scholarly journals Structural derivation and crystal chemistry of apatites

2003 ◽  
Vol 59 (1) ◽  
pp. 1-16 ◽  
Author(s):  
T. J. White ◽  
Dong ZhiLi
Keyword(s):  
Twist Angle ◽  
Charge Compensation ◽  
Cation Ordering ◽  
High Symmetry ◽  
Simple Relationship ◽  
Charge Balance ◽  
Space Groups ◽  
Average Ionic Radius ◽  
Cation Substitutions ◽  
Related Compounds

The crystal structures of the [A(1)2][A(2)3](BO4)3 X apatites and the related compounds [A(1)2][A(2)3](BO5)3 X and [A(1)2][A(2)3](BO3)3 X are collated and reviewed. The structural aristotype for this family is Mn5Si3 (D88 type, P63/mcm symmetry), whose cation array approximates that of all derivatives and from which related structures arise through the systematic insertion of anions into tetrahedral, triangular or linear interstices. The construction of a hierarchy of space-groups leads to three apatite families whose high-symmetry members are P63/m, Cmcm and P63 cm. Alternatively, systematic crystallographic changes in apatite solid-solution series may be practically described as deviations from regular anion nets, with particular focus on the O(1)—A(1)—O(2) twist angle φ projected on (001) of the A(1)O6 metaprism. For apatites that contain the same A cation, it is shown that φ decreases linearly as a function of increasing average ionic radius of the formula unit. Large deviations from this simple relationship may indicate departures from P63/m symmetry or cation ordering. The inclusion of A(1)O6 metaprisms in structure drawings is useful for comparing apatites and condensed-apatites such as Sr5(BO3)3Br. The most common symmetry for the 74 chemically distinct [A(1)2][A(2)3](BO4)3 X apatites that were surveyed was P63/m (57%), with progressively more complex chemistries adopting P63 (21%), P\bar 3 (9%), P\bar 6 (4.3%), P21/m (4.3%) and P21 (4.3%). In chemically complex apatites, charge balance is usually maintained through charge-coupled cation substitutions, or through appropriate mixing of monovalent and divalent X anions or X-site vacancies. More rarely, charge compensation is achieved through insertion/removal of oxygen to produce BO5 square pyramidal units (as in ReO5) or BO3 triangular coordination (as in AsO3). Polysomatism arises through the ordered filling of [001] BO4 tetrahedral strings to generate the apatite–nasonite family of structures.

Topotactic replacement of augite by omphacite in a blueschist rock from north-west Turkey

1978 ◽  
Vol 42 (324) ◽  
pp. 435-438 ◽  
Author(s):  
M. A. Carpenter ◽  
A. Okay
Keyword(s):  
Fluid Phase ◽  
Partial Replacement ◽  
Cation Ordering ◽  
North West ◽  
Space Groups ◽  
Transmission Electron ◽  
Ordering Schemes ◽  
Antiphase Domains ◽  
The Relationship ◽  
Symmetry Change

SummaryPartial replacement of original igneous augite crystals by omphacite during blueschist metamorphism of a dolerite from the Mihalliççik area of north-west Turkey has been studied by transmission electron microscopy. The replacement occurred topotactically, apparently by ion exchange with a fluid phase, which left the basic pyroxene structure unchanged. Cation ordering in the omphacite caused a symmetry change fromC-face centred to primitive with the formation of fine-scale antiphase domains. Selected-area diffraction provides evidence forP2andP2/cspace groups for the ordered omphacite though the best ordered areas show a tendency towardsP2/n(reflections violating then-glide are very weak) and also contain fine, wavy, disordered precipitates approximately parallel to (too).It is suggested that the replacement temperature was below the cation-ordering temperature and that the omphacite grew in a metastable, disordered state. Subsequent ordering occurred under irreversible conditions via a series of intermediate structures. The ordering sequence may illustrate the relationship between different ordering schemes in other blueschist pyroxenes.

