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Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres

Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres All systems of interpenetrating sphere packings that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family are tabulated. Homogeneous sphere packings belonging to 49 different types may be intertwined to systems of interpenetrating sphere packings belonging to 74 types. For all compatible lattice complexes, the coordinate and lattice parameters are given. The corresponding patterns of interpenetration are analysed. For the interpenetration of two, three, four, five and eight sphere packings, eleven, three, five, one and two different patterns, respectively, are distinguished. In addition, four types of interpenetrating layers of spheres were found. Each such sphere configuration splits into two or three subsets of parallel sphere layers with an angle of 90Degrees or of 120Degrees, respectively, between the directions of the normals of the layers. A single sphere layer corresponds either to a honeycomb net or to a net built up from quadrangles and octagons. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres

Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres


Abstract

All systems of interpenetrating sphere packings that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family are tabulated. Homogeneous sphere packings belonging to 49 different types may be intertwined to systems of interpenetrating sphere packings belonging to 74 types. For all compatible lattice complexes, the coordinate and lattice parameters are given. The corresponding patterns of interpenetration are analysed. For the interpenetration of two, three, four, five and eight sphere packings, eleven, three, five, one and two different patterns, respectively, are distinguished. In addition, four types of interpenetrating layers of spheres were found. Each such sphere configuration splits into two or three subsets of parallel sphere layers with an angle of 90Degrees or of 120Degrees, respectively, between the directions of the normals of the layers. A single sphere layer corresponds either to a honeycomb net or to a net built up from quadrangles and octagons.

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References (29)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 2006 International Union of Crystallography
Subject
interpenetrating sphere layers, interpenetrating sphere packings, interpenetration patterns, minimal surfaces, uninodal nets
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S010876730600362X
pmid
16614487
Publisher site
See Article on Publisher Site

Abstract

All systems of interpenetrating sphere packings that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family are tabulated. Homogeneous sphere packings belonging to 49 different types may be intertwined to systems of interpenetrating sphere packings belonging to 74 types. For all compatible lattice complexes, the coordinate and lattice parameters are given. The corresponding patterns of interpenetration are analysed. For the interpenetration of two, three, four, five and eight sphere packings, eleven, three, five, one and two different patterns, respectively, are distinguished. In addition, four types of interpenetrating layers of spheres were found. Each such sphere configuration splits into two or three subsets of parallel sphere layers with an angle of 90Degrees or of 120Degrees, respectively, between the directions of the normals of the layers. A single sphere layer corresponds either to a honeycomb net or to a net built up from quadrangles and octagons.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Apr 14, 2006

Keywords: interpenetrating sphere layers ; interpenetrating sphere packings ; interpenetration patterns ; minimal surfaces ; uninodal nets .

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