Metal-Organic Nanosheets Formed via Defect-Mediated Transformation of a Hafnium Metal-Organic Framework by Cliffe, M, Castillo-Martínez, E, Wu, Y, Lee, J, Forse, A, Firth, F, Moghadam, P, Fairen-Jimenez, D, Gaultois, M, Hill, J, Magdysyuk, O, Slater, B, Goodwin, A, Grey, C

“…We report a hafnium-containing MOF, hcp UiO-67(Hf), which is a ligand-deficient layered analogue of the face-centered cubic fcu UiO-67(Hf). hcp UiO-67 accommodates its lower ligand:metal ratio compared to fcu UiO-67 through a new structural mechanism: the formation of a condensed "double cluster" (Hf12O8(OH)14), analogous to the condensation of coordination polyhedra in oxide frameworks. In oxide frameworks, variable stoichiometry can lead to more complex defect structures, e.g., crystallographic shear planes or modules with differing compositions, which can be the source of further chemical reactivity; likewise, the layered hcp UiO-67 can react further to reversibly form a two-dimensional metal-organic framework, hxl UiO-67. …”

Structural and magnetic properties of topotactically reduced YSr2Mn2O7-x (0 < x < 1.5) by Hayward, M

“…The variation in the anion vacancy distribution of these reduced phases as a function of stoichiometry is discussed in relation to the coordination polyhedra of the metal cations. Temperature-dependent magnetization data indicate strong antiferromagnetic coupling interactions in all samples. …”

Electronic, bonding and optical properties of the LiGaGe2X6 (X = S, Se, and Te) compounds: An ab initio study by Azzi, O., Hacene, F. Boukli, Ferouani, Abdel Karim, Ouahrani, Tarik, Reshak, Ali Hussain

“…We show in this article, through a large body of calculations, the trend in the row of participating anions, S ⟶ Se ⟶ Te, enhances the polarization effect and the coordination structure distortions in the polyhedra groups forming the bonding pattern of the cell. …”

Brochosomes and Other Bioaerosols in the Surface Layer of the Atmosphere of Moscow Metropolis by Dina P. Gubanova, Anna A. Vinogradova, Nataliya V. Sadovskaya

“…They are quasi-spherical hollow porous semi-regular polyhedra (truncated icosahedra) of 0.2–0.7 microns in size, consisting mainly of carbon and oxygen. …”
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Description of Dynamic Recrystallization by Means of An Advanced Statistical Multilevel Model: Grain Structure Evolution Analysis by Peter Trusov, Nikita Kondratev, Andrej Podsedertsev

“…In the framework of this statistical approach, there is no mandatory requirement for continuous filling of the computational domain with crystallites; however, the material grain structure cannot be created arbitrarily. Using the Laguerre polyhedra, we develop a method of grain structure simulation coupled with subsequent processing and transferring of the necessary data on the grain structure to the modified statistical model. …”
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Crystal structure and Hirshfeld surface analysis of bis(μ-4-tert-butoxy-4-oxobut-2-en-2-olato)bis[(4-tert-butoxy-4-oxobut-2-en-2-olato)ethanolzinc(II)] by Olherd O. Shtokvysh, Viktoriya V. Dyakonenko, Lyudmila I. Koval, Vasyl I. Pekhnyo

“…The molecular and crystal structure of the title binuclear Zn2+ complex, [Zn2(C8H13O3)4(C2H5OH)2], with enolated anionic tert-butylacetoacetate and ethanol was analysed. The coordination polyhedra of the Zn atoms are distorted octahedra formed by six oxygen atoms that belong to three ligand molecules and a coordinated ethanol molecule. …”
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About products of interaction of holmium chloride and bromide with carbamide by L. Yu. Alikberova, D. V. Albov, P. S. Kibalnikov, G. A. Fyodorova, V. V. Kravchenko, N. S. Rukk

“…For these compounds, coordination with metal occurs through the oxygen atoms of the water and carbamide molecules. The coordination polyhedra for I and II are distorted tetragonal antiprisms. …”
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Bumpy pyramid folding by Abel, Zachary Ryan, Demaine, Erik D., Demaine, Martin L., Ito, Hiro, Snoeyink, Jack, Uehara, Ryuhei

“…By Alexandrov’s theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov’s theorem for a special class of polyhedra. We also give a polynomial time algorithm that finds the crease pattern to produce the maximum volume triangulated polyhedron.…”
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Positive semidefinite rank by Gouveia, João, Robinson, Richard Z., Thomas, Rekha R., Parrilo, Pablo A, Fawzi, Hamza

“…The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects.…”
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Structural evolution of Ti50Cu50 on rapid cooling by molecular dynamics simulation by Pang, Jianjun, Tan, M. J., Liew, K. M.

