Enumeration of periodic tetrahedral frameworks. II. Polynodal graphs

Treacy, M.M.J.; Rivin, Igor; Balkovsky, E.; Randall, Keith H.; Foster, Martin D.

doi:10.1016/j.micromeso.2004.06.013

Cited by 203 publications

(171 citation statements)

References 30 publications

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“…[40,41] This focus on zeolites led to the following question: in a zeolite framework, is it possible in principle for the tetrahedral geometry to be made ideal and perfect? Or are the small distortions typically seen in crystal structures in fact inevitable, given the framework topology and geometry?…”

Section: The Flexibility Window In Zeolitesmentioning

confidence: 99%

GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

Wells

Sartbaeva

2015

Molecular Simulation

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Template-based geometric simulation is a specialised method for modelling flexible framework structures made up of rigid units using a simplified, localised physical model. The strengths of the method are its ability to handle large all-atom structural models rapidly and at minimal computational expense, and to provide insights into the links between local bonding and steric geometry and global flexibility. We review the implementation of geometric simulation in the 'GASP' software, and its application to the study of materials including zeolites, perovskites and metal -organic frameworks. The latest version (5) of GASP has significant improvements and extensions, in particular an improved algorithm for relaxation of atomic positions, and the capacity to handle both polyhedral and molecular structural units. GASP is freely available to researchers.

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Section: The Flexibility Window In Zeolitesmentioning

confidence: 99%

GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

Wells

Sartbaeva

2015

Molecular Simulation

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“…More recently, Sartbaeva et al (2006), using geometric simulations, have shown that frameworks of real zeolites can be realized at some range of densities called the 'flexibility window'. They argue that the presence of the flexibility window can be used as a criterion for the selection of potential synthetic targets among the millions of hypothetical zeolite frameworks (Treacy et al, 1997(Treacy et al, , 2004Earl & Deem 2006).…”

Section: Introductionmentioning

confidence: 99%

On the collapse of locally isostatic networks

et al. 2009

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We examine the flexibility of periodic planar networks built from rigid corner-connected equilateral triangles. Such systems are locally isostatic, since for each triangle the total number of degrees of freedom equals the total number of constraints. These nets are two-dimensional analogues of zeolite frameworks, which are periodic assemblies of corner-sharing tetrahedra. If the corner connections are permitted to rotate, as if pin-jointed, there is always at least one collapse mechanism in two dimensions (and at least three mechanisms in three dimensions). We present a number of examples of such collapse modes for different topologies of triangular net. We show that the number of collapse mechanisms grows with the size of unit cell. The collapsible mechanisms that preserve higher symmetry of the network tend to exhibit the widest range of densities without sterical overlap.

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“…The rich polymorphism of silica, especially in its low-density forms, allows for fine-tuning of applications (e.g., gas separation membranes) by choosing the best suited polymorph. In addition, 100 000þ hypothetical silica polymorphs have been predicted theoretically as fourfold-connected networks (4CNs) [3][4][5][6][7], a large fraction of which, after accurate theoretical evaluation as silica materials, were found to have comparable energetics to experimentally prepared polymorphs [8,9]. Similarly rich polymorphism has only been further observed for a select group of other inorganic solids, for example, aluminophosphates (AlPO 4 ).…”

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confidence: 99%

“…Arguably, the most thorough study of the energy landscape of any TBSlike system to date was that recently applied to BN [22] which sampled systems with up to only eight atoms per unit cell finding only two hypothetical TBS polymorphs (see above). Evidently, to date, such studies have yielded only a very small number of hypothetical TBS polymorphs with respect to those derived for silica from the enumeration of 4CNs [3][4][5][6][7]. Following this latter topological approach we here sample directly the large and diverse set of 4CNs (with up to 48 atoms per unit cell when realized as a TBS) from a variety of sources.…”

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confidence: 99%

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

2010

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For most inorganic solids, very few dense polymorphs and no low-density polymorphs are observed. Taking a wide range of tetrahedrally-coordinated binary solids (e.g., ZnO, GaN) as a prototypical system, we show that the apparent scarcity of low-density polymorphs is not due to significant structural or energetic limitations. Using databases of periodic networks as sources of novel crystal structures, followed by ab initio energy minimization, we predict a dense spectrum of low-density low-energy polymorphs. The diverse range of materials considered indicates that this is likely to be a general phenomenon. DOI: 10.1103/PhysRevLett.104.175503 PACS numbers: 61.50.Ah, 61.66.Fn, 71.15.Nc, 82.75.Fq The structure and properties of inorganic solids are intimately linked to such an extent that even different structures of the same composition (so-called polymorphs) often have widely differing properties and applications. For boron nitride (BN), for example, the soft hexagonal layered polymorph (h-BN) is used as a lubricant, while the cubic polymorph (wurtzite structure) is extremely hard and is employed as an industrial abrasive. Germanium also exhibits more than one polymorph (or more strictly ''allotrope'' for elemental systems) having very different optical properties; with the diamond structured -germanium having an indirect band gap, and the recently synthesized lowdensity clathrate-II structure [1] a direct gap. Evidently, having access to more than one polymorph can significantly extend the range of properties and applications of a particular compound. For the vast majority of inorganic solids, however, typically only three or fewer distinct polymorphs have been prepared experimentally and a similarly small number of hypothetical polymorphs have been proposed. Moreover, where more than one polymorph is known, these extra phases very rarely have a significantly lower density than the most stable polymorph.In stark contrast to this situation, silica (SiO 2 ) has been prepared as more than 40 polymorphs [2], the majority of which are considerably less dense than -quartz; the most stable polymorph under ambient conditions. The rich polymorphism of silica, especially in its low-density forms, allows for fine-tuning of applications (e.g., gas separation membranes) by choosing the best suited polymorph. In addition, 100 000þ hypothetical silica polymorphs have been predicted theoretically as fourfold-connected networks (4CNs) [3][4][5][6][7], a large fraction of which, after accurate theoretical evaluation as silica materials, were found to have comparable energetics to experimentally prepared polymorphs [8,9]. Similarly rich polymorphism has only been further observed for a select group of other inorganic solids, for example, aluminophosphates (AlPO 4 ). A tantalizing hint that there may as yet exist a greater pool of experimentally accessible polymorphs for many other inorganic solids is given by the recent low temperature deposition synthesis of the tetrahedral wurtzite polymorph of LiBr [10] (after previous theor...

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Enumeration of periodic tetrahedral frameworks. II. Polynodal graphs

Cited by 203 publications

References 30 publications

GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

On the collapse of locally isostatic networks

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

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