scholarly journals The structure of α and β quartz

1925 ◽  
Vol 109 (751) ◽  
pp. 405-427 ◽  
Keyword(s):  
Crystal Structure ◽  
Spatial Relations ◽  
Unit Cell ◽  
Trigonal Axis ◽  
X Rays ◽  
Screw Axis ◽  
X Ray ◽  
Black Disc ◽  
Exact Position ◽  
Group D

The quartz crystal has a trigonal axis and three digonal axes, which are at right angles to the trigonal axis. It has no other element of symmetry. It belongs to Class 18 of the 32 classes into which crystals may be divided by their outside appearance. It was shown in 1913, by the methods of X-ray analysis, which were then new, that the unit cell contains three molecules of SiO 2 , which are so arranged that a revolution of 120° round the principal axis, coupled with a translation c /3 along it, brings each molecule into the exact position previously occupied by one of its companions. The trigonal axis is in fact a screw axis. The value of c is 5·375 A. U. The distance between an axis and each of its six equidistant neighbours is 4·89 A. U. Each silicon molecule possesses a digonal axis. This particular arrangement of molecules is known in mathematical crystallography as that of the space-group D 4 3 or D 6 3 , according to the rotatory sense of the lattice. At this stage of the work four parameters, still remained to be determined before the positions of the atoms in the crystal structure could be defined. The position will be clear from a consideration of fig. 1, which is reproduced from ‘X-rays and Crystal Structure,’ p. 261. Each of the two diagrams in the figure shows the relation between three molecules, forming the content of the unit cell, and derivable from each other in the manner described. In one, the screw axis is in the plane of the paper, in the other at right angles to it. The digonal axes are also shown. The distance of the silicon (black disc) from the axis is one of the unknowns: the spatial relations of the oxygens to the silicons require for their definition three more. The diagram of fig. 2 shows various possible positions of the silicon atoms when projected upon the basal plane. They must lie on certain lines, as shown, in order to satisfy the symmetry conditions.

scholarly journals VI. Tabulated data for the examination of the 230 space-groups by homogeneous X-rays

1924 ◽  
Vol 224 (616-625) ◽  
pp. 221-257 ◽  
Keyword(s):  
Crystal Structures ◽  
Chemical Society ◽  
Unit Cell ◽  
X Rays ◽  
Screw Axis ◽  
Monoclinic System ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Relative Arrangement

The object of the present paper is to express the conclusions of mathematical crystallography in a form which shall be immediately useful to workers using homogeneous X-rays for the analysis of crystal structures. The results are directly applicable to such methods as the Bragg ionisation method, the powder method, the rotating crystal method, etc., and summarise in as compact a form as possible what inferences may be made from the experimental observations, whichever one of the 230 possible space-groups may happen to be under examination. It is only in certain cases that the spacings of crystal planes as determined by the aid of homogeneous X-rays agree with the values of those spacings which would be expected from ordinary crystallographic calculations. In the majority of cases the relative arrangement of the molecules in the unit cell leads to apparent anomalies in the experimental results, the observed spacings of certain planes or sets of planes being sub-multiples of the calculated spacings. The simplest case (fig. 8) of such an apparent anomaly is found in the space-group C 2 2 of the monoclinic system, where the presence of a two-fold screw-axis, because it interleaves halfway the (010) planes by molecules which are exactly like those lying in the (010) planes, except that they have been rotated through 180°, leads to an observed periodicity which is half the periodicity to be inferred from the dimensions of the unit cell, that is, leads to an observed spacing for (010) which is half the calculated. All screw-axes produce similar results, and, in general, a p -fold screw-axis leads to an observed spacing for the plane perpendicular to it which is 1/ p th that to be inferred from the dimensions of the cell. Besides those produced by the screw-axes, other abnormalities arise out of the presence of glide-planes. The simplest case of this is shown by the space-group C s 2 (fig. 4) of the monoclinic system, in which the second molecule is obtained from the first by a reflection in a plane parallel to (010) and half a primitive translation parallel to that plane. If we look along a direction perpendicular to this glide-plane, the projections of the two molecules on the (010) plane are indistinguishable except in position, which is equivalent to saying that, for the purposes of X-ray interference, certain planes perpendicular to this plane of projection are interleaved by an identical molecular distribution. Furthermore, since the translation associated with the glide-plane must always be half a primitive translation parallel to the glide-plane, we know that the interleaving is always a submultiple of the full spacing and the periodicity is again reduced in a corresponding manner. The use of this method for discriminating between the various space-groups of the monoclinic system was described by Sir Wm. Bragg in a lecture to the Chemical Society. In the present paper the method has been extended to the whole of the 230 space-groups possible to crystalline structures. In general, it may be said that if a crystal possesses a certain glide-plane, a certain set of planes lying in the zone whose axis is perpendicular to that glide-plane will have their periodicity reduced by one-half.

scholarly journals Molekül- und Kristallstruktur von C7H7Mo(CO)2-SnCl3 / The Crystal Structure of C7H7Mo(CO)2-SnCl3

