scholarly journals A structure hierarchy for silicate minerals: chain, ribbon, and tube silicates

2020 ◽  
Vol 84 (2) ◽  
pp. 165-244 ◽  
Author(s):  
Maxwell C. Day ◽  
Frank C. Hawthorne
Keyword(s):  
Repeat Unit ◽  
Structural Connectivity ◽  
The Other ◽  
Silicate Minerals ◽  
One Dimensional ◽  
Compositional Range ◽  
Repeat Units ◽  
Sheet Silicates ◽  
Sheet Silicate ◽  
Connectivity Degree

AbstractA structure hierarchy is developed for chain-, ribbon- and tube-silicate based on the connectedness of one-dimensional polymerisations of (TO4)n− tetrahedra, where T = Si4+ plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Such polymerisations are described by a geometrical repeat unit (with ng tetrahedra) and a topological repeat unit (or graph) (with nt vertices). The connectivity of the tetrahedra (vertices) in the geometrical (topological) repeat units is denoted by the expression cTr (cVr) where c is the connectivity (degree) of the tetrahedron (vertex) and r is the number of tetrahedra (vertices) of connectivity (degree) c in the repeat unit. Thus cTr = 1Tr12Tr23Tr34Tr4 (cVr = 1Vr12Vr23Vr34Vr4) represents all possible connectivities (degrees) of tetrahedra (vertices) in the geometrical (topological) repeat units of such one-dimensional polymerisations. We may generate all possible cTr (cVr) expressions for chains (graphs) with tetrahedron (vertex) connectivities (degrees) c = 1 to 4 where r = 1 to n by sequentially increasing the values of c and r, and by ranking them accordingly. The silicate (sensu lato) units of chain-, ribbon- and tube-silicate minerals are identified and associated with the relevant cTr (cVr) symbols. Following description and association with the relevant cTr (cVr) symbols of the silicate units in all chain-, ribbon- and tube-silicate minerals, the minerals are arranged into decreasing O:T ratio from 3.0 to 2.5, an arrangement that reflects their increasing structural connectivity. Considering only the silicate component, the compositional range of the chain-, ribbon- and tube-silicate minerals strongly overlaps that of the sheet-silicate minerals. Of the chain-, ribbon- and tube-silicates and sheet silicates with the same O:T ratio, some have the same cVr symbols (vertex connectivities) but the tetrahedra link to each other in different ways and are topologically different. The abundance of chain-, ribbon- and tube-silicate minerals decreases as O:T decreases from 3.0 to 2.5 whereas the abundance of sheet-silicate minerals increases from O:T = 3.0 to 2.5 and decreases again to O:T = 2.0. Some of the chain-, ribbon- and tube-silicate minerals have more than one distinct silicate unit: (1) vinogradovite, revdite, lintisite (punkaruaivite) and charoite have mixed chains, ribbons and/or tubes; (2) veblenite, yuksporite, miserite and okenite have clusters or sheets in addition to chains, ribbons and tubes. It is apparent that some chain-ribbon-tube topologies are favoured over others as of the ~450 inosilicate minerals, ~375 correspond to only four topologically unique graphs, the other ~75 minerals correspond to ~46 topologically unique graphs.

scholarly journals A structure hierarchy for silicate minerals: sheet silicates

2018 ◽  
Vol 83 (1) ◽  
pp. 3-55 ◽  
Author(s):  
Frank C. Hawthorne ◽  
Yulia A. Uvarova ◽  
Elena Sokolova
Keyword(s):  
Double Layer ◽  
Structural Connectivity ◽  
Single Layer ◽  
Common Species ◽  
Two Dimensional ◽  
Structural Units ◽  
Coordination Polyhedra ◽  
Silicate Minerals ◽  
Sheet Silicates ◽  
Sheet Silicate

AbstractThe structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerisation of coordination polyhedra of higher bond-valence. A hierarchical structural classification is developed for sheet-silicate minerals based on the connectedness of the two-dimensional polymerisations of (TO4) tetrahedra, where T = Si4+ plus As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Two-dimensional nets and oikodoméic operations are used to generate the silicate (sensu lato) structural units of single-layer, double-layer and higher-layer sheet-silicate minerals, and the interstitial complexes (cation identity, coordination number and ligancy, and the types and amounts of interstitial (H2O) groups) are recorded. Key aspects of the silicate structural unit include: (1) the type of plane net on which the sheet (or parent sheet) is based; (2) the u (up) and d (down) directions of the constituent tetrahedra relative to the plane of the sheet; (3) the planar or folded nature of the sheet; (4) the layer multiplicity of the sheet (single, double or higher); and (5) the details of the oikodoméic operations for multiple-layer sheets. Simple 3-connected plane nets (such as 63, 4.82 and 4.6.12) have the stoichiometry (T2O5)n (Si:O = 1:2.5) and are the basis of most of the common rock-forming sheet-silicate minerals as well as many less-common species. Oikodoméic operations, e.g. insertion of 2- or 4-connected vertices into 3-connected plane nets, formation of double-layer sheet-structures by (topological) reflection or rotation operations, affect the connectedness of the resulting sheets and lead to both positive and negative deviations from Si:O = 1:2.5 stoichiometry. Following description of the structural units in all sheet-silicate minerals, the minerals are arranged into decreasing Si:O ratio from 3.0 to 2.0, an arrangement that reflects their increasing structural connectivity. Considering the silicate component of minerals, the range of composition of the sheet silicates completely overlaps the compositional ranges of framework silicates and most of the chain-ribbon-tube silicates.

Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates

2015 ◽  
Vol 79 (7) ◽  
pp. 1675-1709 ◽  
Author(s):  
Frank C. Hawthorne
Keyword(s):  
Long Range ◽  
Double Layer ◽  
Generating Functions ◽  
Single Layer ◽  
Two Dimensional ◽  
Layer Silicate ◽  
Silicate Minerals ◽  
Topological Features ◽  
Sheet Silicates ◽  
Sheet Silicate

AbstractTwo-dimensional nets may be used to generate the stoichiometry and structure of single-layer and double-layer sheet-silicate minerals. Many sheet-silicate minerals are based on the 3-connected plane nets 63, 4.82, (4.6.8)2(6.82)1and (52.8)1(5.82)1, and some more complicated nets, e.g. (5.6.7)4(5.72)1(62.7)1, (4.122)2(42.12)1, (52.8)1(5.62)1(5.6.8)2(62.8)1,have one or two representative structures. Many complicated sheet-silicate minerals are based on sheets of 2-, 3- and 4-connected tetrahedra that may be developed from 3- and 4-connected plane nets by a series of oikodoméic operations on 3- or 4-connected nets that change the topologyof the parent net. There are three classes of oikodoméic operations: (1) insertion of 2- and 3-connected vertices into 3- and 4-connected plane nets; (2,3) replication of single-layer sheets by topological mirror or two-fold-rotation operators, and condensation of the resulting twosingle-layer sheets to form double-layer sheets. The topological aspects of these sheet structures may be described by functions that express stoichiometry in terms of tetrahedron connectivities (formula-generating functions) and functions that associate these formula-generating functionswith specific two-dimensional nets. Using these functions, we may generate formulae and structural arrangements of single-layer and double-layer silicate structures with specific local and long-range topological features.

scholarly journals A Mutation of the Yeast Gene Encoding PCNA Destabilizes Both Microsatellite and Minisatellite DNA Sequences

Genetics ◽  
1999 ◽  
Vol 151 (2) ◽  
pp. 511-519 ◽  
Author(s):  
Robert J Kokoska ◽  
Lela Stefanovic ◽  
Andrew B Buermeyer ◽  
R Michael Liskay ◽  
Thomas D Petes
Keyword(s):  
Dna Polymerase ◽  
Repetitive Dna ◽  
Dna Sequences ◽  
Repeat Unit ◽  
Nuclear Antigen ◽  
Temperature Sensitive ◽  
Dinucleotide Repeats ◽  
Yeast Saccharomyces Cerevisiae ◽  
Dna Polymerase Δ ◽  
Repeat Units

AbstractThe POL30 gene of the yeast Saccharomyces cerevisiae encodes the proliferating cell nuclear antigen (PCNA), a protein required for processive DNA synthesis by DNA polymerase δ and ϵ. We examined the effects of the pol30-52 mutation on the stability of microsatellite (1- to 8-bp repeat units) and minisatellite (20-bp repeat units) DNA sequences. It had previously been shown that this mutation destabilizes dinucleotide repeats 150-fold and that this effect is primarily due to defects in DNA mismatch repair. From our analysis of the effects of pol30-52 on classes of repetitive DNA with longer repeat unit lengths, we conclude that this mutation may also elevate the rate of DNA polymerase slippage. The effect of pol30-52 on tracts of repetitive DNA with large repeat unit lengths was similar, but not identical, to that observed previously for pol3-t, a temperature-sensitive mutation affecting DNA polymerase δ. Strains with both pol30-52 and pol3-t mutations grew extremely slowly and had minisatellite mutation rates considerably greater than those observed in either single mutant strain.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

scholarly journals Two New Polyiodides in the 4,4´-Bipyridinium Diiodide/Iodine System

2012 ◽  
Vol 67 (1) ◽  
pp. 5-10
Author(s):  
Guido J. Reiss ◽  
Martin van Megen
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Complex I ◽  
The Other ◽  
Cyclic Dimer ◽  
Water Molecules ◽  
Spectroscopic Methods ◽  
Halogen Bonds ◽  
One Dimensional ◽  
Hydroiodic Acid

