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Polyhedra
Kinds of Polyhedra Selected AbstractsFast, Exact, Linear BooleansCOMPUTER GRAPHICS FORUM, Issue 5 2009Gilbert Bernstein Abstract We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases. [source] ChemInform Abstract: Crown and Bowl-Shaped Clusters of Uranyl Polyhedra.CHEMINFORM, Issue 19 2010Ginger E. Sigmon Abstract ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a "Full Text" option. The original article is trackable via the "References" option. [source] ChemInform Abstract: A Rare Multi-Coordinate Tellurite, NH4ATe4O9×2H2O (A: Rb or Cs): The Occurrence of TeO3, TeO4, and TeO5 Polyhedra in the Same Material.CHEMINFORM, Issue 47 2008Jun-Ho Kim Abstract ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a "Full Text" option. The original article is trackable via the "References" option. [source] Expanding the Crystal Chemistry of Actinyl Peroxides: Open Sheets of Uranyl Polyhedra in Na5 [(UO2)3(O2)4(OH)3] (H2O)13.CHEMINFORM, Issue 44 2006Karrie-Ann Kubatko Abstract ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF. [source] Fast, Exact, Linear BooleansCOMPUTER GRAPHICS FORUM, Issue 5 2009Gilbert Bernstein Abstract We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases. [source] Hierarchical Convex Approximation of 3D Shapes for Fast Region SelectionCOMPUTER GRAPHICS FORUM, Issue 5 2008Marco Attene Abstract Given a 3D solid model S represented by a tetrahedral mesh, we describe a novel algorithm to compute a hierarchy of convex polyhedra that tightly enclose S. The hierarchy can be browsed at interactive speed on a modern PC and it is useful for implementing an intuitive feature selection paradigm for 3D editing environments. Convex parts often coincide with perceptually relevant shape components and, for their identification, existing methods rely on the boundary surface only. In contrast, we show that the notion of part concavity can be expressed and implemented more intuitively and efficiently by exploiting a tetrahedrization of the shape volume. The method proposed is completely automatic, and generates a tree of convex polyhedra in which the root is the convex hull of the whole shape, and the leaves are the tetrahedra of the input mesh. The algorithm proceeds bottom-up by hierarchically clustering tetrahedra into nearly convex aggregations, and the whole process is significantly fast. We prove that, in the average case, for a mesh of n tetrahedra O(n log2 n) operations are sufficient to compute the whole tree. [source] Magneto,Structural Correlations in Discrete MnII -WV Cyano-Bridged Assemblies with Polyimine LigandsEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 26 2010Robert Podgajny Abstract We present the magneto,structural correlations for two novel discrete cyano-bridged assemblies based on cationic complexes of manganese(II) with diimine ligands and octacyanotungstate(V) ions. The crystal structure of [MnII(terpy)(dmf)(H2O)2][MnII(terpy)(H2O)(dmf)(,-NC)WV(CN)7]2·6H2O (1) (terpy = 2,2,;6,,2,-terpyridine, dmf = dimethylformamide) contains dinuclear {MnIIWV}, cyano-bridged anions, while the crystal structure of [MnII(phen)3]2[MnII(phen)2(,-NC)2WV(CN)6]2(ClO4)2·9H2O (2) (phen = 1,10-phenanthroline) is built of tetranuclear {MnII2WV2}2, square anions. Intramolecular Mn,W magnetic interactions through the cyano bridges are represented by magnetic coupling constants J = ,39 cm,1 for the {MnIIWV}, unit in 1 and J1 = ,25.7 and J2 = ,16.7 cm,1 for the {MnII2WV2}2, unit in 2. J and J1 represent relatively strong W,CN,Mn interactions and are ascribed to the bridges in b positions of TPRS-8 (trigonal prism square-face bicapped) of [W(CN)8]3, polyhedra, favoring the strongest electronic interactions between the d,d orbital of W and the ,* orbitals of CN,, whereas J2 is related to the m vertex of [W(CN)8]3,. The magnetic properties of 1 and 2 are compared with reference compounds and discussed in the context of the type of coordination polyhedra of [W(CN)8]3, as well as the metric parameters of cyano-bridged W,CN,Mn linkages. We found the type of coordination polyhedra and bridging mode of [W(CN)8]3, to be the most important factors influencing the magnitude of the Mn,W magnetic interaction. [source] Systematic Hydrothermal Investigation of Metal Phosphonatobenzenesulfonates by High-Throughput MethodsEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 24 2010Palanikumar Maniam Abstract A high-throughput (HT) investigation using the rigid bifunctional ligand 4-phosphonobenzenesulfonic acid, H2O3P-C6H4 -SO3H (H3L), generated five new phosphonatobenzenesulfonates with copper(II) or lead(II) ions. A comprehensive HT study comprising the screenings of different metal ions, metal salt types and the synthesis optimization were conducted whereby the influence of pH and molar ratios M2+/H3L were investigated. The HT-study led to five new compounds Pb2[(O3P-C6H4 -SO3)(OH)] (1), Cu1.5[(O3P-C6H4 -SO3)(H2O)] (2), NaCu(O3P-C6H4 -SO3)(H2O)3 (3), Cu2[(O3P-C6H4 -SO3)(OH)(H2O)] (4) and Cu3[(O3P-C6H4 -SO3)2(H2O)2] (5). Metal ion screening showed lead(II) and copper(II) to be suitable metal ions. The utilization of discovery and focused arrays allowed to determine the optimal formation fields of the respective compounds. The crystal structures were determined from single-crystal X-ray diffraction and revealed the presence of various MOx polyhedra that form clusters, chains or layers which are connected through the organic linker. IR spectra, thermogravimetric