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Presence of local five-fold symmetry in liquids

A. Di Cicco, F. Iesari, S. De Panfilis, M. Celino,
S. Giusepponi and A. Filipponi

 

Original publication: A. Di Cicco, F. Iesari, S. De Panfilis, M. Celino, S. Giusepponi, and A. Filipponi, Local five-fold symmetry in liquid and undercooled Ni probed by x-ray absorption spectroscopy and computer simulations. Phys. Rev. B Rapid Communications, 89, 060102(R) (2014).
 
Introduction (for non-specialists)
Perfect crystal structures can contain pyramids, cubes, or hexagons, but not pentagons. The five-fold symmetry of a pentagon is impossible to replicate over and over in space to make a conventional crystal. Most solid metals actually form closely packed cubic crystals, but in the 1950s, calculations showed that metals such as copper, gold, silver, and lead might form liquids with local five-fold symmetry, in form of icosahedral structures. It was already known that atoms in a liquid could form small clusters that constantly break and reform. Moreover, five-fold ordering in metals is not entirely unprecedented. Quasicrystals are metal alloys that have a peculiar semi-crystalline five-fold symmetry that never quite repeats itself. The determination of the local structure in liquid matter is a quite challenging task, and most techniques (x-ray and neutron diraction) can only find the relative positions of two atoms at a time, which makes it difficult to pin down the five-fold symmetry prediction. In this publication, the authors exploited the x-ray beam provided at the European Synchrotron Radiation Facility in Grenoble, France, and the technique of x-ray absorption spectroscopy (XAS). Liquid and undercooled liquid nickel, at extremely high temperatures, were put to a test in this work, following a previous effort on liquid copper (2003). XAS normally determines distances between atom pairs, but the researchers extended the usual analysis to pull out more information from the data. In XAS, a photon from the x-ray beam strikes a target atom and kicks out an electron. After this electron scatters from a second, neighboring atom, researchers detect it and can learn the distance between the two atoms. But often the electron scatters o more than one atom, producing a more complicated scattering pattern. Using a sophisticated data-analysis technique (Reverse Monte Carlo coupled with GNXAS multiple-scattering calculations) it has been possible to interpret the scatter produced when the electron hits more than one atom, measuring the local symmetry around the atoms. Moreover, ab-initio computer molecular-dynamics simulations provided further insights to the determination of the local structure. The emerging picture for the liquid structure is that of a mixture of nearly-perfect icosahedral structures embedded in a disordered network. 
 
Summary of scientic results
Presence and signicance of five-fold congurations in liquid metals, prohibited in crystal solids, are investigated by combining x-ray absorption spectroscopy and computer simulations in liquid and undercooled liquid nickel. The presence of icosahedral structures in liquid metals was postulated by Frank to explain their high undercooling properties. 
The debate about presence and amount of icosahedral short-range ordering (ISRO) in undercooled liquids is currently still open, also because of the experimental difficulties to access deeply undercooled states. The EXAFS (Extended X-ray Absorption Fine Structure) data, obtained at the beamline BM29 of the European Synchrotron Radiation Facility (ESRF, Grenoble), was analyzed using a method known as reverse Monte Carlo (RMC). This method consists in the simulation of a cubic cell which reproduces the experimental with some constraints. At equilibrium, different system configurations are found to be consistent with the experimental data. To test the validity of the structural obtained by the RMC, advanced molecular dynamics (MD) simulations were performed obtaining realistic models for the liquid structures. The presence of icosahedral short-range ordering was studied using two different approaches, common-neighbor analysis (CNA) and analysis of the Ŵ6 spherical invariant. The emerging picture for the liquid structure is that of a mixture of nearly-perfect icosahedral structures (14-18% of the total) embedded in a disordered network mainly composed of fragments of highly-distorted or defective icosahedra (40-45% of the total), structures reminiscent of the crystalline phase, and other configurations.
 
Research team and curiosities
The research team included scientists developing experiments and methods for x-ray absorption spectroscopy (Di Cicco, Filipponi, De Panfilis), one brilliant student performing most of the data processing and interpretation (Iesari) and computer simulation experts (Celino and Giusepponi). Di Cicco and Iesari works at the Physics Division in Camerino, S. De Panfilis at the IIT in Roma, A. Filipponi at the L'Aquila University, Celino and Giusepponi at the ENEA Casaccia research centre. The XAS data were collected during one of the last high-temperature runs at the XAFS beamline at ESRF (BM29), optimized by A. Filipponi (and successively by S. De Panfilis) for XAS measurements under extreme conditions. Nowadays, after a revision of the beamline offering at the ESRF, the BM29 beamline has been subsituted by BM23. The original data were finally analyzed and a full interpretation of the local liquid structure was made possible by advanced computer simulations years later. The complementary expertise of various scientists, the enthusiasm of the newcomers, and the availability of both advanced experimental facilities and computing resources in the teams were key factors for the succesful research effort.
 
 
Figure 1: Snapshot of a typical conguration of atomic positions for liquid Ni. A nearly-icosahedral structure is shown in the magnified figure.