Persistent homology and many-body atomic structure for medium-range order in the glass.

@article{Nakamura2015PersistentHA,
  title={Persistent homology and many-body atomic structure for medium-range order in the glass.},
  author={Takenobu Nakamura and Yasuaki Hiraoka and Akihiko Hirata and Emerson G. Escolar and Yasumasa Nishiura},
  journal={Nanotechnology},
  year={2015},
  volume={26 30},
  pages={
          304001
        }
}
The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization… 
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References

SHOWING 1-10 OF 59 REFERENCES
Inorganic glasses, glass-forming liquids and amorphizing solids
We take familiar inorganic oxide glasses and non-oxide glasses and the liquids from which they derive to review the current understanding of their atomic structure, ranging from the local…
Local topology of silica networks
Model-building algorithms based on self-assembly according to local rules have been devised, which permit rapid assembly of vertex-sharing tetrahedral network structures. These have been applied to…
Random packings and the structure of simple liquids. I. The geometry of random close packing
  • J. Finney
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
In his Bakerian Lecture, Bernal (1964) discussed those ideas of restricted irregularity which are physically realized in random packings of equal hard spheres, with particular reference to the…
Short range order and stability of a mechanically alloyed Cr25Nb75 glass determined by total scattering and first principles
The atomic environment and stability of an amorphous Cr25Nb75 alloy was studied on the basis of average atomic coordination, average cluster number density as well as cluster radial distribution of…
Network properties of crystalline polymorphs of silica
Structure, odd lines and topological entropy of disorder of amorphous silicon.
  • F. Wooten
  • Mathematics
    Acta crystallographica. Section A, Foundations of crystallography
  • 2002
A continuous random network model of amorphous silicon, subject to periodic boundary conditions, is partitioned into cells bounded by irreducible rings. An algorithm has been developed to find the…
Ring Configurations in a Random Network Model of Vitreous Silica
THE properties of liquids and glasses may, for many purposes, be classed together. Both lack the extensive regularly repeating groups of atoms that characterize crystalline arrays. X-ray diffraction…
Intermediate-range order in permanently densified vitreous SiO2: A neutron-diffraction and molecular-dynamics study.
TLDR
The structure of pressure-densified vitreous SiO{sub 2} has been investigated using neutron-diffraction and molecular-dynamics techniques and shows substantial changes in the first sharp diffraction peak (FSDP): an indication of modification in the intermediate-range order.
Structural model for amorphous silicon and germanium
The Bakerian Lecture, 1962 The structure of liquids
  • J. D. Bernal
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1964
A satisfactory picture of the structure of liquids has lagged far behind that of other states of matter. Ever since the time of Euler in the eighteenth century or, in a more precise form, since that…
...
...