studies, magnetic susceptibility measurements and elemental analyses were conducted to further characterize the compounds 1, 3, 4 and 5. [source] A Series of Lithium Rare Earth Polyphosphates [LiLn(PO3)4] (Ln = La, Eu, Gd) and Their Structural, Optical, and Electronic PropertiesEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 2 2007Jing Zhu Abstract The structural, optical, and electronic properties of a series of lithium rare earth polyphosphates [LiLn(PO3)4] [Ln = La (1), Eu (2), Gd (3)] have been investigated by means of single-crystal X-ray diffraction, elemental analyses, and spectroscopic measurements, as well as calculations of energy-band structures, density of states, and optical response functions by density functional methods. These LiLn(PO3)4 systems are monoclinic with space group C2/c and Z = 4. Their unit-cell parameters decrease as the ionic radius of Ln3+ decreases (La3+ > Eu3+ > Gd3+). Both (PO4)3, zig-zag chains and infinite chains formed by the alternate connection of LnO8 polyhedra and LiO4 tetrahedra run parallel to the b -axis in the structure. The energy-band structures, density of states, the chemical bonds, and optical properties have been investigated by density functional methods for some of the title compounds. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007) [source] X-ray Crystal Structure of a Sodium Salt of [Gd(DOTP)]5,: Implications for Its Second-Sphere Relaxivity and the 23Na NMR Hyperfine Shift Effects of [Tm(DOTP)]5,EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 23 2003Fernando Avecilla Abstract The X-ray structure of the sodium salt of [Gd(DOTP)]5, shows two different chelates, [Gd(1)(DOTP)]5, and [Gd(2)(DOTP)]5,, bound at either surface of a sheet formed by a cluster of hydrated Na+ ions. Each [Gd(1)(DOTP)]5, anion binds directly to four Na+ ions of this cluster through the free oxygen atoms of the phosphonate groups of the adjacent ligand, while each [Gd(2)(DOTP)]5, unit is connected to the cluster via hydrogen bonds only. The Gd3+ ions in the two moieties do not have any inner-sphere water molecules, and are eight-coordinate. Their coordination polyhedra are twisted square antiprisms, with slightly different twist angles. These m, isomers are found in the crystal structure as racemic mixtures of enantiomers. Only one set of NMR resonances is observed in aqueous solution, corresponding to an averaged m, isomer. In this crystal structure, the Na+ ions bind the phosphonate oxygen atoms of the [Gd(1)(DOTP)]5, anion at positions far removed from the main symmetry axis. This is significantly different from the binding mode(s) previously proposed to be occurring in solution between Na+ and [Tm(DOTP)]5,, based on the interpretation of solution paramagnetic 23Na NMR shifts. This could arise as a result of the effects of the cluster of hydrated Na+ ions that are present, which may hinder axial binding modes and distort lateral binding modes. Further, in the crystal structure, both types of Gd3+ centers have four second-sphere water molecules that are located at distances (4.2,4.5 Ĺ) significantly longer than those previously proposed from the analysis of the NMRD data of [Gd(1)(DOTP)]5,. This is a result of the coordination of Na+ by these water molecules, thus preventing their direct interaction with the phosphonate oxygen atoms. However, in solution such second-sphere water molecules can interact strongly with the phosphonate ligand oxygen atoms, resulting in efficient relaxation if their binding has relatively long lifetimes (> 50 ps). Rotational immobilization will amplify this contribution, thus making it similar to outer-sphere relaxation. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003) [source] Layered [BaM(C3H2O4)2(H2O)4] (M = Fe or Co) Complexes , Spectroscopic, Magnetic and Thermal StudyEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 16 2003Izaskun Gil de Muro Abstract Complexes with formula [BaM(C3H2O4)2(H2O)4], where M = Fe or Co, were synthesised and characterised. These two types of complexes are isostructural and crystallise in the Pccn space group. Their structure consists of two-dimensional networks of octahedral MO6 polyhedra in which the transition metal ions are coordinated by bridging malonate ligands, through the O-C-O atoms. These M-malonate units are extended along the crystallographic [101] plane. Spectroscopic data are consistent with the cations being in a high-spin octahedral symmetry. The two types of compounds exhibit 2D antiferromagnetic interactions as well as weak ferromagnetism below the Néel temperature, as a result of an intralayer misalignment of the spins. Thermal treatment of the metallo-organic precursors gave rise to BaMO3,y oxides at lower temperatures and reaction times than those found in the literature using the ceramic method. