Crystal pattern

From Online Dictionary of Crystallography

Revision as of 17:27, 9 November 2017 by BrianMcMahon (talk | contribs) (Tidied translations and added German and Spanish (U. Mueller))

Synonym: infinite ideal crystal

Motif cristallin (Fr). Unendlicher Idealkristall (Ge). Motivo cristallino(It). 結晶模様 (Ja). Cristal ideal infinito (Sp).

An object in the n-dimensional point space En is called an n-dimensional crystallographic pattern or, for short, crystal pattern if among its symmetry operations:

  1. there are n translations, the translation vectors t1, ... , tn of which are linearly independent;
  2. all translation vectors, except the zero vector 0, have a length of at least d > 0.

When the crystal pattern consists of atoms, it takes the name of crystal structure. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.

See also