Fifty‐nine tetrakaidecahedra as grain models

Hucher, Monique; Grolier, Jacques

doi:10.1111/j.1365-2818.1977.tb00072.x

Cited by 9 publications

(5 citation statements)

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“…We have performed the complete derivation and created the database on 16-and 17-hedra; our results are in absolute accordance with those of the authors of [85][86][87][88][89][90][91][92][93][94]97]. However, the questions remain open if there are effective generation algorithms (those may include certain restrictions on the size and combination of the faces) and a compact encoding of simple polyhedra making it possible to obtain and store data on polyhedra with a greater number of the faces.…”

Section: Generation Of Simple Polyhedrasupporting

confidence: 88%

“…It is significant that all polyhedral cavities of the known clathrate hydrates [1][2][3]84] contain no triangular faces and have the convex type vertices only. The topological types of the simple polyhedra with the numbers of faces f 14 were derived repeatedly [85][86][87][88], mostly commonly the approaches based on the graph theory being used. Modern theoretical and computer methods of the graph theory conceptually allow the solution of the problem of deriving the simple polyhedra with a larger number of faces: all the combinatorial types of those having up to 16 faces have been already derived, and their symmetries have been determined [89][90][91][92][93][94].…”

Section: Generation Of Simple Polyhedramentioning

confidence: 99%

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Phase formation and structure of high-pressure gas hydrates and modeling of tetrahedral frameworks with uniform polyhedral cavities

Komarov

Солодовников

Грачев

et al. 2007

Crystallography Reviews

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2007) Phase formation and structure of highpressure gas hydrates and modeling of tetrahedral frameworks with uniform polyhedral cavities, Crystallography Reviews, 13:4, 257-297, During the last decade, a number of high-pressure gas hydrates have been prepared and structurally characterized. One of the most interesting results obtained is the formation of compounds having tetrahedral water frameworks with uniform polyhedral cavities (e.g., clathrates THF Á 6H 2 O and 2Ar Á 6H 2 O), unprecedented among ambient pressure hydrates. In order to predict, reveal and perform effective investigations of such gas hydrates at high pressures it is plausible to know all possible tetrahedral frameworks of this kind. The solution of this problem demands to elaborate methods of a topological design of the tetrahedral frameworks represented as space-filling packings of uniform polyhedra with trivalent vertices (simple polyhedra). There are two related approaches to solve this problem: tiling of 3D space into symmetrically equal polyhedra (stereohedra) and generation of periodic four-connected nets. At present, the complete set of tetrahedral frameworks built of uniform simple 14-hedra (23 packings) was obtained and more than 800 frameworks were constructed from larger simple stereohedra. This article gives a discussion of structural and energetic characteristics of the frameworks generated, as well as the possibilities of using these results for interpretation of experimental structural data and a deliberate synthesis of clathrate compounds possessing new structures. Experimental and theoretical data show a high probability of finding a whole series of novel high-pressure gas hydrates with the tetrahedral water frameworks built of simple stereohedra. Of these, the most probable structures are those with 14-hedral cavities, these structures having the stoichiometry of six water molecules per cavity. In our opinion, the formation of such hydrates could be expected for guest molecules with van der Waals diameters from 5.8 to 7.2 Å . However, these hydrates cannot be excluded for substantially smaller guests as well, provided that the water framework cavities include two guest molecules. Packing polymorphism (different space filling arrangements of the same stereohedron) revealed in the search for tilings of 3D space into stereohedra offers experimental discovery of this phenomenon, which can be promoted by such delicate effects as the guestguest interaction. The set of the derived water frameworks as stereohedra space-fillings gives opportunities to select starting structure models in the course of a diffraction study of polycrystalline high-pressure gas hydrate samples.

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Section: Generation Of Simple Polyhedrasupporting

confidence: 88%

Section: Generation Of Simple Polyhedramentioning

confidence: 99%

Phase formation and structure of high-pressure gas hydrates and modeling of tetrahedral frameworks with uniform polyhedral cavities

Komarov

Солодовников

Грачев

et al. 2007

Crystallography Reviews

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“…The seven polyhedra of Fig. 2 are among the 59 tetradecahedra with polygonalities between four and six, identified by Hucher & Grolier (1977), but all are non-isomorphic to the tetradecahedra identified by Williams (1968) as space fillers with one rotation.…”

Section: Generation Of Packingsmentioning

confidence: 96%

New types of space-filling polyhedra with fourteen faces

Rosa¹,

Fortes²

1986

Acta Crystallogr A Found Crystallogr

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A study of the staggered packing of identical hexagonal prisms leading to four-connected periodic structures with polyhedral cells of fourteen faces has been undertaken. Special attention was given to those packings that lead to periodic structures with two polyhedra per lattice point, and such that the two polyhedra are related by a pure rotation and/or enantiomorphism. The general solution for packings of this type was obtained and the topology of the intervening polyhedra was determined. It is shown that polyhedra with eight hexagonal faces and six square faces, topologically isomorphic to the truncated octahedron, can be packed with or without a rotation. The polyhedra which can be packed with the respective enantiomorphs (with or without rotation) have four square faces, four pentagonal faces and six hexagonal faces. Each type of packing is compatible with Bravais lattices of any category and each topological solution is compatible with a range of convex shapes.

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“…La revue critique des fondements de quelques unes des théories en présence a été présentée par Paterson [61]. Récemment, la théorie de Goguel 170, 71, 721 a été confrontée à celle de Ito, à propos des micas [73]. Hartman expose comment pour les métaux e t les céramiques, l'observation des angles aux points triples permet d'apprécier les valeurs relatives des énergies de joint de grains.…”

Section: Morphologie De Détail Du Joint Intergranulaireunclassified

Le Joint Intergranulaire Dans Les Roches

Grolier

1975

J. Phys. Colloques

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Vue d'ensemble sur les divers aspects du joint intergranulaire dans les roches et l'intérêt de son étude. L'irrégularité du réseau intergranulaire correspond à l'extrême variabilité de granulométrie et de forme des grains. Importance des modèles structuraux du joint et des théories de son orientation dans l'étude morphogénétique du joint et du grain. Difficulté de révéler dans sa totalité le réseau intergranulaire par des procédés automatiques, bien que le joint intergranulaire soit dans les roches un lieu privilégié pour le développement des phases mineures, l'attaque chimique, la fusion, la fissuration thermique.

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Fifty‐nine tetrakaidecahedra as grain models

Cited by 9 publications

References 3 publications

Phase formation and structure of high-pressure gas hydrates and modeling of tetrahedral frameworks with uniform polyhedral cavities

Phase formation and structure of high-pressure gas hydrates and modeling of tetrahedral frameworks with uniform polyhedral cavities

New types of space-filling polyhedra with fourteen faces

Le Joint Intergranulaire Dans Les Roches

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