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003). [source] Synthesis and Microstructural Characterisation of Two New One-Dimensional Members of the (A3NiMnO6),(A3Mn3O9), Homologous Series (A = Ba, Sr)EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 13 2003María Hernando Abstract Two new members of the one-dimensional (A3NiMnO6),(A3Mn3O9), homologous series, with the compositions (Sr0.75Ba0.25)5NiMn3O12 and Sr9Ni2Mn5O21, have been synthesised. Their structures can each be described as a hexagonal array of infinite one-dimensional chains of face-sharing polyhedra, running parallel to the c axis and separated by the Sr/Ba cations. The structure of (Sr0.75Ba0.25)5NiMn3O12, which constitutes the (, = 3, , = 2) member of the series, is made up of three face-sharing octahedra linked by one trigonal prism. For Sr9Ni2Mn5O21 (, = 2, , = 1) the sequence of polyhedra along the chains corresponds to a motif consisting of two octahedra,one trigonal prism,three octahedra,one trigonal prism. The manganese atoms occupy the octahedral sites in both phases, while the Ni2+ cations are distributed in the trigonal-prismatic sites in a disordered way. Only a small fraction of these (close to 20%) is located at the centres of the trigonal prisms, 80% being displaced towards the rectangular faces of the polyhedra and giving rise to a square-planar-like coordination. Both oxides present twinned microstructures, as evidenced by SAED and HREM. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003) [source] Comparison of methods to model the gravitational gradients from topographic data basesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Christopher Jekeli SUMMARY A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1, elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical,vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods. [source] Expression and immunocytochemical analysis of Autographa californica nucleopolyhedrovirus (AcMNPV) orf74 geneINSECT SCIENCE, Issue 5 2006SHI-HENG AN Abstract Autographa californica nucleopolyhedrovirus orf74 (Ac74) is located between 62 311 and 63 108bp in the AcMNPV genome, which encodes 265 amino acid residues with a predicted 31 kDa molecular weight. The homologues of Ac74 were searched using BLASTP in protein databases, GenBank/EMBL and SWISS-PROT. The result revealed that deduced Ac74 protein was homologous to the predicted products from 10 lepidoptera NPV ORFs. The multiple sequence alignments of Ac74 and its 10 homologues manifested only one amino acid residue was completely conserved. The transcript analysis revealed that the transcript of Ac74 was detected from 24,72 hours post-infection (hpi). The product of Ac74 was detected at 24 hpi and lasted until 72 hpi by Western blot using anti-Ac74 antiserum, consistent with reverse transcriptase polymerase chain reaction results. These results suggested Ac74 was expressed during the later stages of infection. The product of Ac74 was 31 kDa in size, consistent with predicted molecular weight. The subcellular localization of Ac74 proteins manifested Ac74 protein in the cytoplasm, and was hardly present in the nucleus at 24 hpi. The fluorescence was also observed in polyhedra, except cytoplasm at 72 hpi. Together, Ac74 is a functional protein with 3 1kDa molecular weight and is located in the cytoplasm and the polyhedra. [source] Iterative algorithm for optimal fiducials under weak perspective projectionINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2009Alfred M. Bruckstein Abstract In previous work, we designed space fiducials with the aim of making camera pose determination as noise-insensitive as possible. These fiducials turned out to be sets of points that formed concentric regular polyhedra. Here, we apply an idea of Dementhon and Davis and test and analyze an iterative linear algorithm in conjunction with our optimal fiducials to increase the accuracy of the computed camera pose. We also analyze under what circumstances this iterative algorithm is guaranteed to converge to the correct solution. Comprehensive computer simulations illustrate the behavior of the algorithm and the degree of improvement in pose determination in case of convergence. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 27,36, 2009 [source] Nanoparticles of CdCl2 with closed cage structuresISRAEL JOURNAL OF CHEMISTRY, Issue 1 2001Reshef Tenne Nanoparticles of various layered compounds having a closed cage or nanotubular structure, designated also inorganic fullerene-like (IF) materials, have been reported in the past. In this work IF -CdCl2 nanoparticles were synthesized by two methods. In one technique, a high temperature evaporation and subsequent condensation of dried cadmium chloride powder was used. In the other method, electron beam irradiation of the source powder led to its recrystallization into closed nanoparticles with a nonhollow core. The two methods are shown to produce nanoparticles of different topologies. While mostly spherical nested structures are obtained from the high temperature process, polyhedra with hexagonal or elongated rectangular characters are obtained by the electron beam induced process. The analysis also shows that, while the source (dried) powder is orthorhombic cadmium chloride monohydrate, the crystallized IF cage consists of the anhydrous 3R polytype which is not stable as bulk material in ambient atmosphere. Consistent with previous observations, this study shows that the seamless structure of the IF materials can stabilize phases, which are otherwise unstable in ambient conditions. [source] A comparative in situ Rietveld refinement study: thermal decomposition and transformation of CoAl and CoZnAl layered double hydroxidesJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2008Rune E. Johnsen Rietveld refinement based on in situ X-ray powder diffraction (XRPD) data was combined with thermogravimetric analysis (TGA) and mass spectrometry (MS) to study and compare the phase transformations, thermal stability, microstructural and structural changes of two cobalt-containing nitrate-based layered double hydroxides (LDHs) upon heating in a controlled inert atmosphere of nitrogen. The XRPD data were collected, using