True Unit Cell Research Articles

Etude structurale des composés Fe 0,25TiSe 2 et Co 0,25TiSe 2 à cristaux maclés. Surstructures et degré d'ordre des lacunes

Fe 0.25TiSe 2 and Co 0.25TiSe 2 crystals have been studied. Meriedric twins are detected by means of X-ray diffraction, from extinction rules observed on the apparent cells that are multiples of the C6 hexagonal unit cell ( a′, c′). In Fe 0.25TiSe 2 [quasi-orthohexagonal monoclinic I true unit cell: a (≈a′ 3 1 2 ) = 3.566(1) × 3 1 2 ; b (≈a′) = 3.566(1); c (≈2c′) = 5.964(1) × 2 Å; β ≈ 90°] existence of a M 3□ X 4 ordering of vacancies, previously observed on powders, is confirmed by this study. In Co 0.25TiSe 2, the true unit cell is monoclinic F, (a ≈ 2a′ 3 1 2 , b ≈ 2a′, c ≈ 2c′) . The basic C6 lattice is apparently undistorted and the structure may be described through a hexagonal unit cell ( a 1 = b 1 = 2 a′; c 1 = 2 c′); on the studied crystal we have found a 1 = 7.1014(9); b 1 = 7.0993(8); c 1 = 11.800(2) Å; γ 1 = 119.97(3)°. The structure refinement ( R = 0.036 from 120 “ C6” reflections; R = 0.056 from 70 superstructure reflections) is carried out with the M 5□ 3 X 8 model, 2 c′ variety, space group C2 m . Assuming Co atoms to be in vacancy-containing layers, occupation rates of 0.55 on “metal” sites and 0.092 on “vacant” sites are found.

Structural transformation in Mg 2NiH 4

X-Ray diffraction measurements show that on heating Mg 2NiH 4 in a 1 atm pressure H 2 atmosphere, above ∼250°C it transforms into a cubic structure, metal atoms in CaF 2 arrangement, a = 6.525 Å. It is concluded that the H atoms are in tetrahedral clusters, and that the structure is only weakly ionic. This conclusion is also supported by NMR measurements. The 20°C structure of Mg 2NiH 4 is shown to be describable primarily as a slight monoclinic distortion of the cubic unit cell; a = 6.594 Å, b = 6.412 Å, c = 6.490 Å and β = 93.1°. However, weak small angle lines show that a longer range order exists and that the true unit cell, which we have not determined, must be very large. To what extent the cubic phase should be considered a high temperature and/or low concentration (Mg 2NiH 4−ϵ) phase is not resolved.

Lattice Distortion of PbZrO3

A slight orthorhombic distortion of perovskite type crystal lattice of antiferroelectric PbZrO 3 which is very close to tetragonal, was successfully detected by compairing carefully the observed and the calculated X-ray diffraction profiles of the powder diffractometry data. The prototypic cubic perovskite cell changes the shape into monoclinic, a m = c m =4.158, b m =4.110 A and β=90^°5.6' at room temperature, confirming Shatalova et al .'s result. In contrast to the Shatalova's result, however, the lattice slightly contracts along the direction of antiparallel shift of Pb ions rather than the extension. The true orthorhombic unit cell is a =2 a m cos (β/2), b =4 a m sin (β/2) and c =2 b m .

A Redetermination of Diphenanthro[5,4,3-abcd: 5′,4′,3′-jklm]perylene

Abstract It has been shown that the true unit cell of diphenanthro[5,4,3-abcd: 5′,4′,3′-jklm]perylene consists of three subcells in which the atomic arrangements differ slightly from each other. The model for the ordered structure has been deduced from the consideration of weak reflections. The average structure of the subcell with a=30.80, b=3.837, c=19.87 Å, β=112.5°, and Z=4 has been redetermined. The final R value is 0.103 for 1244 independent reflections. The two naphthanthrone planes in the molecule make an angle of 36°, which shows a large distortion from a planar structure.