1975 ◽  
Vol 30 (1-2) ◽  
pp. 22-25 ◽  
Author(s):  
M. L. Ziegler ◽  
H.-E. Sasse ◽  
B. Nuber
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Title Compound ◽  
Three Dimensional ◽  
Unit Cell ◽  
Fourier Methods ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Group D

The structure of the title compound has been determined from three dimensional X-ray data by Patterson and Fourier methods. The crystals are orthorombic, with unit cell dimensions a = 1181,50 pm, b = 943,68 pm, c = 1181,50 pm, space group D2h16 and Z = 4. Least squares refinement, by use of 1540 independent reflections measured on a diffractometer has reached R = 5,9%.There are discrete C7H7Mo(CO)2 SnCl3 molecules, the molybdenum-tin bond has been dicussed together with the corresponding bonds in other C7H7Mo(CO)2 SnR3 compounds.

scholarly journals The variation with temperature of the intensity of reflection of X-rays from quartz and its bearing on the crystal structure

1925 ◽  
Vol 107 (743) ◽  
pp. 561-570 ◽  
Keyword(s):  
Crystal Structure ◽  
Unit Cell ◽  
Equal Weight ◽  
X Rays ◽  
Trigonal Symmetry ◽  
X Ray ◽  
Trigonal System ◽  
The Subject ◽  
Prismatic Cell

Since the appearance of Sir William Bragg’s first work on the structure of martz (these ‘Proceedings,’ A, vol. 89, p. 595 (1914)) this mineral has been the subject of many investigations. It has lent itself very well to study by the older crystallographic methods, by which, from symmetry considerations, has been placed in the trapezohedral class of the trigonal system, i. e ., it exhibits trigonal symmetry about one ( c ) axis and digonal symmetry about ree others, lying symmetrically in a plane perpendicular to the first and intersecting in it. Two enantiomorphous forms were found to exist. Investigation by the X-ray spectrometer method enabled Bragg to give the dimensions of the unit triangular prismatic cell as a = 4·89 Å. U. and = 5·375 Å. U., whilst density considerations clearly indicated that three olecules were associated with such a unit cell. It was also shown that the three molecules were associated with the unit cell in such a way that planes of equal weight occurred at o , c /3, 2 c /3, c , etc., along the vertical c axis.

Is there a non-channeling orientation?

1990 ◽  
Vol 48 (4) ◽  
pp. 412-413
Author(s):  
J. A. Eades ◽  
K. K. Christenson ◽  
M. L. Andreessen
Keyword(s):  
Crystal Structure ◽  
Electron Flux ◽  
Standard Form ◽  
Incident Beam ◽  
Unit Cell ◽  
X Rays ◽  
Host Crystal ◽  
X Ray ◽  
Incident Electron Beam ◽  
Channeling Effect

In the standard form of ALCHEMI, the aim is to calculate the fraction of an impurity that is substitutional on each different sublattice of the host crystal. The result is calculated from the ratios of the of the intensities of the x rays emitted by the elements present. The ratios vary as a function of the angle of the incident electron beam because of electron channeling in the crystal structure. The channeling has the effect of making the electron density different in different parts of the unit cell. If the x-ray yield of one element goes up, the electron yield of any other element on the same sites (i.e. the same sublattice) in the crystal structure will go up in the same proportion. This variation can be used to calculate the fraction on each site.The calculation requires the measurement of the x-ray ratios at at least one angle with a strong channeling effect but also requires the measurement of the ratios at a condition of the incident beam that is “nonchanneling”, that is when the electron flux is uniform across the unit cell.

scholarly journals Crystal Structure Refinements of Four Monazite Samples from Different Localities

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao
Keyword(s):  
Crystal Structure ◽  
Electron Probe ◽  
Unit Cell Volume ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Large Unit Cell ◽  
A Site

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β = 103.584(2)°, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β = 103.817(3)°, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.

scholarly journals X-ray crystal structure of a malonate-semialdehyde dehydrogenase fromPseudomonassp. strain AAC

2017 ◽  
Vol 73 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Matthew Wilding ◽  
Colin Scott ◽  
Thomas S. Peat ◽  
Janet Newman
Keyword(s):  
Crystal Structure ◽  
Search Model ◽  
Molecular Replacement ◽  
X Rays ◽  
X Ray Diffraction ◽  
Acetyl Coa ◽  
Space Group ◽  
X Ray ◽  
Semialdehyde Dehydrogenase

The NAD-dependent malonate-semialdehyde dehydrogenase KES23460 fromPseudomonassp. strain AAC makes up half of a bicistronic operon responsible for β-alanine catabolism to produce acetyl-CoA. The KES23460 protein has been heterologously expressed, purified and used to generate crystals suitable for X-ray diffraction studies. The crystals belonged to space groupP212121and diffracted X-rays to beyond 3 Å resolution using the microfocus beamline of the Australian Synchrotron. The structure was solved using molecular replacement, with a monomer from PDB entry 4zz7 as the search model.

