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Structural peculiarities? Aperiodic crystals, modulated phases, composite structures

  • Andreas Schönleber ORCID logo EMAIL logo
Veröffentlicht/Copyright: 31. Mai 2023
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Physical Sciences Reviews
Aus der Zeitschrift Physical Sciences Reviews Band 9 Heft 8

Abstract

According to a general understanding, a crystal structure is defined by a lattice and the content of the unit cell of this lattice. As consequence a crystal exhibits three-dimensional periodicity with respect to the atoms. However, an increasing number of known crystal structures does not follow this idea of periodicity, but shows an aperiodic arrangement of its atoms. This group of so-called “aperiodic crystals” contains quasicrystals, modulated phases and composite structures. The latter two can be properly described within the higher-dimensional superspace approach to enable an accurate crystal-chemical analysis. Here the superspace is a mathematical tool, in which periodicity can be recovered in a higher-dimensional space. In the first part of this review the basic concept of periodic and aperiodic crystals is presented and similarities and differences of modulated phases, composite structures and quasicrystals are discussed. In a second part the higher-dimensional superspace approach is introduced in reciprocal and in direct space and the implementation of symmetry in superspace is reviewed. In the last part representative examples and the origin of aperiodicity in the crystal structures are discussed.

Keywords: higher-dimensional superspace; incommensurate structure; long-range order; quasiperiodic lattice; superspace symmetry
Corresponding author: Andreas Schönleber, Laboratory of Crystallography, University of Bayreuth, 95447 Bayreuth, Germany, E-mail:

  1. Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.

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Received: 2019-05-25
Accepted: 2023-04-25
Published Online: 2023-05-31

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Reviews
  3. Dipeptidyl peptidase IV: a multifunctional enzyme with implications in several pathologies including cancer
  4. Structural peculiarities? Aperiodic crystals, modulated phases, composite structures
  5. Crystalline materials in art and conservation: verdigris pigments – what we know and what we still don’t know
  6. Corn starch nanocomposite films reinforced with nanocellulose
  7. Cassava starch nanocomposite films reinforced with nanocellulose
  8. Regulations for food packaging materials
  9. Process intensification using immobilized enzymes
  10. Succinic acid: applications and microbial production using organic wastes as low cost substrates
  11. Microbial electrotechnology – Intensification of bioprocesses through the combination of electrochemistry and biotechnology
  12. Biopolymer conjugation with phytochemicals and applications
https://doi.org/10.1515/psr-2018-0140
Schlagwörter für diesen Artikel
higher-dimensional superspace; incommensurate structure; long-range order; quasiperiodic lattice; superspace symmetry

Artikel in diesem Heft

  1. Frontmatter
  2. Reviews
  3. Dipeptidyl peptidase IV: a multifunctional enzyme with implications in several pathologies including cancer
  4. Structural peculiarities? Aperiodic crystals, modulated phases, composite structures
  5. Crystalline materials in art and conservation: verdigris pigments – what we know and what we still don’t know
  6. Corn starch nanocomposite films reinforced with nanocellulose
  7. Cassava starch nanocomposite films reinforced with nanocellulose
  8. Regulations for food packaging materials
  9. Process intensification using immobilized enzymes
  10. Succinic acid: applications and microbial production using organic wastes as low cost substrates
  11. Microbial electrotechnology – Intensification of bioprocesses through the combination of electrochemistry and biotechnology
  12. Biopolymer conjugation with phytochemicals and applications
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