Five-Fold Symmetry in Liquids

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Entry by Emily Redston, AP 226, Fall 2012


Five-fold symmetry in liquids by F. Spaepen. Nature 408, 781-82 (2000)


liquid structure, symmetry, x-ray scattering, hard sphere, dense random packing


Figure 1. (a) and (b) show two options for the arrangement of atoms in a 13-atom cluster. (a) is the cuboctahedral configuration (eight tetrahedra and six half-octahedra), while (b) is the icosahedral configuration (composed of 20 tetrahedra). (c) illustrates that five tetrahedra can be packed around a common edge (the red line), but will leave a gap of approximately 7 degrees.

Even though liquids are essential ingredients in soft matter, researchers have only recently begun to understand their structure. Previous theories describing liquids as disordered crystals or as dense gases have fallen short, and it has accepted that the liquid structure is a well-defined phase in its own right. While there are still many unanswered questions, the current method is to explain the liquid structure as a dense packing of tetrahedral building blocks. Ideally one would like to have a simple structural method for describing the liquid structure as we already have with the periodicity of crystal structures. Unfortunately, since the atomic structure of a liquid changes over space and time, conventional scattering experiments using X-rays or electrons or neutrons can only provide directionally average information.

Reichert et al [1] were the first to report direct evidence for polytetrahedral structures in a monatomic liquid trapped at a solid interface; they saw the characteristic five-fold symmetry of the bonds. Typical crystalline solids (like the face-centered cubic structure) are formed by maximizing their long-range order. The polytetrahedral packing in liquids, on the other hand, maximizes the short-range density of the structure. The densest local configuration that can be created with hard spheres is a tetrahedron. Five tetrahedra can be packed around a common edge, but they leave a gap of about 7°, which require very little energy to move (Fig. 1c). The thermal disorder of liquids, the ease by which is flows, and the rapidity by which its atoms diffuse can be qualitatively understood by the redistribution of these 7° gaps. Tetrahedral packing leads to five-fold symmetry, which is incompatible with long-range periodicity. Thus polytetradral short-range order favours disordered or amorphous structures. Bernal's dense random packing of hard spheres explains the scattering data from liquids the best.

A complete understanding of the structure of simple structures is extremely important and relevant to a lot of work done in soft matter. Currently we know that liquids contain many configurations with five-fold symmetry. I find it a little surprising that something that seems so simple turned out to be such a complicated problem. I'm very interested to see where our understand will be down the road, and whether we'll ever have the complete picture with liquids that we have with crystalline solids.

[1] H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, Nature 408 839-841 (2000)