Application of Computational Homology to Metallic Glass Structures

  • Akihiko Hirata
  • Kaname Matsue
  • Mingwei Chen
Part of the SpringerBriefs in the Mathematics of Materials book series (BRIEFSMAMA, volume 2)


In this chapter, we apply homology computations to metallic glass structures. The analysis yields the manner of distortion or spatial inhomogeneity of the local atomic structures by showing the topological connectivity of three-dimensional atomic distributions, thereby revealing the hidden structural order of metallic glasses.


Metallic Glass Voxel Size Atomic Radius Betti Number Atomic Cluster 
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    A. Hirata, L.J. Kang, T. Fujita, B. Klumov, K. Matsue, M. Kotani, A.R. Yavari, and M.W. Chen. Geometric frustration of icosahedron in metallic glasses. Science, 341(6144):376–379, 2013.Google Scholar
  2. 2.
    CHomP: Computational Homology Project.

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan
  2. 2.The Institute of Statistical MathematicsTachikawaJapan

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