Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space groups

HAL Id: hal-03134241

https://hal.archives-ouvertes.fr/hal-03134241

Submitted on 11 Feb 2021

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space

groups

T Janssen, J Birman, Françoise Dénoyer, V Koptsik, Jean-Louis Verger-Gaugry, D Weigel, A Yamamoto, S Abrahams, V Kopsky

To cite this version:

T Janssen, J Birman, Françoise Dénoyer, V Koptsik, Jean-Louis Verger-Gaugry, et al.. Report of

a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic

crystal classes, Bravais classes and space groups. Acta Crystallographica Section a Foundations of

Crystallography, Wiley-Blackwell, 2002, 58, pp.605-621. �hal-03134241�

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space

groups

T. Janssen ^‡ , J. L. Birman ^§ , F. D´enoyer ^∗ , V. A. Koptsik , J.-L. Verger-Gaugry ^† , D. Weigel ^a , A. Yamamoto ^b ,

S. C. Abrahams ^c and V. Kopsky ^d

‡

Institute of Theoretical Physics, University of Nijmegen, NL-6525ED Nijmegen, The Netherlands,

§

Department of Physics, City University of New York, New York, NY 10031, USA,

∗

Laboratoire de Physique des Solides, Bˆatiment 510, Universit´e Paris-Sud, 91405 Or- say Cedex, France,

Institute of Physics, Moscow State University, Moscow 119899, Russia,

†

Institut Fourier, University Joseph Fourier Grenoble, CNRS URA 188, BP 74- Do- maine Universitaire, 38402- Saint Martin dH`eres, France.

a

Laboratoire de Chimie-Physique du Solide, Ecole Centrale Paris, Chatenay Malabry, F-92295 France,

b

Advanced Materials Laboratory, NIMS, Tsukuba, Ibaraki, 305-0044 Japan,

c

Physics Department, Southern Oregon University, Ashland, OR 97520, USA

d

Institute of Physics, Czech Academy of Science, Na Slovance 2, Prague 8, 18040 Czech Republic.

Abstract. The Second Report of the Subcommittee on the Nomenclature

of n- Dimensional Crystallography recommends specific symbols for

R-irreducible groups in 4 and higher dimensions (nD), for centrings,

for Bravais classes, for arithmetic crystal classes and for space groups

(space-group types). The relation with higher-dimensional crystallo-

graphic groups used for the description of aperiodic crystals is briefly

discussed. The Introduction discusses the general definitions used in

the Report.