A tangent formula derived from Patterson-function arguments. VI. structure solution from powder patterns with systematic overlap

1999 ◽  
Vol 32 (1) ◽  
pp. 89-97 ◽  
Author(s):  
Jordi Rius ◽  
Carles Miravitlles ◽  
Hermann Gies ◽  
Josep M. Amigó
Keyword(s):  
Hexagonal Lattice ◽  
Direct Methods ◽  
High Alumina ◽  
High Symmetry ◽  
Powder Diffraction Data ◽  
Patterson Function ◽  
Space Groups ◽  
Peak Overlap ◽  
Structure Solution ◽  
Alumino Silicate

Besides accidental peak overlap, systematic overlap constitutes one of the principal limitations for the solution of crystal structures from powder diffraction data. Unlike accidental overlap which affects all types of structures, systematic overlap is restricted to high-symmetry structures (e.g.65% of the space groups compatible with a hexagonal lattice). In this work, the direct-methods sum function is adapted to cope with data extracted from patterns containing systematic overlap. Preliminary results indicate that at least for moderate-size inorganic structures, systematic overlap should not represent a serious drawback for the application of direct methods. In contrast to the usual two-stage procedures employed for solving structures with accidental overlap, here both multiplet decomposition and phase refinement are carried out simultaneously. This procedure is illustrated using two examples: the dominant crystalline phase of a hydrated high-alumina cement and the fibrous alumino-silicate `aerinite'.

scholarly journals The crystal chemistry of holtite

2009 ◽  
Vol 73 (6) ◽  
pp. 1033-1050 ◽  
Author(s):  
L. A. Groat ◽  
E. S. Grew ◽  
R. J. Evans ◽  
A. Pieczka ◽  
T. S. Ercit
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Distinct Species ◽  
Cation Ordering ◽  
Charge Balance ◽  
Crystallographic Site ◽  
Alluvial Deposits ◽  
X Ray ◽  
Three Samples ◽  
Lower Silesia

AbstractHoltite, approximately (Al,Ta,□)Al6(BO3)(Si,Sb3+,As3+)Σ3O12(O,OH,□s)Σ3, is a member of the dumortierite group that has been found in pegmatite, or alluvial deposits derived from pegmatite, at three localities: Greenbushes, Western Australia; Voron'i Tundry, Kola Peninsula, Russia; and Szklary. Lower Silesia, Poland. Holtite can contain >30 wt.% Sb2O3, As2O3, Ta2O5, Nb2O5, and TiO2 (taken together), but none of these constituents is dominant at a crystallographic site, which raises the question whether this mineral is distinct from dumortierite. The crystal structures of four samples from the three localities have been refined to R1 = 0.02—0.05. The results show dominantly: Al, Ta, and vacancies at the Al(l) position; Al and vacancies at the Al(2), (3) and (4) sites; Si and vacancies at the Si positions; and Sb, As and vacancies at the Sb sites for both Sb-poor (holtite I) and Sb-rich (holtite II) specimens. Although charge-balance calculations based on our single-crystal structure refinements suggest that essentially no water is present, Fourier transform infrared spectra confirm that some OH is present in the three samples that could be measured. By analogy with dumortierite, the largest peak at 3505-3490 cm-1 is identified with OH at the O(2) and O(7) positions. The single-crystal X-ray refinements and FTIR results suggest the following general formula for holtite: Al7-[5x+y+z]/3 (Ta,Nb)x□[2x+y+z]\3,BSi3-y(Sb,As)yO18-y-z(OH)z, where x is the total number of pentavalent cations, y is the total amount of Sb + As, and z ⩽ y is the total amount of OH. Comparison with the electron microprobe compositions suggests the following approximate general formulae Al5.83(Ta,Nb)0.50□0.67BSi2.50(Sb,As)0.50O17.00(OH)0.50 and Al5.92(Ta,Nb)0.25□0.83BSi2.00(Sb,As)1.00O16.00(OH)1.00 for holtite I and holtite II respectively. However, the crystal structure refinements do not indicate a fundamental difference in cation ordering that might serve as a criterion for recognizing the two holtites as distinct species, and anion compositions are also not sufficiently different. Moreover, available analyses suggest the possibility of a continuum in the Si/(Sb + As) ratio between holtite I and dumortierite, and at least a partial continuum between holtite I and holtite II. We recommend that use of the terms holtite I and holtite II be discontinued.

