Ab-initio Construction of Some Crystalline 3D Euclidean Networks
Date
2003
Authors
Hyde, Stephen
Ramsden, Stuart
Di Matteo, Tiziana
Longdell, Jevon
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
We describe a technique for construction of 3D Euclidean (E3) networks with partially-prescribed rings. The algorithm starts with 2D hyperbolic (H2) tilings, whose symmetries are commensurate with the intrinsic 2D symmetries of triply periodic minimal surfaces (or infinite periodic minimal surfaces, IPMS). The 2D hyperbolic pattern is then projected from H2 to E3, forming 3D nets. Examples of cubic and tetragonal 3-connected nets with up to 288 vertices per unit cell, each linking a pair of 6-rings and a single 8-ring, are derived by projection onto the P, D, Gyroid and I-WP IPMS. A single example of a projection from close-packed trees in H2 to E3 (via the D surface) is also shown, that leads to a quartet of interwoven equivalent chiral nets. The configuration describes the channel system of a novel quadracontinuous branched minimal surface that is a chiral foam with four identical, open bubbles.
Description
Keywords
Keywords: Algorithms; Trees (mathematics); Euclidean networks; Crystalline materials; algorithm; article; atom; calculation; chemical structure; crystal structure; crystallography; energy; force; geometry; rotation; solid state Chemical frameworks; Crystalline graphs; Hyperbolic geometry
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Source
Solid State Sciences
Type
Journal article