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 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 Density functional study of Li/Na adsorption properties of single-layer and double-layer antimonenes

RSC Advances ◽  
2019 ◽  
Vol 9 (56) ◽  
pp. 32608-32619
Author(s):  
Huilan Wei ◽  
Jianping Sun ◽  
Yifan Hu ◽  
Zhao Li ◽  
Mei Ai
Keyword(s):  
Double Layer ◽  
Density Functional ◽  
Single Layer ◽  
Adsorption Properties ◽  
Functional Study ◽  
Two Dimensional ◽  
Density Functional Study

β-Antimonene, a stable two-dimensional material, has been successfully prepared recently.

scholarly journals Connectivity and formula-generating functions for sheet-silicate minerals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1089-C1089
Author(s):  
Frank Hawthorne
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Unit Cell ◽  
Two Dimensional ◽  
Silicate Minerals ◽  
Topological Features ◽  
Unit Cells ◽  
Sheet Silicate ◽  
Symmetry Operations

Silicate sheets may be described by two-dimensional nets in which the vertices of the net are occupied by tetrahedra, and the edges of the net represent linkages between tetrahedra. A plane net must contain 3-connected vertices, but not all vertices need to be 3-connected. Simple silicate structures may thus be generated from simple 3-connected plane nets (e.g. 63, 4.82, 4.6.8, (4.6.8)2(6.82)1, etc.). More complicated silicate nets may be generated by various "building operations": (1) Insertion: insertion of 2- and 4-connected vertices into 3-connected plane nets; (2) Repetition: generation of double (or triple) nets by topological symmetry operations that retain transitivity at the junction between the repeated elements. Diversity is also introduced within the sheets of tetrahedra by [1] adjacent apical tetrahedron vertices pointing in the same or different directions, and [2] by folding of the sheets. For simple structures, net type strongly affects the stoichiometry of the resultant structure as the unit cells of the various nets are of different sizes (and shapes), although the stoichiometry may also be affected by non-tetrahedral components. Building operations strongly affect the stoichiometry of the resultant sheet, and this effect may be quantified. We define a formula-generating function F(k,l,...) that generates the formula of a sheet with specific topological features denoted by the indices k,l,... . A simple 3-connected net results in sheets of the form (T2O5)n where n denotes the number of (T2O5)n in the unit cell of the underlying net (for 63, n = 1; for 4.82, n = 2; for (4.6.8)2(6.82)1, n = 3, etc). Plane nets with k 3-connected vertices and l inserted 2-connected vertices result in sheets of the form [T(k+l) O(2.5k+3l)], where (...) are subscripted. Single- and double-sheet structures may be generated from the function F(k,l) = T(N{k+l}) O(N{3k+2.5l}-n{N-1}) where N = 1 and 2 for single- and double-sheets, respectively, and (...) are subscripted.

Cracking at the fold in double layer coated paper: the influence of latex and starch composition

TAPPI Journal ◽  
2019 ◽  
Vol 18 (2) ◽  
pp. 93-99
Author(s):  
SEYYED MOHAMMAD HASHEMI NAJAFI ◽  
DOUGLAS BOUSFIELD, ◽  
MEHDI TAJVIDI
Keyword(s):  
Mechanical Properties ◽  
Double Layer ◽  
Starch Content ◽  
Single Layer ◽  
Double Layers ◽  
Coated Paper ◽  
Coated Papers ◽  
Coating Layers ◽  
Scanned Images ◽  
Packaging Paper

Cracking at the fold of publication and packaging paper grades is a serious problem that can lead to rejection of product. Recent work has revealed some basic mechanisms and the influence of various parameters on the extent of crack area, but no studies are reported using coating layers with known mechanical properties, especially for double-coated systems. In this study, coating layers with different and known mechanical properties were used to characterize crack formation during folding. The coating formulations were applied on two different basis weight papers, and the coated papers were folded. The binder systems in these formulations were different combinations of a styrene-butadiene latex and mixtures of latex and starch for two different pigment volume concentrations (PVC). Both types of papers were coated with single and double layers. The folded area was scanned with a high-resolution scanner while the samples were kept at their folded angle. The scanned images were analyzed within a constant area. The crack areas were reported for different types of papers, binder system and PVC values. As PVC, starch content, and paper basis weight increased, the crack area increased. Double layer coated papers with high PVC and high starch content at the top layer had more cracks in comparison with a single layer coated paper, but when the PVC of the top layer was low, cracking area decreased. No measurable cracking was observed when the top layer was formulated with a 100% latex layer.

Single layer versus double layer suture for anastomosis of the gastrointestinal tract

2009 ◽  
Author(s):  
Alvaro Sanabria ◽  
Gabriel Gomez ◽  
Eduardo Valdivieso ◽  
C Bermudez
Keyword(s):  
Gastrointestinal Tract ◽  
Double Layer ◽  
Single Layer ◽  
Layer Versus

Single layer versus double layer suture for anastomosis of the gastrointestinal tract

2005 ◽  
Author(s):  
Alvaro Sanabria ◽  
Gabriel Gomez ◽  
Eduardo Valdivieso ◽  
C Bermudez
Keyword(s):  
Gastrointestinal Tract ◽  
Double Layer ◽  
Single Layer ◽  
Layer Versus

scholarly journals Homogeneous 2D and 3D alignment of cardiomyocyte in dilated cardiomyopathy revealed by intravital heart imaging

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kiyoshi Masuyama ◽  
Tomoaki Higo ◽  
Jong-Kook Lee ◽  
Ryohei Matsuura ◽  
Ian Jones ◽  
...  
Keyword(s):  
Heart Failure ◽  
Dilated Cardiomyopathy ◽  
Cardiac Dysfunction ◽  
Three Dimensional ◽  
Single Layer ◽  
Specific Pattern ◽  
Two Dimensional ◽  
Heart Imaging ◽  
Novel Method ◽  
2D And 3D

AbstractIn contrast to hypertrophic cardiomyopathy, there has been reported no specific pattern of cardiomyocyte array in dilated cardiomyopathy (DCM), partially because lack of alignment assessment in a three-dimensional (3D) manner. Here we have established a novel method to evaluate cardiomyocyte alignment in 3D using intravital heart imaging and demonstrated homogeneous alignment in DCM mice. Whilst cardiomyocytes of control mice changed their alignment by every layer in 3D and position twistedly even in a single layer, termed myocyte twist, cardiomyocytes of DCM mice aligned homogeneously both in two-dimensional (2D) and in 3D and lost myocyte twist. Manipulation of cultured cardiomyocyte toward homogeneously aligned increased their contractility, suggesting that homogeneous alignment in DCM mice is due to a sort of alignment remodelling as a way to compensate cardiac dysfunction. Our findings provide the first intravital evidence of cardiomyocyte alignment and will bring new insights into understanding the mechanism of heart failure.

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