Skip to main content
padlock icon - secure page this page is secure

Incommensurate crystallography without additional dimensions

Buy Article:

$59.00 + tax (Refund Policy)

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non‐modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Affiliations: Laboratoire de Cristallographie, IPSB-FSB, École Polytechnique Fédérale de Lausanne, Le Cubotron, Dorigny, CH-1015 Lausanne, Switzerland

Publication date: July 1, 2013

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more