synchrotron X-ray radiation, with a time resolution of 107,s, which made it possible to carry out detailed structural studies of the initial layered double hydroxides as well as their decomposition products: spinel for a CoAl,NO3 LDH and spinel/zincite for a CoZnAl,NO3 LDH. Correlating these data with those from the TGA,MS analyses gives us information about the transformation mechanisms. Rietveld refinements of the two spinel phases reveal remarkable differences. The a axis of the spinel formed by decomposition of the CoAl,NO3 LDH increases almost linearly from approximately 598 to 1163,K, mainly due to the dominating thermal expansion, whereas the a axis of the spinel formed by decomposition of the CoZnAl,NO3 shows a more complex temperature dependency. Between approximately 698 and 1073,K, the a axis is almost constant due to pronounced chemical interaction with an additional amorphous phase and the zincite phase, whereas from 1073 up to 1163,K it increases linearly. Calculations, based on the results of the Rietveld refinements, of the size of the octahedral and tetrahedral coordination polyhedra in the spinel show that the octahedra shrink and the tetrahedra expand with increasing temperature. The unusual thermal behaviour of the octahedra is discussed and attributed to the low formation temperature of the cobalt aluminium spinel phase. Finally, the intensity of a low-angle scattering (LAS) signal observed in the XRPD patterns was correlated with the decomposition of the LDH, and determination of the specific surface areas gave the temperature-dependent BET surface areas. [source] FOX, `free objects for crystallography': a modular approach to ab initio structure determination from powder diffractionJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2002Vincent Favre-Nicolin A new program has been developed for ab initio crystal structure determination from powder diffraction data (X-ray and neutron). It uses global-optimization algorithms to solve the structure by performing trials in direct space. It is a modular program, capable of using several criteria for evaluating each trial configuration (e.g. multi-pattern). It is also modular in the description of the crystal content, with the possibility of describing building blocks in the sample, such as polyhedra or molecules, and with automatic adaptive handling of special positions and sharing of identical atoms between neighbouring building blocks. It can therefore find the correct structure without any assumption about the connectivity of the building blocks and is suitable for any kind of material. Several optimization algorithms (simulated annealing, parallel tempering) are available, with the possibility of choosing the convergence criterion as a combination of available cost functions. This program is freely available for Linux and Windows platforms; it is also fully `open source', which, combined with an object-oriented design and a complete developer documentation, ensures its future evolution. [source] Completion of crystal structures from powder data: the use of the coordination polyhedraJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2000Angela Altomare Direct methods applied to powder diffraction data often provide well located heavy atoms and unreliable light-atom positions. The completion of the crystal structure is then not always straightforward and may require a considerable amount of user intervention. The heavy-atom connectivity provided by the trial solution may be used to guess the nature of the coordination polyhedra. A Monte Carlo procedure is described which, in the absence of a well defined structural model, is able to locate the light atoms correctly under the restraints of the experimental heavy-atom connectivity model. The correctness of the final model is assessed by criteria based on the agreement between the whole experimental diffraction pattern and the calculated one. The procedure requires little CPU computing time and has been implemented as a routine of EXPO [Altomare et al. (1999). J. Appl. Cryst.32, 339,340]. The method has proved to be sufficiently robust against the distortion of the coordination polyhedra and has been successfully applied to some test structures. [source] A theoretical study on the structures and energetics of hypothetical TiM(NCN)3 compounds of the 3d transition metalsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2005Maxence Launay Abstract Quasi-ternary cyanamides and carbodiimides of general formula AB(NCN)3 with A , B have neither been predicted nor synthesized. Thus, hypothetical compounds of that kind containing 3d transition metals were considered (A = Ti, B = Mn, Fe, Co, Ni, Cu) by means of density-functional calculations on 34 structural models, most of which were derived from chemically related phases. After performing structure optimizations based on the local-density approximation, the relative energetic orderings are rationalized in terms of geometrical factors such as molar volumes and polyhedral connections. Total-energy generalized-gradient calculations evidence that the most stable models are enthalpically favored with respect to the elements. Even at ambient temperatures, the ternary phases are predicted as being thermodynamically stable in terms of their Gibbs free formation energies, especially if energetically competing and low-lying binaries (TiC, TiN) can be excluded by a kinetic reaction control. The best models are characterized by low-spin magnetic transition metals found in octahedral coordination, and the TiN6 and MN6 polyhedra either share faces or edges. