Densely packed tetrahedra clusters displaying diamond-like superstructures--颗粒学报PARTICUOLOGY

Jenczyk, J. (2021). Densely packed tetrahedra clusters displaying diamond-like superstructures. Particuology, 58, 147-152. https://doi.org/10.1016/j.partic.2021.03.006

Densely packed tetrahedra clusters displaying diamond-like superstructures

Jacek Jenczyk ^*

NanoBioMedical Centre, Adam Mickiewicz University, Wszechnicy Piastowskiej 3, 61-614 Poznań, Poland

10.1016/j.partic.2021.03.006

Volume 58, October 2021, Pages 147-152

Received 4 January 2021, Revised 17 March 2021, Accepted 18 March 2021, Available online 31 March 2021, Version of Record 6 April 2021.

E-mail: jacjen@amu.edu.pl

Highlights

• Two special tetrahedra packing clusters are presented and discussed.

• Diamond and double-diamond, periodic superstructures are presented.

• The modified clusters tile 3D Euclidean space R³ through periodic tessellations.

• New plesiohedron is defined.

Abstract

Two special tetrahedra packing clusters were analytically calculated and discussed. Diamond and double-diamond, periodic superstructures emerge. Both structures exemplify an efficient, congruent tetrahedra space tiling strategy. The diamond superstructure exhibits a remarkable packing density of φ ∼ 0.76 exceeding maximal density for the packing of equal spheres. The presented architectures display long range order with specific, repetitive structural motifs. Due to their simple tetrahedral symmetry, the investigated clusters have the potential to become interesting, unique sub-units both in construction technology and in self-assembled systems design. The modified structure of presented cluster can entirely tile three-dimensional Euclidean space R³ through periodic tessellations. Moreover, detailed analysis of the cluster enables definition of a new plesiohedron.

Graphical abstract

Keywords

Tessellation; Space tiling; Tetrahedra packing; Quasicrystals; Plesiohedra

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