Structural Analysis of Metallic Glasses with Computational Homology
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.
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0th Betti number 200 atomic clusters abelian groups algebraic viewpoint amorphous structures Analysis of Metallic atomic clusters atomic configurations atomic radii boundary maps bulk metallic glasses Change in b0 Chap Ck(X cluster units Cn(X Computational Homology configurations in metallic connected components constructed coordination numbers corresponding counts the number crystal structures cubical chain complexes cubical homology cubical set X2 defined Definition denoted distribution function g(r electron diffraction elementary chains elementary cubes example face-centered cubic Figure finite geometric objects Glasses with Computational Hirata holes homological analysis homological information homology class homology computations homology groups homology theory homomorphisms icosahedron identify IIIx integers isomorphic k-chains Mathematics of Materials matrix Mayer–Vietoris exact sequences metallic bond normalized radius normalized ratio b0 number of atoms pair distribution function persistent homology quotient group rings simplicial complexes Smith normal form SROs structural analysis structure of metallic topological features torsion coefficients voxel