A hydrogen-bonded tetramer in (2RS,4SR)-7-bromo-2-(2-methylphenyl)-2,3,4,5-tetrahydro-1H-naphtho[1,2-b]azepin-4-ol and a three-dimensional hydrogen-bonded framework in (2RS,4SR)-2-(3-methylthiophen-2-yl)-2,3,4,5-tetrahydro-1H-naphtho[1,2-b]azepin-4-ol

2013 ◽  
Vol 69 (4) ◽  
pp. 448-452 ◽  
Author(s):  
Andrés F. Yépes ◽  
Alirio Palma ◽  
Justo Cobo ◽  
Christopher Glidewell
Keyword(s):  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Space Groups ◽  
Dimensional Array ◽  
Compound Ii ◽  
Related Compounds ◽  
Hydrogen Bonded

(2RS,4SR)-7-Bromo-2-(2-methylphenyl)-2,3,4,5-tetrahydro-1H-naphtho[1,2-b]azepin-4-ol, C21H20BrNO, (I), and (2RS,4SR)-2-(3-methylthiophen-2-yl)-2,3,4,5-tetrahydro-1H-naphtho[1,2-b]azepin-4-ol, C19H19NOS, (II), both crystallize withZ′ = 2 in the space groupsP21/candCc, respectively; compound (II) crystallizes as a nonmerohedral twin, with twin fractions 0.183 (2) and 0.817 (2). The molecules of (I) are linked by O—H...O and O—H...N hydrogen bonds to form a cyclic centrosymmetricR44(16) tetramer. The molecules of (II) are linked by O—H...O hydrogen bonds to form aC22(4) chain and these chains are weakly linked by a single C—H...π(thienyl) interaction to form a three-dimensional array. Comparisons are made with some related compounds.

Anisotropic thermal expansion of Lan(Ti,Fe)nO3n+ 2(n= 5 and 6)

2013 ◽  
Vol 69 (2) ◽  
pp. 137-144 ◽  
Author(s):  
Alexander Wölfel ◽  
Philipp Dorscht ◽  
Frank Lichtenberg ◽  
Sander van Smaalen
Keyword(s):  
Thermal Expansion ◽  
Crystal Structures ◽  
Structural Phase ◽  
Weighted Average ◽  
Charge Compensation ◽  
Layered Compounds ◽  
Direction Parallel ◽  
Chemical Order ◽  
Different Temperatures ◽  
Related Compounds

Crystal structures are reported for two perovskite-related compounds with nominal compositions La5(Ti0.8Fe0.2)5O17and La6(Ti0.67Fe0.33)6O20at seven different temperatures between 90 and 350 K. For both compounds no evidence of a structural phase transition in the investigated range of temperatures was found. The thermal expansions are found to be anisotropic, with the largest thermal expansion along a direction parallel to the slabs of these layered compounds. The origin of this anisotropy is proposed to be a temperature dependence of tilts of the octahedral (Ti,Fe)O6groups. It is likely that the same mechanism will determine similar anisotropic thermal behaviour of other compoundsAnBnO3n + 2. The crystal structures have revealed partial chemical order of Ti/Fe over theBsites, with iron concentrated towards the centers of the slabs. Local charge compensation is proposed as the driving force for the chemical order, where the highest-valent cation moves to sites near the oxygen-rich borders of the slabs. A linear dependence on the site occupation fraction by Fe of the computed valences leads to extrapolated valence values close to the formal valence of Ti4+for sites fully occupied by Ti, and of Fe3+for sites fully occupied by Fe. These results demonstrate the power of the bond-valence method, and they show that refined oxygen positions are the weighted average of oxygen positions in TiO6and FeO6octahedral groups.

scholarly journals Diamagnetic anisotrophy of crystals in relation to their molecular structure

1936 ◽  
Vol 156 (889) ◽  
pp. 597-613 ◽  
Keyword(s):  
Single Molecule ◽  
Difficult Problem ◽  
High Symmetry ◽  
Simple Relationship ◽  
Trial And Error ◽  
Intensive Study ◽  
Mathematical Relationship ◽  
X Ray ◽  
Triclinic System ◽  
Structure Of Molecular Crystals

