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The geometrical properties of the icosahedral ordered structure formed in liquid and glassy phases of metallic glasses are investigated by using molecular dynamics simulations. We investigate the Zr-Cu alloy system as well as a simple model for binary alloys, in which we can change the atomic size ratio between alloying components. In both cases, we found the same nature of icosahedral order in liquid and glassy phases. The icosahedral clusters are observed in liquid phases as well as in glassy phases. As the temperature approaches to the glass transition point Tg, the density of the clusters rapidly grows and the icosahedral clusters begin to connect to each other and form a medium-range network structure. By investigating the geometry of connection between clusters in the icosahedral network, we found that the dominant connecting pattern is the one sharing seven atoms which forms a pentagonal bicap with five-fold symmetry. From a geometrical point of view, we can understand the mechanism of the formation and growth of the icosahedral order by using the Regge calculus, which is originally employed to formulate a theory of gravity. The Regge calculus tells us that the distortion energy of the pentagonal bicap could be decreased by introducing an atomic size difference between alloying elements and that the icosahedral network would be stabilized by a considerably large atomic size difference

Dynamics and Geometry of Icosahedral Order in Liquid and Glassy Phases of Metallic Glasses