This addresses the important question of how the clusters are connected and

This addresses the important question of how the

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This addresses the important question of how the clusters are connected and packed to fill the 3D space, giving rise to MRO. We now describe the (dense) geometric/topological packing of the quasi-equivalent clusters. To differentiate several important candi- date schemes, we make use of the common-neighbour analysis 36 . In the present study, the quasi-equivalent clusters were treated as rigid balls, each occupying the volume of the coordination polyhedron of the solute atom at centre. As shown in Fig. 5a, in the Ni 81 B 19 , Ni 80 P 20 and Zr 84 Pt 16 systems, the solute-centred clusters are packed with appreciable icosahedral topological order, as evidenced from the prominent presence of the 555 icosahedral signature pairs, as well as the 544 and 433 pairs (the 555 index represents a perfect fivefold ring of common neighbours and the latter two correspond to the defective/distorted rings 36 ). Very similar results were found in the RMC configuration of the Ni–P system; see Supplementary Fig. S5. The 421 and 422 indices, signatures for close-packed face- centred cubic (f.c.c.) and hexagonal close-packed (h.c.p.), are insignificant. Note that the common-neighbour analysis indices above reveal Figure 5 | The packing of the solute-centred quasi-equivalent clusters, showing their MRO. a , The cluster common-neighbour analysis showing that the local clusters in the MGs exhibit icosahedral type ordering. The typical cluster connections, exhibiting the fivefold symmetry, are detailed for Ni 81 B 19 , Ni 80 P 20 and Zr 84 Pt 16 in b , c and d , respectively. For each local cluster, the Voronoi index is given to indicate its identity. FS, ES and VS denote face-sharing, edge-sharing and vertex-sharing, respectively. The red dashed circles delineate the clusters and suggest the quasi-equivalence of the clusters. The bonds for the centre cluster are not connected for clarity. ARTICLES NATURE | Vol 439 | 26 January 2006 422
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© 2006 Nature Publishing Group the presence of fragments (see Supplementary Fig. S5) of icosahedra, but not necessarily any perfect icosahedra. This can be termed ‘icosahedral ordering’, a term often used to describe local topological SRO in undercooled liquids 37,38 and glasses 12 (such as the Zr–Pt glass discussed here). Here it is short range for the packing of clusters, but already medium range from the standpoint of atomic (solute) correlation beyond one cluster. The icosahedral-type MRO (cluster) ordering is a general feature regardless of the types of SRO inside the clusters, as shown in Fig. 5b–d, where the intracluster packing varies from the TTP order in Ni–B, to the BSAP in Ni–P, to the icosahedral SRO in Zr–Pt, as illustrated above. The tendency for icosahedral order is not surprising, as in all these alloy systems, each of the clusters has an average of 12–13 neighbouring clusters of about the same size (see Supplementary Fig. S6 for the cluster–cluster common-neighbour analysis). This indicates dense packing, hence favouring f.c.c., h.c.p., or icosahedral order. The icosahedral
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