Abstract
The present paper addresses the long-standing composition puzzle of eutectic points by introducing a new structural tool for the description of short-range-order structural unit, the cluster-plus-glue-atom model. In this model, any structure is dissociated into a 1st-neighbor cluster and a few glue atoms between the clusters, expressed by a cluster formula [cluster]gluex. This model is applied here to establish the structural model for eutectic liquids, assuming that a eutectic liquid consist of two subunits issued from the relevant eutectic phases, each being expressed by the cluster formula for ideal metallic glasses, i.e., [cluster](glue atom)1 or 3. A structural unit is then composed of two clusters from the relevant eutectic phases plus 2, 4, or 6 glue atoms. Such a dual cluster formulism is well validated in all boron-containing (except those located by the extreme phase diagram ends) and in some commonly-encountered binary eutectics, within accuracies below 1 at.%. The dual cluster formulas vary extensively and are rarely identical even for eutectics of close compositions. They are generally formed with two distinctly different cluster types, with special cluster matching rules such as cuboctahedron plus capped trigonal prism and rhombidodecahedron plus octahedral antiprism.
Highlights
We have developed a so-called cluster-plus-glue-atom model that suits for short-range-order structure descriptions in quasicrystals, amorphous alloys[16], and solid solutions[17]
The structure can be expressed by a cluster formula [cluster]gluex, where the cluster is the coordination polyhedron representative of the 1st-neighbor short-range order of the structure, and the glue atoms between the clusters mark the short-range-order feature on and beyond the 2nd neighbors
Thereof we propose the first assumption for modeling the eutectic liquids: 1) A eutectic liquid is comprised of two subunits issued from the two eutectic phases
Summary
Α -Co has the Mg structure, which presents a unique twinned cuboctahedron CN12 cluster, typical for the hexagonal close-packed metals This CN12 [Co-Co12] cluster together with CN9 [B-Co9] from BCo3, plus four B glue atoms, explain the experimental eutectic as Figure 2. The B13Hf87 eutectic is bounded by β -Hf (W) and BHf (ClNa), the latter being characterized by two octahedral clusters [B-Hf6] and [Hf-B6] Both clusters, giving phase formulas of the same size of two atoms, but the former one is more densely packed (B being a small atom in the octahedral interstice site of Hf) and is taken as the principal cluster: B13Hf87 → [B-Hf6 + Hf-Hf14]B2 = B3Hf21 = B12.5Hf87.5 (Fig. 7 and Table 1). This B-C system exemplifies the eutectic systems possessing covalent bonding, signifying the universality of the present formulism for binary eutectics
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