In order to determine the fine structure of molecular crystals by means of a Fourier analysis of X-ray data, it is usually necessary that the configuration and orientation of the molecules should be known with considerable accuracy. Only in a few cases can this information be obtained directly from the X-ray data. Typical examples of crystals for which this has been done are hexamethylbenzene and cyanuric triazide, both layer lattice structures, and hexamethylene tetramine in the crystal of which the molecule itself possesses high symmetry. In other cases, e. g ., anthracene, naphthalene, etc., the “trial and error” structure has been obtained by an intensive study of the X-ray data, a difficult problem involving much expenditure of time and trouble. Any independent physical methods which indicate the approximate orientation of the molecules in the crystals are therefore greatly to be welcomed. Krishnan and his collaborators, in a series of recent papers, have emphasized the fact that a knowledge of the optical and diamagnetic anisotrophy of the crystal may, in favourable cases, give very direct information concerning the shape and orientation of the molecules. They point out also that, given the diamagnetic anisotrophy of the crystal and the accurate orientation of the molecules in the crystal, the principal diamagnetic susceptibilities of a single molecule can be directly calculated. It is important, therefore, that the exact mathematical relationship between the crystal and molecular diamagnetic susceptibilities and the molecular orientations relative to the crystal axes should be correctly formulated. Triclinic System The triclinic system is in one sense the most complicated and in another the simplest of all the classes. The directions of the three principal diamagnetic susceptibilities, x 1 , x 2 , x 3 , do not bear any simple relationship to the crystal axes and must therefore be located by experimental investigation; but, on the other hand, since the unit cell contains but one or perhaps two molecules centrosymmetrically arranged, the connexion between molecular and crystal anisotrophy is a very simple one.

Symmetry analysis of the behavior of the family R6M23 compounds upon hydrogenation

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Agnieszka Kuna ◽  
Wiesława Sikora
Keyword(s):  
Magnetic Moments ◽  
Structural Transformations ◽  
Elementary Cell ◽  
Symmetry Analysis ◽  
Crystallographic Structure ◽  
High Symmetry ◽  
Space Groups ◽  
The Family ◽  
Hydrogen Deuterium ◽  
Free Parameters

AbstractSymmetry analysis was applied in this work to discuss the behavior of the family R6M23 compounds upon hydrogenation (deuteration), where different structural transformations and magnetic properties, depending on the type of R and M atoms and hydrogen (deuterium) concentrations, have been found. The crystallographic structure of these compounds is described by the Fm3m space group and contain 116 atoms per unit cell occupying the positions 24e(R), 4b, 24d, 32f1 and 32f2(M). Additionally in the elementary cell, there could be up to 100 atoms of hydrogen (or deuterium) occupying the interstitial positions 4a, 32f3, 96j1 and 96k1. The symmetry analysis in the frame of the theory of space groups and their representation gives the opportunity to find all possible transformations from high symmetry parent structure to the structures with symmetry belonging to one of its subgroups. For a given transformation it indicates possible displacements of atoms from initial positions in the parent structure, ordering of hydrogen over interstitial sites and also ordering of magnetic moments, described by the smallest possible number of free parameters. The analysis was carried out by means of the MODY computer program for vectors k = (0; 0; 0) and k = (0; 0; 1) describing the changes of translational symmetry and all positions occupied by the R, M and D atoms.

scholarly journals Voltage‐extrapolative charge balance controller with charge compensation for flyback converter operating in DCM

2019 ◽  
Vol 12 (11) ◽  
pp. 2713-2721 ◽  
Author(s):  
Xiaofeng Zhang ◽  
Run Min ◽  
Bin Ji ◽  
Donglai Zhang ◽  
Yi Wang ◽  
...  
Keyword(s):  
Charge Compensation ◽  
Charge Balance ◽  
Flyback Converter

scholarly journals Three closely related 4,5,6,7-tetrahydro-1H-pyrazolo[4,3-c]pyridines: synthesis, molecular conformations and hydrogen bonding in zero, one and two dimensions

