively. So weargue that bond orientational ordering is a key to the physical understanding ofcrystallization, quasicrystallization, glass transition, water-like anomaly and liquid–liquidtransition. A unified description of these phenomena may be possible along thisline.