BeP 2: A tetrahedral structure of type order-disorder which obeys a coordination rule for short-range order

Single-crystal studies on BeP 2 indicate that this compound possesses an OD structure. The substructure has a tetragonal unit cell with: a = 3.546 Å, c = 15.01 Å, Z = 4, space group: I4 1 amd . The final R factor has a value of 0.033. The atom sites in this substructure correspond to the sites of diamond if the latter is described with a tetragonal cell, where a = ( 2 1 2 2 )a diamond and c = 3 a diamond. A short-range order governs the occupation of these sites with Be and P atoms. Each Be has four tetrahedral P neighbors and every P has two Be and two P neighbors. Consideration of the maxima on the diffuse streaks between the sharp reflections of the substructure leads to an intermediate unit cell with a = 7.09 Å and c = 30.02 Å. Coordination considerations allow a structure proposal to be formulated for this intermediate structure which is triclinic but pseudotetragonal. The true unit cell is also pseudotetragonal with a = 7.09 Å and c = N · 15.01 Å, where N is a large integer.

The interpretation of quasi-kinematical single-crystal electron diffraction intensity data from paraffins

Single-crystal hk0 electron diffraction patterns from thin ( ≤ 240 Å) rhomboid n-hexatriacontane (n-C36H74) crystals contain intensity data which are well fit by the commonly observed O⊥ methylene subcell phasing model but not by a true unit cell model which contains two mutually displaced monolayers. The apparent diffraction from a monolayer in these lamellar crystals is thought to be due to bend distortions of the crystal plate. Intensity data conform to a kinematical interpretation as a first approximation, thus allowing a priori structural elucidation, but eventually will require an n-beam dynamical correction.

Effect of Oxide Additions on the Polymorphism of Tantalum Pentoxide: III. "Stabilization" of the Low Temperature Structure Type.

The "low temperature structure type" of Ta2O5 has been found to occur in two distinct forms with the lowest temperature form having a unit cell 14 times the subcell and an intermediate temperature form with a unit cell 11 times the subcell. The two types form intermediate partially ordered mixtures which are apparently in thermal equilibrium at various temperatures between ~ 1000 and 1350 °C. The addition of MoO3, WO3, SiO2, GeO2, ZrO2, TiO2, B2O3 and Al2O3 each affect the multiplicity of the true unit cell in different ways. WO3, SiO2, GeO2, B2O3, and Al2O3 form phases structurally similar to "low-Ta2O5" which are stable up to the solidus temperatures of the corresponding systems.

Crystal Structure of Cubic Deuterium Chloride

IN an earlier communication1 we stated that the X-ray powder diffraction pattern of solid deuterium chloride recorded at 118.5° K and the corresponding neutron powder diffraction pattern recorded at 111.5° K showed the same set of lines, confirming that the face centred cubic unit cell derived from the X-ray diffraction pattern was the true unit cell of the structure. Further analysis of the two diffraction patterns led to the conclusion that the observed face centred cubic structure was the statistical average of a disordered structure. The neutron diffraction pattern available at that time, however, did not provide enough information to determine the exact nature of the disorder.

Structural Differences between the Alkali Imidodisulphates

IT has long been known from goniometric measurements1 that there are morphological similarities between ammonium and potassium imidodisulphates (or iminodisulphonates), NH(SO3NH4)2 and NH(SO3K)2. The crystal structure of the potassium salt2, which has recently been refined3, conforms accurately to the space-group C 2/c. Preliminary X-ray examination of single crystals at room temperature revealed4 that ammonium imidodisulphate differs somewhat in structure from the potassium salt in that its true unit cell has a b-axis three times as long (3 × 7.74 = 23.2 A) as a pseudo-cell isomorphous with the potassium salt. Rubidium imidodisulphate appears to have a five-fold superlattice since, on b-axis photographs, a few reflexions can be seen on up to four additional weak layer-lines between adjacent strong layer-lines. In both salts, reflexions on the extra layer-lines are of very low intensity. We have investigated these structural irregularities by means of X-ray diffraction and broad-line nuclear-magnetic-resonance spectroscopy.