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1180,1188, 2005 [source] Distance bound for nonconvex polyhedral models in close proximityJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue S1 2006P. Jiménez In many applications, it suffices to know a lower bound on the distance between objects, instead of the exact distance itself, which may be more difficult to compute. Such an easy-to-compute lower bound on the distance between two nonconvex polyhedra is presented here, which does not require a decomposition of the original polyhedra into convex entities. Furthermore, a suitable preprocessing of the polyhedra permits lowering the effort needed to compute this lower bound, and improves its quality. Experimental evidence is presented of the promise of this approach for assembly applications. © 2006 Wiley Periodicals, Inc. [source] Using estimated thermodynamic properties to model accessory phases: the case of tourmalineJOURNAL OF METAMORPHIC GEOLOGY, Issue 7 2007V. J. VAN HINSBERG Abstract Accessory phases and minor components in minerals are commonly ignored in thermodynamic modelling. Such an approach seems unwarranted, as accessory phases can represent a significant element reservoir and minor components can substantially change their host mineral's stability field. However, a lack of thermodynamic data prohibits assessment of these effects. In this contribution, the polyhedron method is used to estimate the thermodynamic properties of tourmaline, a common and widespread accessory phase, stable over a range of P,T,X conditions. The polyhedron method allows ,H, S, V, CP and Vm(T,P) properties to be estimated from a linear stoichiometric summation over the fractional properties of its polyhedron constituents. To allow for estimates of tourmaline, fractional thermodynamic properties for BIII and BIV 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. Evaluation of the estimated properties using experimental and natural equilibria between tourmaline and melts, minerals and hydrothermal fluids, shows that reliable semi-quantitative results are obtained. The boron contents in fluids coexisting with tourmaline are calculated to within an order of magnitude of measured content, and where anchor-points are available, agreement improves to within a factor of 2. Including tourmaline in petrogenetic modelling of metamorphic rocks indicates that its presence leads to disappearance of staurolite and garnet, among others, and modifies the XMg of coexisting phases, in line with observations on natural rocks. [source] A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra I: enthalpy, entropy and molar volumeJOURNAL OF METAMORPHIC GEOLOGY, Issue 3 2005V. J. VAN HINSBERG Abstract The thermodynamic properties of silicate minerals can be described as a linear combination of the fractional properties of their constituent polyhedra. In contrast, given the thermodynamic properties of these polyhedra, the thermodynamic properties of minerals can be estimated, where only the crystallography of the mineral needs to be known. Such estimates are especially powerful for hypothetical mineral end-members or for minerals where experimental determination of their thermodynamic properties is difficult. In this contribution the fractional enthalpy, entropy and molar volume for 35 polyhedra have been determined using weighted multiple linear regression analysis on a data set of published mineral thermodynamic properties. The large number of polyhedra determined, allows calculation of a much larger variety of phases than was previously possible and the larger set of minerals used provides more confident fractional properties. The OH-bearing minerals have been described by partial and total hydroxide coordinated components, which gives better results than previous models and precludes the need of a S,V term to improve estimates of entropy. However, the fractional thermodynamic properties only give adequate results for silicate minerals and double oxides, and should therefore not be used to estimate the properties of other minerals. The thermodynamic properties of ,new' minerals are calculated from a linear stoichiometric combination of their constituent polyhedra, resulting in estimates generally with associated uncertainty of <5%. The quality of such data appears to be of sufficient accuracy for thermodynamic modelling as shown for meta-bauxites from the Alps and the Aegean, where the effect of Zn on the P,T stability of staurolite can be both qualitatively and quantitatively reproduced. [source] Reactions leading to the formation and breakdown of stilpnomelane in the Otago Schist, New ZealandJOURNAL OF METAMORPHIC GEOLOGY, Issue 4 2000G. Li Semi-pelitic rocks ranging in grade from the prehnite,pumpellyite to the greenschist facies from south-eastern Otago, New Zealand, have been investigated in order to evaluate the reactions leading to formation and breakdown of stilpnomelane. Detrital grains of mica and chlorite along with fine-grained authigenic illite and chlorite occur in lower-grade rocks with compactional fabric parallel to bedding. At higher grades, detrital grains have undergone dissolution, and metamorphic phyllosilicates have crystallized with preferred orientation (sub)parallel to bedding, leading to slaty cleavage. Stilpnomelane is found in metapelites of the pumpellyite,actinolite facies and the chlorite zone of the greenschist facies, but only rarely in the biotite