2017 ◽  
Vol 73 (3) ◽  
pp. 298-304
Author(s):  
Belakavadi K. Sagar ◽  
Kachigere B. Harsha ◽  
Hemmige S. Yathirajan ◽  
Kanchugarakoppal S. Rangappa ◽  
Ravindranath S. Rathore ◽  
...  
Keyword(s):  
Hydrogen Bonds ◽  
Pyridine Ring ◽  
Chair Conformation ◽  
Two Dimensions ◽  
Relative Orientation ◽  
Molecular Conformations ◽  
Space Groups ◽  
Related Compounds ◽  
Trifluoromethyl Groups ◽  
Centrosymmetric Dimers

In each of 1-(4-fluorophenyl)-5-methylsulfonyl-3-[4-(trifluoromethyl)phenyl]-4,5,6,7-tetrahydro-1H-pyrazolo[4,3-c]pyridine, C21H19F4N3O2S, (I), 1-(4-chlorophenyl)-5-methylsulfonyl-3-[4-(trifluoromethyl)phenyl]-4,5,6,7-tetrahydro-1H-pyrazolo[4,3-c]pyridine, C21H19ClF3N3O2S, (II), and 1-(3-methylphenyl)-5-methylsulfonyl-3-[4-(trifluoromethyl)phenyl]-4,5,6,7-tetrahydro-1H-pyrazolo[4,3-c]pyridine, C22H22F3N3O2S, (III), the reduced pyridine ring adopts a half-chair conformation with the methylsulfonyl substituent occupying an equatorial site. Although compounds (I) and (II) are not isostructural, having the space groups Pbca and P212121, respectively, their molecular conformations are very similar, but the conformation of compound (III) differs from those of (I) and (II) in the relative orientation of the N-benzyl and methylsulfonyl substituents. In compounds (II) and (III), but not in (I), the trifluoromethyl groups are disordered over two sets of atomic sites. Molecules of (I) are linked into centrosymmetric dimers by C—H...π(arene) hydrogen bonds, molecules of (II) are linked by two C—H...O hydrogen bonds to form ribbons of R 3 3(18) rings, which are themselves further linked by a C—Cl...π(arene) interaction, and a combination of C—H...O and C—H...π(arene) hydrogen bonds links the molecules of (III) into sheets. Comparisons are made with the structures of some related compounds.

Symmetry and space Groups

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Fundamental Property ◽  
Natural World ◽  
Symmetry Operation ◽  
Bravais Lattice ◽  
High Symmetry ◽  
Space Group ◽  
Space Groups ◽  
The Difference ◽  
Symmetry Operations ◽  
The Way

A certain degree of symmetry is apparent in much of the natural world, as well as in many of our creations in art, architecture, and technology. Objects with high symmetry are generally regarded with pleasure. Symmetry is perhaps the most fundamental property of the crystalline state and is a reason that gemstones have been so appreciated throughout the ages. This chapter introduces some of the fundamental concepts of symmetry—symmetry operations, symmetry elements, and the combinations of these characteristics of finite objects (point symmetry) and infinite objects (space symmetry)—as well as the way these concepts are applied in the study of crystals. An object is said to be symmetrical if after some movement, real or imagined, it is or would be indistinguishable (in appearance and other discernible properties) from the way it was initially. The movement, which might be, for example, a rotation about some fixed axis or a mirror-like reflection through some plane or a translation of the entire object in a given direction, is called a symmetry operation. The geometrical entity with respect to which the symmetry operation is performed, an axis or a plane in the examples cited, is called a symmetry element. Symmetry operations are actions that can be carried out, while symmetry elements are descriptions of possible symmetry operations. The difference between these two symmetry terms is important. It is possible not only to determine the crystal system of a given crystalline specimen by analysis of the intensities of the Bragg reflections in the diffraction pattern of the crystal, but also to learn much more about its symmetry, including its Bravais lattice and the probable space group. As indicated in Chapter 2, the 230 space groups represent the distinct ways of arranging identical objects on one of the 14 Bravais lattices by the use of certain symmetry operations to be described below. The determination of the space group of a crystal is important because it may reveal some symmetry within the contents of the unit cell.

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