A framework for the detailed classification of general crystal structures, based on an arithmetic criterion, has been proposed in recent years. In this paper it is shown how this method can also be applied to enumerate colored crystals. To illustrate this approach, the systematic classification in the simplest case, i.e. of `2-color 2-lattices', in two and three dimensions (two- and three-dimensional crystals with two differently colored atoms per unit translational cell) is presented. 51 distinct types of 2-color 2-lattices are found in three dimensions (ten types in two dimensions); this gives a complete catalog of the simplest crystal structures that are theoretically possible for two-element compounds. Among the 51 2-lattices, all those which already have a Strukturberichte denomination are retrieved, as well as the 22 `black-and-white lattices' considered in the theory of magnetic crystals. The symmetry hierarchies and symmetry-breaking possibilities for 2-color 2-lattices are also determined in two and three dimensions.

The arithmetic symmetry of colored crystals: classification of 2-color 2-lattices

ZANZOTTO, GIOVANNI
2004

Abstract

A framework for the detailed classification of general crystal structures, based on an arithmetic criterion, has been proposed in recent years. In this paper it is shown how this method can also be applied to enumerate colored crystals. To illustrate this approach, the systematic classification in the simplest case, i.e. of `2-color 2-lattices', in two and three dimensions (two- and three-dimensional crystals with two differently colored atoms per unit translational cell) is presented. 51 distinct types of 2-color 2-lattices are found in three dimensions (ten types in two dimensions); this gives a complete catalog of the simplest crystal structures that are theoretically possible for two-element compounds. Among the 51 2-lattices, all those which already have a Strukturberichte denomination are retrieved, as well as the 22 `black-and-white lattices' considered in the theory of magnetic crystals. The symmetry hierarchies and symmetry-breaking possibilities for 2-color 2-lattices are also determined in two and three dimensions.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1376603
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
  • OpenAlex ND
social impact