zone of the greenschist facies. Illite or phengite is ubiquitous, whereas chlorite occurs only rarely with stilpnomelane upgrade of the pumpellyite-out isograd. Chemical and textural relationships suggest that stilpnomelane formed from chlorite, phengite, quartz, K-feldspar and iron oxides. Stilpnomelane was produced by grain-boundary replacement of chlorite and by precipitation from solution, overprinting earlier textures. Some relict 14 Ĺ chlorite layers are observed by TEM to be in the process of transforming to 12 Ĺ stilpnomelane layers. The AEM analyses show that Fe is strongly partitioned over Mg into stilpnomelane relative to chlorite (KD,2.5) and into chlorite relative to phengite (KD,1.9). Modified A,FM diagrams, projected from the measured phengite composition rather than from ideal KAl3Si3O10(OH)2, are used to elucidate reactions among chlorite, stilpnomelane, phengite and biotite. In addition to pressure, temperature and bulk rock composition, the stilpnomelane-in isograd is controlled by variations in K, Fe3+/Fe2+, O/OH and H2O contents, and the locus of the isograd is expected to vary in rocks of different oxidation states and permeabilities. Biotite, quartz and less phengitic muscovite form from stilpnomelane, chlorite and phengite in the biotite zone. Projection of bulk rock compositions from phengite, NaAlO2, SiO2 and H2O reveals that they lie close to the polyhedra defined by the A,FM minerals and albite. Other extended A,FM diagrams, such as one projected from phengite, NaAlO2, CaAl2O4, SiO2 and H2O, may prove useful in the evaluation of other low-grade assemblages. [source] Raman and infrared spectroscopic study of the molybdate-containing uranyl mineral calcurmoliteJOURNAL OF RAMAN SPECTROSCOPY, Issue 7 2008Ray L. Frost Abstract Raman and infrared spectra of calcurmolite were recorded and interpreted from the uranium and molybdenum polyhedra, water molecules and hydroxyls point of view. UO bond lengths in uranyl and MoO bond lengths in MoO6 octahedra were calculated and OH,O bond lengths were inferred from the spectra. The mineral calcurmolite is characterised by bands assigned to the vibrations of the UO2 units. These units provide intense Raman bands at 930, 900 and 868 and 823 cm,1. These bands are attributed to the anti-symmetric and symmetric stretching modes of the UO2 units, respectively. Raman bands at 794, 700, 644, 378 and 354 cm,1 are attributed to vibrations of the MoO4 units. The bands at 693 and 668 cm,1 are assigned to the anti-symmetric and symmetric Ag modes of the terminal MO2 units. Similar bands are observed at 797 and 773 cm,1 for koechlinite and 798 and 775 cm,1 for lindgrenite. It is probable that some of the bands in the low wavenumber region are attributable to the bending modes of MO2 units. Copyright © 2008 John Wiley & Sons, Ltd. [source] Solid-state NMR characterization of 69Ga and 71Ga in crystalline solidsMAGNETIC RESONANCE IN CHEMISTRY, Issue 9 2006Jason T. Ash Abstract Gallium model systems containing four- and six-coordinate gallium sites have been investigated using solid-state NMR. Measurement of the isotropic chemical shift and electric field gradient (EFG) have been performed at 9.4 T on ,-Ga2O3, ,-Ga2O3, LiGaO2, NaGaO2, KGaO2, Ga2(SO4)3, and LaGaO3 using a variety of techniques on both NMR active nuclei (69Ga and 71Ga) including static, high speed magic-angle spinning (MAS), satellite transition (ST) spectroscopy, and rotor-assisted population transfer (RAPT). The chemical shift is found to correlate well with the coordination number, with four-coordinate gallium having values of approximately 50 ppm and six-coordinate gallium having values near 225 ppm (referenced to 1 M gallium nitrate solution). The magnitude of the EFG is found to be correlated to the distortion of the gallium polyhedra, with the strained systems having EFGs of 3 × 1021 Vm,2 or more, while the less strained systems have values of 1.5 × 1021 Vm,2 or less. A plot of chemical shift versus EFG suggests that solid-state NMR of gallium oxyanions can be more discriminating than liquid state NMR chemical shifts alone. Copyright © 2006 John Wiley & Sons, Ltd. [source] Ferric iron in SNC meteorites as determined by Mössbauer spectroscopy: Implications for martian landers and martian oxygen fugacityMETEORITICS & PLANETARY SCIENCE, Issue 12 2003M. Darby DYAR Also, considerable current effort is being made to understand the oxygen fugacity of martian magmas because of the effect of fO2 on mineral chemistry and crystallization processes. For these 2 reasons, the present study was conceived to acquire room temperature Mössbauer spectra of mineral separates and whole rock samples of 10 SNC meteorites. The results suggest that mineral identification using remote application of this technique will be most useful when the phases present have distinctive parameters arising from Fe in very different coordination polyhedra; for example, pyroxene coexisting with olivine can be discriminated easily, but opx versus cpx cannot. The MER goal of using Mössbauer spectroscopy to quantify the relative amounts of individual mineral species present will be difficult to satisfy if silicates are present because the lack of constraints on wt% FeO contents of individual silicate phases present will make modal calculations impossible. The remote Mössbauer spectroscopy will be most advantageous if the rocks analyzed are predominantly oxides with known stoichiometries, though these phases are not present in the SNCs. As for the detection of