NQR and Crystal Structure of 4,5-Dichloroimidazole, C3H2N2Cl2

1992 ◽  
Vol 47 (1-2) ◽  
pp. 177-181 ◽  
Author(s):  
Shi-Qi Dou ◽  
Alarich Weiss
Keyword(s):  
Crystal Structure ◽  
Phase Transition ◽  
Temperature Dependence ◽  
Room Temperature ◽  
Unit Cell ◽  
Space Group ◽  
Temperature Range ◽  
Temperature Coefficients ◽  
Group D

AbstractThe two line 35Cl NQR spectrum of 4,5-dichloroimidazole was measured in the temperature range 77≦ T/K ≦ 389. The temperature dependence of the NQR frequencies conforms with the Bayer model and no phase transition is indicated in the curves v ( 35Cl)= f(T). Also the temperature coefficients of the 35Cl NQR frequencies are "normal". At 77 K the 35Cl NQR frequencies are 37.409 MHz and 36.172 MHz and at 389 K 35.758 MHz and 34.565 MHz. The compound crystallizes at room temperature with the tetragonal space group D44-P41212, Z = 8 molecules per unit cell; at 295 K : a = 684.2(5) pm, c = 2414.0(20) pm. The relations between the crystal structure and the NQR spectrum are discussed.

scholarly journals Synchrotron Nano-Diffraction Study of Thermally Treated Asbestos Tremolite from Val d’Ala, Turin (Italy)

Minerals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 311 ◽  
Author(s):  
Carlotta Giacobbe ◽  
Jonathan Wright ◽  
Dario Di Giuseppe ◽  
Alessandro Zoboli ◽  
Mauro Zapparoli ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Heat Treatment ◽  
Risk Management ◽  
Structure Analysis ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Adverse Health Effects ◽  
Nano Crystalline ◽  
Original Fibre

Nowadays, due to the adverse health effects associated with exposure to asbestos, its removal and thermal inertization has become one of the most promising ways for reducing waste risk management. Despite all the advances in structure analysis of fibers and characterization, some problems still remain that are very hard to solve. One challenge is the structure analysis of natural micro- and nano-crystalline samples, which do not form crystals large enough for single-crystal X-ray diffraction (SC-XRD), and their analysis is often hampered by reflection overlap and the coexistence of multiple fibres linked together. In this paper, we have used nano-focused synchrotron X-rays to refine the crystal structure of a micrometric tremolite fibres from Val d’Ala, Turin (Italy) after various heat treatment. The structure of the original fibre and after heating to 800 °C show minor differences, while the fibre that was heated at 1000 °C is recrystallized into pyroxene phases and cristobalite.

scholarly journals Zur Kenntnis eines Barium-Oxoniobat-Tellurats: Ba2Nb2TeO10 / On a Barium-Oxoniobate-Tellurate: Ba2Nb2TeO10

1996 ◽  
Vol 51 (10) ◽  
pp. 1407-1410 ◽  
Author(s):  
B. Wedel ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Crystal Structure ◽  
Solid State ◽  
Single Crystals ◽  
Solid State Reactions ◽  
Orthorhombic Symmetry ◽  
X Ray ◽  
Lattice Constants ◽  
Group D ◽  
Symmetry Space ◽  
Symmetry Space Group

Single crystals of Ba2Nb2TeO10) have been prepared by solid state reactions in air. X-ray investigations led to orthorhombic symmetry, space group D152h-Pbca, a = 7.242(4), b = 12.433(3), c = 9.932(3) Å. Z = 4. Nb5+ and Te6+ show octahedral coordination by O2- . The crystal structure is characterized by planes of edge- and corner-sharing NbO6- and TeO6octahedra. It is shown that in spite of nearly identical lattice constants of Ba2Nb2TeO10 with compounds of the composition M0,5BaNbTe2O9 the so far unknown crystals of these substances may not be derived from the Ba2Nb2TeO10 type.

Über die Kristallstruktur von KSc2 F7 / The Crystal Structure of KSc2 F7

1985 ◽  
Vol 40 (6) ◽  
pp. 726-729 ◽  
Author(s):  
Klaus Güde ◽  
Christoph Hebecker
Keyword(s):  
Crystal Structure ◽  
Single Crystals ◽  
Unit Cell ◽  
Space Group ◽  
X Ray ◽  
Monoclinic Unit Cell ◽  
R Value ◽  
Ray Methods

Abstract Single crystals of KSc2F7 have been prepared from a mixture of KF and ScF3 . The samples were investigated by X-ray methods. KSc2F7 crystallizes orthorhombically with a = 10.643(2), b = 6.540(1), c = 4.030(1) Å. These data indicate a close crystallographic connection to the monoclinic unit cell of KIn2F7 [1], But in contrast to KIn2F7 , KSc2 F7 crystallizes in space group No. 65. Cmmm - D192h. The R-value for 341 observed independent reflections is 0.060.

Sign in / Sign up

Export Citation Format

Share Document