“…Due to the existence of bcc clusters and the other distorted polyhedra other than full icosahedra, the structural analysis reconfirms the inference from the Gibbs free energy calculation.…”
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Actuation of DNA cages and their potential biological applications by Entwistle, N

“…<p>DNA cages are polyhedra self-assembled from synthetic oligonucleotides in a one-pot process. …”

Structural study of amorphous CoFeB thin films exhibiting in-plane uniaxial magnetic anisotropy by Kirk, D, Kohn, A, Borisenko, K, Lang, C, Schmalhorst, J, Reiss, G, Cockayne, D

“…These simulations find a range of local coordination polyhedra present in the material. Despite an average coordination number of approximately 8 for the transition-metal component, a degree of medium-range order, and a stoichiometry close to Co50 Fe50, large local deviations from this octahedral value mean that the structure is not based on bcc-type basic units. © 2009 The American Physical Society.…”

Polyamorphism in aluminate liquids by McMillan, P, Wilson, M, Wilding, M

“…However, the data indicate that changes occur among the packing geometries and clustering of the Al-O and Y-O coordination polyhedra, i.e., within the second-nearest-neighbour shell defined by the metal-metal (i.e., Y-Y, Y-Al and Al-Al) interactions. …”

Structural changes in supercooled Al2O3-Y2O3 liquids. by Wilding, M, Wilson, M, Benmore, C, Weber, J, McMillan, P

“…We show that the incipient liquid-liquid phase transition behaviour is correlated with local density fluctuations that represent different coordination polyhedra surrounding oxygen ions. The difference in energy and volume associated with this sampling of high and low density basins in the underlying energy landscape is consistent with independent verifications of the volume and enthalpy differences between different amorphous forms. …”

Complex cation order in anion-deficient Ba(n)YFe(n-1)O(2.5n) perovskite phases. by Luo, K, Hayward, M

“…A rationalization for the observed structures is presented on the basis of the need to minimize lattice strain while maintaining the integrity of the local YO6 and FeO4 coordination polyhedra. The n = 4 member of the series, Ba4YFe3O10, adopts a cation and anion-vacancy disordered structure, which is attributed to dilution of the structure directing effects at extreme Y:Fe stoichiometric ratios. …”

Using estimated thermodynamic properties to model accessory phases: the case of tourmaline by Van Hinsberg, V, Schumacher, J

“…To allow for estimates of tourmaline, fractional thermodynamic properties for B III and B IV polyhedra were derived. Mixing contributions to molar volume were evaluated and symmetrical mixing parameters derived for Al-Mg, Al-Fe and Al-Li interaction on tourmaline's Y-site and T-site Al-Si interaction. …”

CAD construction method of 3D building models for GIS analysis by Boguslawski, Pawel, M. Gold, Christopher, Abdul Rahman, Alias

“…. – in this case they are polyhedra, sometimes of a complex shape. These allow for visualisation and analysis of a wide area like a city, but micro-scale analysis of interiors is not possible. …”

Comparative Study of the Compressibility of M₃V₂O₈ (M = Cd, Zn, Mg, Ni) Orthovanadates by Daniel Díaz-Anichtchenko, Daniel Errandonea

“…We found that the studied vanadates have an anisotropic response to compression and that the change in volume is basically determined by the compressibility of the divalent-cation coordination polyhedra. A systematic discussion of the bulk modulus of M₃V₂O₈ orthovanadates will also be included.…”
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Sr9La2(WO6)4 containing [WO6] octahedra by Rayko Simura, Tomoki Watanabe, Hisanori Yamane

“…The structure of Sr9La2(WO6)4 can be described on the basis of the double-perovskite structure with [WO6] and [(Sr/La)Ox] polyhedra alternately placed, and a vacancy (□).…”
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Effect of Reducing the Size and Number of Faces of Polyhedral Specimen on Wood Characterization by Ultrasound by Cinthya Bertoldo, Geise Aparecida Pereira, Raquel Gonçalves

“…This research aimed to verify whether it is possible to reduce the polyhedra dimension without affecting the results of the elastic parameters obtained in wood characterization by ultrasound. …”
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