atoms. It is tempting to surmise that the excess solute atoms might belocated at the interstitial ‘vacancies’ of the densely packed clusters9.But we found instead that a different kind of building unit emerges.In ourab initiocalculated systems, the connection between soluteatoms takes the form of ‘strings’. For instance, two neighbouringsolute atoms form an isolated pair surrounded by the solvent atoms,and the resulting configuration may be termed ‘extended clusters’. Inthe Zr80Pt20metallic glass (Fig. 6a) a solute pair is seen to have a totalCN of,17. Similarly, string-like solute atoms are apparent insystems with higher solute concentrations (for example, Fig. 6b foramorphous Al75Ni25). The dense packing of the extended clusters, viaedge-, vertex-, or face-sharing, constitutes the second type of MRO.This type of packing becomes significant when the solute concen-tration reaches roughly 20–30%, depending on theR* ratio.As the number of the direct bonds among solutes further increaseswith enriched solute concentration, more and more solute–solutecontacts become unavoidable. A pronounced first-neighbour solute–solute pair correlation peak in the partial RRDFs emerges, asmeasured before for glasses such as Ni–Nb (ref. 43; SupplementaryFig. S7). When the solute interconnection percolation threshold iseventually reached, a network of the solute atoms takes form (Fig. 6cfor amorphous Ni63Nb37). The string- or ring-like interconnectionreduces the number of like bonds (increases the number of unlikebonds), when compared to aggregated solute atoms, leading toenergy reduction. This is illustrated in Supplementary Fig. S9:when the Zr70Pd30glass44is cooled from 1,800 to 300 K, thesolute–solute connection becomes more network-like. The acute(solute–solute–solute) bond angles observed at high temperaturesdisappear, reflecting the tendency to order the solute atoms in string-like and ring-like medium-range arrangements that reduce thenumber of like bonds. The solute–solute CN in this open andextended connection is generally no more than 3 to 7. This net-work-type arrangement of the solute atoms leads to a much-involvedthird type of MRO. The concept of connected random network haspreviously been proposed in ref. 45. We have thus uncovered a wholespectrum of atomic packing schemes, which vary not only withR*but also with solute concentration.Limitations of modelsWe should briefly discuss the inherent limitations of the modellingtechniques. The rapid quenching used for theab initiosystems didFigure 6|Configurations of solute atoms at increasing soluteconcentrations.a, Extended clusters in the form of ‘lone pairs’ (here, twoatom-sharing icosahedra with CN¼17) in the Zr80Pt20MG.b, Extendedclusters in the form of ‘strings’ in the Al75Ni25MG. The dense packing ofsuch ‘extended’ clusters constitutes the second type of MRO.c, The solutenetwork formed in the Ni63Nb37MG, in which the solute concentration ishigh. The network-like arrangement of the solute atoms gives rise to a
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