Multidimensional period doubling structures

Lee, Jeong Yup; Flom, Dvir; Ben-Abraham, Shelomo I.

doi:10.1107/s2053273316004897

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…The work reported in this paper is part of a project generalizing one-dimensional sequences and two-dimensional structures to higher dimensions (Ben-Abraham & Quandt, 2011;Ben-Abraham et al, 2013, 2014Lee et al, 2016). A preliminary short report on the present subject was published in the Proceedings of ICQ 13 (Flom & Ben-Abraham, 2017).…”

Section: Introductionmentioning

confidence: 99%

Multidimensional color codes for chair tilings

Ben-Abraham¹,

Flom²

2022

Acta Cryst Sect A

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Ordered aperiodic structures have been of interest to the crystallographic community for several decades, and study of them has in turn led to the study of lattice substitution systems, model sets and chair tilings. In this work a color code for chair tilings in arbitrary dimensions is presented. In two and three dimensions, it is expedient to translate the digital codes into colors. An explicit example of a three-dimensional color coding covering one octant is constructed. The tiling is then extended to the whole three-dimensional space and an indication is given of how to do this in arbitrary dimensions. Illustrations of some four-dimensional objects are also shown. The principle of color coding can be applied to other complex tilings such as brick tiling.

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Section: Introductionmentioning

confidence: 99%

Multidimensional color codes for chair tilings

Ben-Abraham¹,

Flom²

2022

Acta Cryst Sect A

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Theoretical Calculation into the Structures and MD Simulation of CL‐20/DNDA5 Cocrystal

Wang

Hao

et al. 2021

Crystal Research and Technology

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For studying the cocrystal cell structure and molecular dynamics (MD) simulation of CL‐20/DNDA5 (2,4‐dinitro‐2,4‐dinitropentane), cocrystal construction is predicted on ten kinds of space group of crystal cell. MD simulations are performed at the temperatures of 203, 223, 253, 273, 303, and 323 K. The results show that the cell parameters belonging to P21/C are similar to those of CL‐20/DNDA5 cocrystals which are prepared in the lab. With the decrease of temperature, the energy decreases by about 17.7 kcal mol–1 for every 1 K decrease on average. The radial distribution function shows that the main driving force for the formation of CL‐20/DNDA5 cocrystal is mainly the hydrogen bond formed by H provided by CL‐20 and O provided by DNDA5, the van der Waals force and other hydrogen bonds play an auxiliary role. The Hirshfeld surface analysis shows that the contribution of the CL‐20/DNDA5 O···H to the contact point at Hirshfeld surface is 4.5% higher than that of CL‐20 and the nitro of DNDA5 has the stronger electron donating ability. The morphology of cocrystal growth shows that both the simulated ideal crystal morphology and the single crystal prepared by the experiment belong to prismatic crystal.

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Dehydration of microporous vanadosilicates: the case of VSH-13Na

Danisi

Armbruster²

2018

Acta Crystallogr Sect B

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Microporous VSH-13Na of composition Na 2 (VO)(Si 4 O 10 )Á3H 2 O was synthesized under mild hydrothermal conditions and studied by single-crystal X-ray diffraction at room temperature and 398 K. Its vanadosilicate framework, consisting of sheets of silicate tetrahedra connected by vanadyl-type squarebased pyramids, closely resembles that of the mineral cavansite, Ca(VO)-(Si 4 O 10 )Á4H 2 O. Due to the disorder in the orientation of the short apical vanadyl groups, the topological symmetry of VSH-13Na was originally described in space group Imma. However, when analysing the systematic absences in our dataset, only the 2 1 screw axis along b was strictly fulfilled suggesting monoclinic space group P12 1 1. The resulting structure in P2 1 with a = 14.364 (4), b = 9.134 (2), c = 10.373 (3) Å , = 90.056 (7) , V = 1360.9 (7) Å 3 was interpreted as a case of allotwinning of two polytypes with topologically idealized orthorhombic symmetry: A ($ 62%) with antiparallel orientation of the vanadyl groups in adjacent (100) layers and B ($ 38%) with all vanadyl groups in adjacent layers oriented in the same way. At 398 K, the structure of VSH-13Na became fully dehydrated and adopted the unit-cell parameters a = 12.584 (16), b = 9.525 (13), c = 9.696 (14) Å , = 90.10 (4) , V = 1162 (3) Å 3 (space group P2 1 ). Release of H 2 O caused severe contraction of T-O-T angles and the unit-cell volume decreased by $ 15%. Despite their structural similarity, the VSH-13Na framework seems to be more flexible upon dehydration compared with cavansite, whose structure collapsed before removal of the last H 2 O molecule. Thus, the presence of monovalent or divalent extraframework cations plays a key role in the dehydration process of natural and synthetic vanadosilicates.

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Multidimensional period doubling structures

Cited by 3 publications

References 11 publications

Multidimensional color codes for chair tilings

Multidimensional color codes for chair tilings

Theoretical Calculation into the Structures and MD Simulation of CL‐20/DNDA5 Cocrystal

Dehydration of microporous vanadosilicates: the case of VSH-13Na

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