This book introduces the application of computational homology for structural analysis of metallic glasses. Metallic glasses, relatively new materials in the field of metals, are the next-generation structural and functional materials owing to their excellent properties. To understand their properties and to develop novel metallic glass materials, it is necessary to uncover their atomic structures which have no periodicity, unlike crystals. Although many experimental and simulation studies have been performed to reveal the structures, it is extremely difficult to perceive a relationship between structures and properties without an appropriate point of view, or language. The purpose here is to show how a new approach using computational homology gives a useful insight into the interpretation of atomic structures. It is noted that computational homology has rapidly developed and is now widely applied for various data analyses. The book begins with a brief basic survey of metallic glasses and computational homology, then goes on to the detailed procedures and interpretation of computational homology analysis for metallic glasses. Understandable and readable information for both materials scientists and mathematicians is also provided.

Reflecting the fast pace of research in the field, the Second Edition of Bulk Metallic Glasses has been thoroughly updated and remains essential reading on the subject. It incorporates major advances in glass forming ability, corrosion behavior, and mechanical properties. Several of the newly proposed criteria to predict the glass-forming ability of alloys have been discussed. All other areas covered in this book have been updated, with special emphasis on topics where significant advances have occurred. These include processing of hierarchical surface structures and synthesis of nanophase composites using the chemical behavior of bulk metallic glasses and the development of novel bulk metallic glasses with high-strength and high-ductility and superelastic behavior. New topics such as high-entropy bulk metallic glasses, nanoporous alloys, novel nanocrystalline alloys, and soft magnetic glassy alloys with high saturation magnetization have also been discussed. Novel applications, such as metallic glassy screw bolts, surface coatings, hyperthermia glasses, ultra-thin mirrors and pressure sensors, mobile phone casing, and degradable biomedical materials, are described. Authored by the world’s foremost experts on bulk metallic glasses, this new edition endures as an indispensable reference and continues to be a one-stop resource on all aspects of bulk metallic glasses.

This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors. The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.

The formation of metallic glasses and dual-phase composite/hybrid materials is reviewed, as well as the glass transition process and the resulting structural phenomena. These materials exhibit high strength, extreme hardness, good wear resistance and large elastic deformation. Due to their excellent structural, functional, magnetic, chemical and biological properties metallic glasses are suitable for a great many applications, including in such areas as microelectromechanical devices, pressure sensors, orthopaedic screws and precision surgical instruments. Metallic Glasses, Metallic Glass Composites, Crystal/Glass Transition, Nano-Crystallization, Phase Separations, Supercooled Liquids, Glassy Nanocomposites, Nanoscale Quasicrystals, Mechanical Properties, Nanoscale Wear Resistance, Bauschinger Effect, Cryogenic Temperature, Porous Glasses, Nanocomposite Alloys, Soft Magnetic Alloys, Hard Magnetic Alloys, Magnetocaloric Effect, Corrosion Resistant Alloys, Surface Oxides, Catalysts

Bulk metallic glasses are a new emerging field of materials with many desirable and unique properties. These amorphous materials have many diverse applications from structural applications to biomedical implants. This book provides a complete overview of bulk metallic glasses. It covers the principles of alloy design, glass formation, processing, atomistic modeling, computer simulations, mechanical properties and microstructures.

This thesis consists of an in-depth study of investigating microstructure-property relationships in bulk metallic glasses using a novel quantitative approach by which influence of the second phase features on mechanical properties can be independently and systematically analyzed. The author evaluates and optimizes the elastic and plastic deformation, as well as the overall toughness of cellular honeycombs under in-plane compression and porous heterostructures under uniaxial tension. The study reveals three major deformation zones in cellular metallic glass structures, where deformation changes from collective buckling showing non-linear elasticity to localized failure exhibiting a brittle-like deformation, and finally to global sudden failure with negligible plasticity as the length to thickness ratio of the ligaments increases. The author found that spacing and size of the pores, the pore configuration within the matrix, and the overall width of the sample determines the extent of deformation, where the optimized values are attained for pore diameter to spacing ratio of one with AB type pore stacking.

Abstract: Metallic glasses are metallic alloy systems with disordered atomic structure. Due to their unique amorphous structure, they exhibit an extraordinary set of properties that are ideal for a wide variety of applications ranging from electrical transformers, armor-piercing projectiles, sporting goods and fuel cells to precision gears for micromotors. In particular, owing to their exceptional mechanical properties like near-theoretical strength (1-3 GPa), large elastic strain range (2-3%), and unusual formability above the glass transition temperature, metallic glasses have tremendous potential in structural applications. Unfortunately, their unique structure also gives rise to significant limitations, such as limited ductility at room temperature due to rapid localization of plastic flow in shear bands. However, when the test volumes approach the size of a shear band nucleus (~50-500 nm), it is believed that shear band formation and propagation can be constrained, leading to enhanced plasticity and failure strength. This study investigates the phenomenon of strain localization using both experimental and computational techniques. On the experimental front, sample size effects on strength, plasticity and deformation modes were explored in a Zr-based bulk metallic glass via micron- and sub-micron scale compression testing. Specimens with diameters ranging from 200 nm to a few microns were fabricated using Focused Ion Beam technique and were tested under uniaxial compression in a nanoindentation set-up with a flat punch tip. Effect of extrinsic factors like specimen geometry and machine stiffness on deformation behavior was discussed. Shear banding was shown to be more stable at this length scale than in macro-scale testing because of a smaller specimen to load frame stiffness ratio. It was found that as the specimen size is reduced to below 300 nm, the deformation mode changes from being discrete and inhomogeneous to more continuous flow including both localized and non-localized contributions at low strains. Moreover, the magnitude of strain bursts was found to decrease with decrease in specimen size. Furthermore, Weibull statistical analysis was performed to investigate the effect of specimen size on yield strength in this metallic glass. It was revealed that the dispersion in strengths increases dramatically with decrease in sample size, attributed to the size distribution of the defects responsible for shear banding. The findings are crucial in designing systems which promote plasticity in metallic glasses by suppressing the shear-band instability and also in direct application of these materials for structural purposes as small components in micro- and nano-scale systems. On the computational front, Molecular Dynamics (MD) simulations have been employed to generate Zr-Cu metallic glass structures. In order to analyze and better understand and visualize the concepts of "free" volume and flow defects in metallic glasses, an electron density model was developed as an upgrade to the traditional hard sphere approaches. Simple tension and shear modes of deformation were simulated using MD in Zr-Cu system, and role of open volume in deformation was studied using the electron density model. In uniaxial tension simulations, effect of temperature and deformation rate is examined, and the process of accumulation of free volume to the point of catastrophic failure is visualized using the Electron Density model. In shear simulations, we find that the as-quenched glass structures undergo homogeneous deformation and do not exhibit any strain localization. However, it is found that by incorporating a cylindrical void in the glass structure as a source of "free" volume, it is possible to induce strain localization. It was found that a critical void diameter of 8 Angstroms was required to successfully initialize strain localization in this system.