Mathematical Crystallography 2021

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Chemistry: Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 2454

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Guest Editor
1. Kola Science Center, Russian Academy of Sciences, Fersmana str. 14, 184209 Apatity, Russia
2. Department of Crystallography, Institute of Earth Sciences, St. Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia
Interests: mineralogy; crystallography; structural complexity; uranium
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Special Issue Information

Dear Colleagues,

Despite the enormous success of experimental crystallography achieved in the 20th century, the very problem of the emergence of order and symmetry in discrete structures is far from being completely understood. This Special Issue invites contributions on various mathematical aspects of modern crystallography, starting from diffraction theory and disorder and ending at deeply mathematical problems of symmetry, sphere packings, polyhedral, and discrete point sets.

Prof. Dr. Sergey V. Krivovichev
Guest Editor

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Keywords

  • crystals
  • crystal structure
  • symmetry
  • long-range order
  • sphere packings
  • discrete point systems
  • polyhedral arrangements
  • lattices
  • space groups
  • quasicrystals

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Published Papers (1 paper)

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Research

16 pages, 4427 KiB  
Article
Complexity of Molecular Nets: Topological Approach and Descriptive Statistics
by Alexander M. Banaru and Sergey M. Aksenov
Symmetry 2022, 14(2), 220; https://doi.org/10.3390/sym14020220 - 24 Jan 2022
Cited by 12 | Viewed by 2548
Abstract
The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of Cx [...] Read more.
The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of CxHyOz characterized by the structural class P21/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDPmol). The values of the molecular coordination number (CNmol) and critical coordination number (CNcrit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CNmol, CNcrit, and the complexity parameters is obtained. More than a half of the considered structures has CNmol = 14 and CNmol′ = 9 with the Wyckoff set of edges e5dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of HmolNet is of the logistic distribution type and is distributed near 0.85HmolNet with a small standard deviation. The contribution of Hmol into HmolNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts. Full article
(This article belongs to the Special Issue Mathematical Crystallography 2021)
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