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There are at least three fundamental states of matter, depending upontemperature and pressure: gas, liquid, and solid (crystal). These states areseparated by first-order phase transitions between them. In both gas and liquidphases the complete translational and rotational symmetry exist, whereas in asolid phase both symmetries are broken. In intermediate phases between liquidand solid, which include liquid crystal and plastic crystal phases, only one ofthe two symmetries is preserved. Among the fundamental states of matter, theliquid state is most poorly understood. We argue that it is crucial for abetter understanding of liquid to recognize that a liquid generally has atendency to have local structural order and its presence is intrinsic anduniversal to any liquid. Such structural ordering is a consequence of many bodycorrelations, more specifically, bond angle correlations, which we believe arecrucial for the description of the liquid state. We show that this physicalpicture may naturally explain difficult unsolved problems associated with theliquid state, such as anomalies of water-type liquids (water, Si, Ge, ...),liquid-liquid transition, liquid-glass transition, crystallization andquasicrystal formation, in a unified manner. In other words, we need a neworder parameter representing low local free-energy configuration, which is bondorientational order parameter in many cases, in addition to density orderparameter for the physical description of these phenomena. Here we review ourtwo-order-parameter model of liquid and consider how transient local structuralordering is linked to all of the above-mentioned phenomena. The relationshipbetween these phenomena are also discussed.

the european physical journal. e, soft matter and biological physics/the european physical journal. e, soft matter

Bond orientational ordering in liquids: Towards a unified description of  water-like anomalies, liquid-liquid transition, glass transition, and  crystallization