| Metallic glasses deserve our attention for its special interior structure and excellent mechanical, physical and chemical properties. Because the formation of metallic glasses are related with compositions, especially the bulk metallic glasses are sensitive to the compositions, researchers have proposed structure models and empirical criteria to guide the design of metallic glasses, but these models can not provide quantitative compositions. Our previous works have been successful in understanding Zr-based bulk metallic glasses using the criteria of electron concentration-constant, atomic size-constant and cluster line. However, the physical mechanism of the above mentioned three kinds of criteria are not unified. This paper aims at solving the unified mechanism and the composition rule of bulk metallic glasses basing on cluster structure characteristics.First, a new structural model, cluster-resonance model, is put forward that combines the so-called 'cluster-plus-glue-atom'model and the globale resonance model of Haussler. Next the electrochemical potential equilibrium calculation method is proposed. According to this method, the number of glue atoms could be determined based on the equilibrium of the electrochemical potentials between cluster and glue atom parts. Then the composition formula of ideal metallic glasses is determined. The key points of the cluster resonance structural model are as follows:(1) An ideal glassy structure contains a dominating local cluster order so that compositionally the structure is described by cluster formula [center-shell] (glue atom)x, in terms of the cluster-plus-glue-atom model, where center-shell refers to the cluster and x the number of glue atoms matching one cluster;(2) The local cluster order is extended to a longer-range one by spherical periodicity owning to the global resonance between the electron and atomic subsystems. A consequence is the correlation between the cluster radius r-cluster, spherical periodicity,λFr, and Fermi wavevector, kF, and eventually Fermi energy (equivalent to electrochemical potential of electronsμ), rcluster=1.25λFr=1.25π/kF,μcluster=EF=h2kF2/2m=0.5881/rcluster2(eV)(3) Equilibrium of electrochemical potential of electrons is assumed so that the potentials as calculated from different atomic clusters in a given system should reach the same potential value after adjusting the relative proportions of each cluster. The equilibrium between the dominating cluster and the cluster centered by the glue site gives x, the number of glue atoms in the Cluster formula,μcluster=x*μglue,μglue=0.588/rglue2(eV),x=μcluster/μglue=(rglue/rcluster)2.In addition, the theoretical composition of ideal metallic glass deduced from the cluster resonance model is quite consistent with experimental data. This criterion unifies the the electron concentration-constant criterion, the atomic size-constant criterion, the cluster line and deep euectic point criterion. Besides, this cluster resonance model could also be applied in deciphering euectic compositions.At last, from the cluster resonance model, a theoretical calculation method of electron concentration e/a of an ideal metallic glass can be deduced. The ideal close packing of equi-spheres satisfies the nearest neighbor coordination number of N=12.566 as solved by Egami, and then the electron concentration (number of free electrons per atom) expression can be simplified as e/a=23.614/Z. The experimental results of the electron concentration of metallic glass compositions in Cu-Zr, Ni-Zr, Co-B and Ni-Nb based alloys all lie close to the theoretical curve, which proves that ideal metallic glasses described by the cluster resonance model have definite electron concentration e/a. It is concluded tha the e/a vlaue is determined by the cluster structure, the cluster packing and the glue atoms. The results not only prove the Hume-Rothery phase nature of metallic glasses but also support the validity of cluster formula.
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