Space fullerenes: A computer search for new Frank-Kasper structures

Mathieu Dutour Sikirić; Olaf Delgado-Friedrichs; Michel Deza

doi:10.1107/S0108767310022932

Space fullerenes: A computer search for new Frank-Kasper structures

Mathieu Dutour Sikirić
, Olaf Delgado-Friedrichs
, Michel Deza

Research output: Contribution to journal › Article › peer-review

64 Citations (Scopus)

Abstract

A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E³by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank-Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank-Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.

Original language	English
Pages (from-to)	602-615
Number of pages	14
Journal	Acta Crystallographica Section A: Foundations of Crystallography
Volume	66
Issue number	5
DOIs	https://doi.org/10.1107/S0108767310022932
Publication status	Published - 1 Sept 2010

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abstract = "A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E3by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank-Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank-Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.",

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AU - Delgado-Friedrichs, Olaf

AU - Deza, Michel

PY - 2010/9/1

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N2 - A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E3by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank-Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank-Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.

AB - A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E3by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank-Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank-Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.

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Space fullerenes: A computer search for new Frank-Kasper structures

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