This conclusion was also corroborated by our analysis of the rather broad bond

This conclusion was also corroborated by our analysis

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chemical structure. This conclusion was also corroborated by our analysis of the rather broad bond-angle distribution (see Supplemen- tary Fig. S4). On the other hand, despite the large number of the geometrically distinct polyhedron types, certain polyhedra appeared with high frequencies (20–40%; see Fig. 4). A closer inspection suggests that they are Kasper polyhedra, which are the deltahedra that involve the minimum number of disclinations 30,31 . The atomic packing con- figurations of different Kasper polyhedra are shown in Fig. 3. In the Ni–P glass, the percentages of the Z10 (Z ¼ CN) Kasper polyhedron (the bi-capped square archimedean antiprism, BSAP, with Voronoi index k 0,2,8,0 l ), and the Z11 Kasper polyhedra (with k 0,2,8,1 l ) are 16.2% and 10.6%, respectively, while in the Ni 81 B 19 MG, the Z9 Kasper polyhedron (TTP, with k 0,3,6,0 l ) and the Z10 Kasper polyhedra are dominant (at 17.8% and 7.1%, respectively). In comparison, prominent icosahedral local order is found in the Zr 84 Pt 16 MG, where the occurrences of the Z12 and Z11 Kasper polyhedra are 14.1% and 9.0%, respectively. Therefore, it is evident that the Kasper polyhedron SRO is the main underlying topological SRO in the MGs. The preference for a particular type, as seen in Fig. 3 together with the shift of the main peak, is controlled by the effective atomic size ratio between the solute and solvent atoms, R *. With decreasing R *, the preferred polyhedra type changes from the Frank–Kasper 32 type (for R * . 1.2) to the icosahedral type ( R * < 0.902, as for Zr–Pt with R * ¼ 0.90), and then to the BSAP type ( R * < 0.835, as in Ni–P with R * ¼ 0.78), and then to the TTP type ( R * < 0.732, as in Ni–B with R * ¼ 0.69); see Figs 3 and 4. As pointed out above, some MGs, notably TM–metalloid systems (Ni–B, Pd–Si and so on), indeed exhibit the TTP local order, similar to that in corresponding crystalline compounds 33 . But this should be understood as a geo- metrical consequence and only specific to a small number of MGs that meet the R * requirement for the formation of TTP ( R * < 0.732). Our results not only validate the important role of the relative size Figure 3 | CN distribution of the solute atoms in several representative MGs, obtained from ab initio calculations. The average CN changes with the effective atomic size ratio, and for each glass the majority of the solute atoms ( . 75% of total) have two dominant CNs. Also shown are the Kasper polyhedra corresponding to the different CNs. The Kasper polyhedra are the dominant coordination polyhedra in the relaxed MGs. Figure 4 | The occurrences of different coordination polyhedra (with different Voronoi indices) of the solute atoms in the MGs. The bars outlined in red show the frequency of the dominant Kasper polyhedra. Note that only the polyhedra with a population of . 2% are shown. NATURE | Vol 439 | 26 January 2006 ARTICLES 421
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© 2006 Nature Publishing Group between the solute and solvent atoms 9,10,34 , but also explicitly specify the packing topologies for the various CNs.
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