| Metallic glasses are characterized by long-range disorders and short-range orders. Understanding their structures is of great significance to their composition and property design. In earlier works, our group proposed a cluster-plus-glue-atom model which described the structures of metallic glasses in terms of a local atomic cluster part and a glue atom part. Ideal metallic glasses can always be expressed by cluster formulas [cluster](glue atoms)1,3, where the cluster is the principal cluster in a relevant devitrification phase. After introducing the electronic resonance effect, this model was transformed into a cluster-resonance model that led to a constant number of valence electrons per unit cluster formula for all ideal metallic glasses, regardless of their chemical compositions. In this work, the contents and applications of the cluster-plus-glue-atom model are expanded and the issued cluster-resonance model is revised. The ideal cluster formulas of metallic glasses in bulk binary and typical ternary metallic glass forming systems are built using the revised model. The eutectic composition rule in binary glass forming systems is specially focused to answer "Stockdale/Hume-Rothery eutectic puzzle". Our contributions are summarized into the following four aspects:1) To clarify the selection criteria for the principal clusters in the cluster-based models and to answer the doubt on non-integer constant of the electron number per unit cluster formula,the cluster criteria are first refined and the cluster-resonance model is revised. A unit cluster formula is shown to possess a constant24electrons, to amend the original cluster-resonance model that indicates a constant electron number being close to e/u=23.6. The principal cluster definition is further refined to better represent the short-range order structure in the relevant crystalline phase. A multi-component cluster close-packing criterion is established on the basis of cluster dense packing. The principal clusters have the largest cluster isolation (largest effective cluster size) and high atomic packing efficiencies (closeness to ideal dense packing). The calculation of atomic density pa in the model is then revised that leads to a revised cluster-resonance model. The universal cluster formulas for ideal metallic glasses are shown to possess a constant total electron number e/u=24.2) The revised cluster-resonance model, issued from the cluster-plus-glue-atom model, is used to explain the glass-forming compositions of binary bulk metallic glasses, including Cu-(Zr,Hf), Ni-(Nb,Ta), Al-Ca and Pd-Si. The selection of the principal clusters and the establishment of24-electron cluster formulas [cluster](glue atoms)1,3are formalized. The ideal cluster formulas of all the known binary bulk metallic glasses are then:[Cu8Zr5]Cu≈Cu64.3Zr35.7(e/u=23.7),[Zr7Cu10]Zr≈Cu55.6Zr44.4(23.4),[Zr7Cu8]Zr=Cu50Zr50(24.2),[Cu8Hf5]Cu≈Cu64.3Hf35.7(23.7),[Ni7Nb6]Ni3=Nb37.5Ni62.5(23.5),[Ni-Ni6Ta6]Ni3=Ni62.5Ta37.5(23.1),[Ta-Ni6Ta6]Ni3=Ni56.25Ta43.75(23.8),[Ca9Al6]Ca3≈Ca66.7Al33.3(23.8) and [Pd11Si3]Pd3≈Pd82.4Si17.6(24.0), where the electron numbers of the real cluster formulas in the brakets are close to24.3) The ideal cluster formulas of ternary metallic glasses are established, and the statistical results of experimental compositions are fully explained. Two kinds of ternary ideal cluster formulas are presented. In the first, ideal ternary cluster formulas are obtained by substitutions in binary cluster formulas by the third component, as in systems Ca-Mg-(Cu, Zn), Cu-(Al, Ti)-Zr, La-Al-(Cu, Ni), Mg-Cu-Y, Ni-Nb-Zr, Pd-Cu-Si and Pd-Ni-P. In the second, the principal clusters of ideal ternary cluster formulas are derived from ternary crystalline phases, as in Zr-Al-Co and Zr-Al-Ni systems. The24-electron rule is confirmed in these systems. The seven most stable ternary glass-forming compositions from the statistical experimental results are fully explained by cluster formulas with different total atoms, A44B38C18≈A7B6C3, A44B43C13≈A7B7C2and A56B32C12≈A9B5C2using16-atom formulas, A55B28C17≈A10B5C3using18, A65B25C10=A13B5C2, A70B20C10=A14B4C2and A65B20C15=A13B4C3using20.4) Eutectic composition rules in binary systems are analysed by cluster formulas, and Stockdale/Hume-Rothery puzzle is quantitatively explained. It is assumed that a eutectic consists of two kinds of stable liquids in equal proportion. A binary eutectic is explained by the equal-proportion mixing of two principal cluster formulas where each principal cluster is matched with one or three glue atoms. A eutectic cluster formula is then composed of two principal clusters plus two, four or six glue atoms. The24-electron cluster formulas are correlated to glass formation:the principal cluster far away from the eutectic point has a high glass forming ability. This rule is verified in Cu-(Hf,Zr), Ni-(Nb,Ta), Al-Ca and Pd-Si systems. Alloying elements are classified into five types, tiny, small, middle, large and super, according to their atomic radii. The close-packed clusters are determined by the relative atomic radius ratio in the different eutectic systems formed by two types of these atoms, and then general eutectic formulas are obtained. The Stockdale/Hume-Rothery eutectic puzzle, that eutectic points are near the ratio8/1,5/1,3/1,2/1and3/2, is quantitatively explained. |
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