The reaction of bipyridine with hydroiodic acid in the presence of iodine gave two new polyiodide-containing salts best described as 4,4´-bipyridinium bis(triiodide), C10H10N2[I3]2, 1, and bis(4,4´-bipyridinium) diiodide bis(triiodide) tris(diiodine) solvate dihydrate, (C10H10N2)2I2[I3]2 · 3 I2 ·2H2O, 2. Both compounds have been structurally characterized by crystallographic and spectroscopic methods (Raman and IR). Compound 1 is composed of I3 − anions forming one-dimensional polymers connected by interionic halogen bonds. These chains run along [101] with one crystallographically independent triiodide anion aligned and the other triiodide anion perpendicular to the chain direction. There are no classical hydrogen bonds present in 1. The structure of 2 consists of a complex I144− anion, 4,4´-bipyridinium dications and hydrogen-bonded water molecules in the ratio of 1 : 2 : 2. The I144− polyiodide anion is best described as an adduct of two iodide and two triiodide anions and three diiodine molecules. Two 4,4´-bipyridinium cations and two water molecules form a cyclic dimer through N-H· · ·O hydrogen bonds. Only weak hydrogen bonding is found between these cyclic dimers and the polyiodide anions.

scholarly journals The use of fractional calculus for the optimal placement of electronic components on a linear array

2015 ◽  
Vol 28 (1) ◽  
pp. 77-84
Author(s):  
Mey de ◽  
Mariusz Felczak ◽  
Bogusław Więcek
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Forced Convection ◽  
Linear Array ◽  
The Other ◽  
Simple Solution ◽  
Optimal Placement ◽  
Critical Component ◽  
Electronic Components ◽  
One Dimensional

Cooling of heat dissipating components has become an important topic in the last decades. Sometimes a simple solution is possible, such as placing the critical component closer to the fan outlet. On the other hand this component will heat the air which has to cool the other components further away from the fan outlet. If a substrate bearing a one dimensional array of heat dissipating components, is cooled by forced convection only, an integral equation relating temperature and power is obtained. The forced convection will be modelled by a simple analytical wake function. It will be demonstrated that the integral equation can be solved analytically using fractional calculus.

(1R*,5R*,7R*,8S*)-3-(3,4-Dihydroxybenzoyl)-4-hydroxy-8-methyl-1,5,7-tris(3-methyl-2-butenyl)-8-(4-methyl-3-pentenyl)bicyclo[3.3.1]non-3-ene-2,9-dione

2007 ◽  
Vol 63 (3) ◽  
pp. o1282-o1284 ◽  
Author(s):  
Bruno Ndjakou Lenta ◽  
Diderot Tchamo Noungoue ◽  
Krishna Prasad Devkota ◽  
Patrice Aime Fokou ◽  
Silvere Ngouela ◽  
...  
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Medicinal Plant ◽  
Chair Conformation ◽  
The Other ◽  
Aryl Group ◽  
One Dimensional ◽  
Compound C ◽  
Bicyclic System ◽  
Symphonia Globulifera

The title compound, C38H50O6, also known as guttiferone A, was isolated from the medicinal plant Symphonia globulifera. It is a benzophenone derivative where one aryl group is derivatized to give a bicyclic system which has two prenyl groups attached to the bridgehead. One of the cyclohexane rings in the bicyclic system is in a chair form, while the other has a distorted half-chair conformation. In addition to an intramolecular O—H...O hydrogen bond, intermolecular O—H...O hydrogen bonds link molecules into one-dimensional chains.

A novel one-dimensional CoIIcoordination polymer:catena-poly[[hexaaquacobalt(II)] [[diaquabis(sulfato-κO)cobalt(II)]-μ-4,4′-bipyridine-κ2N:N′] [[triaqua(sulfato-κO)cobalt(II)]-μ-4,4′-bipyridine-κ2N:N′]]

2012 ◽  
Vol 68 (9) ◽  
pp. m265-m268 ◽  
Author(s):  
Kai-Long Zhong ◽  
Ming-Yi Qian
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
The Other ◽  
Water Molecules ◽  
Supramolecular Network ◽  
Sulfate Ion ◽  
Sulfate Ions ◽  
One Dimensional ◽  
The Third ◽  
Hydrogen Bonding Interactions

The title compound, {[Co(H2O)6][Co(SO4)(C10H8N2)(H2O)3][Co(SO4)2(C10H8N2)(H2O)2]}n, contains three crystallographically unique CoIIcentres, all of which are in six-coordinated environments. One CoIIcentre is coordinated by two bridging 4,4′-bipyridine (4,4′-bipy) ligands, one sulfate ion and three aqua ligands. The second CoIIcentre is surrounded by two N atoms of two 4,4′-bipy ligands and four O atoms,i.e.two O atoms from two monodentate sulfate ions and two from water molecules. The third CoIIcentre forms part of a hexaaquacobalt(II) ion. In the crystal structure, there are two different one-dimensional chains, one being anionic and the other neutral, and adjacent chains are arranged in a cross-like fashion around the mid-point of the 4,4′-bipy ligands. The structure features O—H...O hydrogen-bonding interactions between sulfate anions and water molecules, resulting in a three-dimensional supramolecular network.

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