martian oxygen fugacity, no evidence exists in the SNC samples studied of a relationship between Fe3+ content and fO2 as calculated by independent methods. Possibly, all of the Fe3+ observed in olivine is the result of dehydrogenation rather than oxidation, and this process may also be the source of all the Fe3+ observed in pyroxene. The observed Fe3+ in pyroxene also likely records an equilibrium between pyroxene and melt at such low fO2 that little or no Fe3+ would be expected. [source] Preface: phys. stat. sol. (b) 245/3PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2008Christopher W. Smith This is the third Special Issue of physica status solidi (b) focusing on materials with a negative Poisson's ratio or other ,anomalous' physical properties. This issue contains selected papers from the First International Conference on Auxetics and Anomalous Systems held at the University of Exeter, UK, on 4,6 September 2006. Around 50 participants from all over the world as well as from a wide range of scientific and engineering disciplines contributed to what was a highly successful conference. This conference follows in the footsteps of two previous workshops held at the Mathematical Research and Conference Centre in B,dlewo near Pozna,, Poland, in 2004 and 2005 [1, 2]. The papers selected for this issue publish recent results obtained for ,anomalous systems' in experiment, theory and computer simulations. In the following we summarize very briefly their contents. Alderson and Coenen compare the performance of auxetic composites to similar systems with conventional positive Poisson's ratios. They find that there are indeed differences which appear to arise from the change of the overall Poisson's ratio of the composite, some beneficial like a rise in impact tolerance at low impact rates, and others deleterious such as the reduced tolerance at higher impact rates. This is one of the first investigations of possible applications for auxetic materials. The two papers by Gaspar and Koenders both examine the effects of disorder upon anomalous properties, especially negative Poisson's ratio. In the first one Gaspar demonstrates how a mean strain estimate fails to predict negative values of Poisson's ratio because of an inability to account for local fluctuations in elastic properties. For instance it is shown that the volume fraction of auxetic regions in an globally auxetic material (measured experimentally) are smaller than a mean strain homogenisation would require. Koenders and Gaspar explore the elastic properties, and especially Poisson's ratio, of a heterogeneous 2D network of bending beams. They predict auxetic behaviour arising from localised disorder in the packing, and therefore effective locally aggregated elastic properties of the beams. In the three articles by Gatt et al. and Grima et al. models based on simple geometry are used to explain the behaviour of seemingly disparate systems, i.e. 2D honeycombs systems and zeolite SiO2 networks. Two papers concerning honeycombs demonstrate relationships between elastic properties and structure and the bounds for auxetic behaviour. The paper concerning the zeolite Natrolite uses numerical force field based energy minimisation methods to simulate the response of this particular zeolite to applied forces and then simplifies the predicted properties even further by considering structural units as rigid 2D polyhedra linked by flexible hinges. In a similar vein, though using a different approach and concerning a very different form of matter, Heyes shows how the heterogeneity in an assembly of particles in a liquid can affect the elastic properties of a liquid and notably the infinite frequency Poisson's ratio. Heyes uses the Molecular Dynamics approach to simulate a Lennard,Jones fluid under various pressures, notably comparing behaviour under positive and negative pressures. In their first paper Jasiukiewicz and co-authors derive elastic constants of 2D crystals for all four classes of 2D crystalline solids: hexagonal (isotropic), quadratic, rectangular, and oblique systems. In their second paper they demonstrate conditions required for auxetic behaviour of 2D crystals. Auxetic solids are further divided into those with some negative Poisson's ratios (auxetic), all negative Poisson's ratios (completely auxetic) and no negative Poisson's ratios (non-auxetic). Lakes and Wojciechowski consider counterintuitive properties of matter, like negative compressibility, negative Poisson's ratio, negative thermal expansion, negative specific heat, and negative pressure. They present and interpret experimental observations of negative bulk modulus in pre-strained foams. They propose also a constrained microscopic model which exhibits negative compressibility. Finally, they solve a very simple thermodynamic model with negative thermal expansion. Martin et al. take a long stride toward a real world application of auxetic materials with a wide ranging study starting with numerical modelling of a wingbox section to experimental testing in a wind tunnel. They show that an auxetic core in a wing box section can allow a passive aero-elastic response which can be tailored by careful design of the core so that camber, and thus drag, is reduced with increasing airspeed but without sacrificing structural integrity. Miller et al. consider another anomalous physical property, negative thermal expansivity, and its application in the form of particulate composites for amelioration of stresses arising from thermal