Hirata A., Matsue K., Chen M. Structural Analysis of Metallic Glasses with Computational Homology

Springer Japan KK, 2016. – 79 p. – ISBN10: 4431560548Describes for the first time the application of computational homology for atomic structures of glasses
Introduces a successful example of the collaborative work between materials and mathematical researchers
Provides readable and understandable mathematical information for non-specialist readers, especially materials scientists
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.
Topics
Mathematical Applications in the Physical Sciences
Category Theory, Homological Algebra
Math. Applications in ChemistryCrystal and Amorphous Structures
Benefits of Topological Analysis
Metallic Glasses
Structure Models
Experimental Difficulty in Determining Structures
Overview of Cubical Homology
The Fundamental Idea of Homology
Cubical Sets and Chains
Boundary and Cubical Chain Complexes
Cubical Homology and Betti Numbers
Remarks and Guide to the Literature
Application of Computational Homology to Metallic Glass Structures
Calculation Procedures
Homological Analysis for Metallic Glass Structures
Homological Analysis for Crystal Structures
Structural Features of Metallic Glasses Viewed by HomologyAppendix: Several Topics About Homology