Prediction of Glass-Forming Compositions in Metallic Systems: Copper-Based Bulk Metallic Glasses in the Cu-Mg-Ca System
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INTRODUCTION
IT is well known that the nucleation and growth of a crystalline phase in certain metallic alloy melts can be kinetically bypassed upon cooling to produce a metastable amorphous solid. Since the discovery of the first amorphous alloy over 40 years ago,[1] the ability to predict the distinct atomic structures responsible for the extraordinary properties associated with metallic glasses and strong liquids remains one of the great unsolved problems in condensed-matter physics. Early structural models for glasses were based on a purely amorphous (random) arrangement.[2–4] However, it has been realzed that ‘‘purely’’ amorphous materials rarely exist in nature, with atomic interaction, atomic packing efficiency, and structural relaxation playing an important role in the structure and stability of a vitreous solid.[5–10] From a historical perspective, Stockdale[11] originally suggested in 1935 that the compositions of eutectic points in binary alloys should correspond to simple whole-number ratios of each atomic species. This notion was supported by Hume-Rothery and Anderson in 1960,[12] who plotted the frequency of occurrence of binary eutectic compositions vs alloy stoichiometry and found clear maxima at compositions corresponding to KEVIN J. LAWS, Senior Research Fellow, KARL F. SHAMLAYE and KENNETH WONG, Postdoctoral Students, BULENT GUN, Research Fellow, and MICHAEL FERRY, Professor, are with the Australian Research Council Centre of Excellence for Design in Light Metals, School of Materials Science and Engineering, University of New South Wales, Sydney, 2052, Australia. Contact e-mail: k.laws@unsw. edu.au This article is based on a presentation given in the symposium ‘‘Bulk Metallic Glasses VI,’’ which occurred during the TMS Annual Meeting, February 15–19, 2009, in San Francisco, CA, under the auspices of TMS, the TMS Structural Materials Division, TMS/ASM: Mechanical Behavior of Materials Committee. Article published online May 14, 2010 METALLURGICAL AND MATERIALS TRANSACTIONS A
whole-number ratios. Here, it was suggested that such a finding was due to local atomic short-range order and that the eutectic liquid structure consisted of icosahedral atomic arrangements.[13] More recently (2004), Miracle et al.[7,8] used a geometrically based theory to define efficient atomic packing orientations (clusters) in metallic glasses. Here, for each solute and solvent atom, the radius ratio R, for optimal efficient atomic packing in a single surrounding shell consisting of atoms N, was determined. Based on the frequency of occurrence of a given radius ratio among known bulk metallic glassforming alloys, a strong correlation between efficiently packed clusters and integer coordination numbers of N = 9, 10, 12, 15, and 17 was recognized,[14] which has been supported by experimental data for a number of metallic glass-forming systems using various diffraction techniques and atomic simulation models.[15–17] Following from this work, Miracle[9,10] developed a simplified model to describe the structures of metallic glasses consisti
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