View source for Five-fold symmetry in liquids

Original entry:  Donald Aubrecht,  APPHY 226,  Spring 2009

"Five-fold symmetry in liquids"<br>
Frans Spaepen<br>
Nature <b>408</b> 781-782 (2000)


== Soft Matter Keywords ==
structure of liquids, X-ray scattering

[[Image:Spaepen-symmetry.jpg|400px|thumb|right|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.]]

== Summary ==
Dr. Spaepen presents a short article on determining the structure of liquids and comments on recent work that has gotten closer to validating models with experimental data.  He notes that to this point, attempts to describe liquids as disordered crystals have failed and describing them as dense gases is too complex.  The favorite approach thus far has been to describe a liquid as a dense packing of tetrahedral building blocks.  A persistent challenge for condensed matter physicists has been to find a simple structural description of liquids, akin to the periodicity of crystals and sparsity for gases.  The liquid phase is now accepted as a well-defined phase, not merely a heavily defective crystal or a random assembly of micro-crystals, so work is on-going to characterize liquid structure.

== Practical Application of Research ==
Understanding the structure of liquids in a detailed manner is necessary to see how defects allow the local shear flow that causes viscous flow and how defects affect atomic diffusion.  In addition, understanding the interface between a solid and its liquid melt will provide insight into nucleation and growth of crystals, which could prove valuable for industrial solidification processes, such as glass making.

== Liquid Structure ==
In addition to providing a introduction to motivate the study of liquid structure, this short article highlights recent work by Reichert et al. [1].  Using a clever experimental set-up, Reichert reports the first direct evidence for polytetrahedral structure in a monoatomic liquid trapped at a solid interface.  The polytetrahedral configurations in liquid lead were trapped by aligning them against a crystalline silicon wall.  This region was then imaged with totally internally reflected X-rays, which are sensitive only to the structure of the interface.  The scattering pattern of these X-rays shows characteristic five-fold symmetry of the bonds, indicating that polytetrahedral structure is found in liquids.

Polytetrahedral packing can be considered as an attempted to maximize the short-range density of a structure, since the densest local configuration achievable with hard spheres is a tetrahedron.  Packing tetrahedra together leads to structures such as those indicated in Figure 1.  1(c) illustrates five tetrahedra packed around an edge, resulting in a gap of ~7 degrees.  Moving the gap between tetrahedra in the ring requires minimal energy.  The thermal disorder of a liquid, the ease by which it flows, and the rapidity by which its atoms diffuse can be understood as redistributions of these gaps.  As Reichert's paper indicates five-fold symmetry in liquid structure, studying polytetrahedral structures and their defects may lead to insight into liquid structure.


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

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written by Donald Aubrecht