mismatch. They show via experiments that particles with a negative coefficient of thermal expansion may be used as a composite reinforcer to reduce overall thermal expansion and behave according to the standard volume fraction based models. Narojczyk and Wojciechowski examine the effects of disorder upon the bulk elastic properties of 3D fcc soft sphere systems in terms of particle size. Systems, such as colloids, can be thought of in such terms. The study shows that higher order moments of probability distribution do not influence the bulk elastic properties much, but that lower moments such as the standard deviation of particle size influence the elastic properties greatly. The "hardness" of the particle interaction potential is also important in this context. In general, it is shown that the effect of increasing polydispersity is to increase the Poisson's ratio, except the [110] [10] directions. Scarpa and Malischewsky in their paper on Rayleigh waves in auxetic materials show how the Rayleigh wave speed is affected by the Poisson's ratio. The behaviour is complex and depends upon the homogeneity within the material, for instance slowing with decreasing Poisson's ratio in isotropic solids, but showing the reverse trend and increased sensitivity to Poisson's ratio in laminate composites. Scarpa et al. explore the buckling behaviour of auxetic tubes via three types of model, a simple beam mechanics and Eulerian buckling model, a 3D linear elastic FE model and a bespoke non-linear continuum model. The more sophisticated models provide increasing insight into the buckling behaviour though the simple beam model predicts reasonably well in the pre-buckling linear region. Some unexpected and interesting behaviour is predicted by the continuum model as the Poisson's ratio approaches the isotropic limit of ,1, including increasing sensitivity to Poisson's ratio and rapid mode jumping between integer wave numbers. The paper by Shilko et al. presents an analysis of a particular kind of friction joint, a double lap joint, and explores the effects of altering the elastic properties of one component, in particular it's Poisson's ratio. The manuscript introduces the evolution of smart materials from monolithic materials, and the classification of composites exhibiting negative Poisson's ratios. The paper then presents the case of a double lap joint and performs a sensitivity type study, via a 2D FE model, of the effects of changing the elastic properties and degree of anisotropy of one section of the model on various parameters defining the limits of functionality of the joint. The main finding is that an enhanced shear modulus, via a negative Poisson's ratio, can endow such a friction joint with superior performance. Manufacturing of auxetic materials on a commercial scale has proved to be the largest obstacle to their fuller exploitation. The paper by Simkins et al. explores one route for post processing of auxetic polymers fibres produced by a conventional melt extrusion route. Simkins et al. showed that a post process thermal annealing treatment, with carefully optimised parameters, was able to even out otherwise inhomogenous auxetic properties, and moreover improve other elastic and fracture properties often sacrificed for auxetic behaviour. We gratefully acknowledge the support given by the sponsors of the conference, namely the EPSRC of the UK and Auxetic Technologies Ltd. (UK). We also thank the Scientific Committee, the Organising Committee, and all the participants of the conference. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A special class of simple 24-vertex polyhedra and tetrahedrally coordinated structures of gas hydratesACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2010M. I. Samoylovich It is established that the eight-dimensional lattice E8 and the Mathieu group M12 determine a unique sequence of algebraic geometry constructions which define a special class of simple 24-vertex, 14-face polyhedra with four-, five- and six-edge faces. As an example, the graphs of the ten stereohedra that generate most known tetrahedrally coordinated water cages of gas hydrates have been derived a priori. A structural model is proposed for the phase transition between gas hydrate I and ice. [source] Exciton,phonon interaction and Raman spectra of [(CH3)2NH2]5Cd2CuCl11 crystalsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 11 2004V. Kapustianik Abstract Temperature evolution of the exciton,phonon interaction (EPI) in ((CH3)2NH2)5Cd2CuCl11 solid solution was studied on the basis of absorption spectroscopy data. The obtained values of effective phonon energies were compared with the data of Raman spectroscopy. It is shown that the (T) and E, parameters of Urbach's rule show the continuous anomalous change characteristic of the second-order phase transition at T1 = 176 K. The anomalous behaviour of the EPI and other spectral parameters at T0 = 310,315 K was related to the complex co-operative effect involving weakening of the hydrogen bonds and variation of the Jahn,Teller distortion of metal,halogen polyhedra with temperature. This process takes place only within the copper,chlorine sublattice and due to this would be hardly related to the usual phase transition. At the same time, the considered temperature change of the tetragonal distortion of the metal,halogen octahedra is followed by nonfulfillment of Urbach's rule in the temperature range TT0. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||||||||||||||||||||||||||