41. The thorium dioxide–thorium tetrafluoride system

The thorium dioxide --thorium tetrafluoride system has been studied by x- ray diffraction. Thorium tetrafluoride dissolves in thoria to the extent of about 25 mole%, the cell constant a increasing from 5.586 to 5.633 kX. The arrangement of the anions in these mixed crystals is discussed. No solid solubility of thoria in thorium tetrafluoride was observed. Thorium oxyfluoride, ThOF/sub 2/, was formed by the reaction of equimolar mixtures of thorin and the tetrafluoride at 900 deg in an inert atmosphere. Diffraction photographs showed that the true unit cell of the oxyfluoride is orthorhombic and not hexagonal as previously suggested. The deviation from hexagonal symmetry is probably due to the oxygen and fluorine atoms' segregating into distinct sets of lattice sites. Attempts to prepare disordered thorium oxyfluoride with a random anion distribution were unsuccessful. (auth)

Constitution of Calycanine

SOME time ago, on the suggestion of Prof. A. R. Todd, calycanine was examined by X-ray methods1,2 in order to decide whether a constitution originally suggested by Barger, Madinaveitia and Strouli3 for a molecule C16H10N2 is in harmony with the crystallographic symmetry and the unit cell dimensions. That investigation established the approximate dimensions of a monoclinic unit cell as a = 13.7 A., b = 4.45 A., c = 9.7 A., I = 107°, and showed that the space group is P21/a — C2h5, provided that a few very weak reflexions are neglected. If these reflexions are taken into account, it was suggested that the above cell should be regarded as a pseudo-cell, the true unit cell having a doubled c-axis, 2 × 9.7 A. Fairly detailed suggestions were advanced as to the probable crystal structure, but the chemical synthesis which Prof. A. R. Todd intended to carry out has not been completed because of the War.

An X-ray Study of Stretched Rubber

Abstract With the more extensive data from new x-ray films of the diffraction pattern of stretched rubber made in a cylindrical camera, an attempt has been made to find the true unit cell. No really satisfactory solution has been reached. The leading possibilities are described. They are characterized by a change of the angle between the two independent sets of planes which reflect the two strong equatorial spots from 90°, the value which first suggests itself, to 109.5°. The new choice is shown to be consistent with all the evidence. It has the great advantage of resolving fairly well the familiar discrepancy between measured and calculated values of the density of the crystals in stretched rubber. The new value from the unit cell is 1.00. A necessary consequence of the x-ray data is that the carbon atoms of a molecular chain are not co-planar in stretched rubber. The reason appears to be the large repulsive forces which would have to exist in that configuration. In rotations on the single bonds during stretching and retraction the interatomic forces are probably repulsions in the dominating pairs. Repulsions give a plausible explanation of the form of the outer part of the stress-strain curve.

An X-ray Study of Stretched Rubber

Abstract With the more extensive data from new x-ray films of the diffraction pattern of stretched rubber made in a cylindrical camera, an attempt has been made to find the true unit cell. No really satisfactory solution has been reached. The leading possibilities are described. They are characterized by a change of the angle between the two independent sets of planes which reflect the two strong equatorial spots from 90°, the value which first suggests itself, to 109.5°. The new choice is shown to be consistent with all the evidence. It has the great advantage of resolving fairly well the familiar discrepancy between measured and calculated values of the density of the crystals in stretched rubber. The new value from the unit cell is 1.00. A necessary consequence of the x-ray data is that the carbon atoms of a molecular chain are not co-planar in stretched rubber. The reason appears to be the large repulsive forces which would have to exist in that configuration. In rotations on the single bonds during s...

X-ray analysis of the crystal structure of durene

The crystal structure of durene, 1. 2. 4. 5. (sym.)-tetramethyi benzene, C 6 H 2 (CH 3 ) 4 , has not previously been examined by the X-ray method, but the class and axial ratios are given by Groth as monoclinic prismatic a : b : c = 2·4609:1:1·9975, β = 115°27' with the (100) face most prominently developed. The present work confirms these measurements to within the limits of experimental error (about ½%), but it is found that the axial directions used above define a cell which contains an identical molecule at the centre of the ac face. It is therefore necessary to select a new axis in order to define the true unit cell. The relation of Groth’s axial directions to the cell now chosen is illustrated in fig. 1, the b axis being perpendicular to the paper. The X-ray work, recorded by means of rotation, oscillation, and moving film photographs, leads to the following values for the axial lengths, etc.:— a = 11·57 ± 0·05 A. b = 5·77 ± 0·02 A. c = 7·03 ± 0·05 A. β = 113·3° { h 01} halved when h is odd, (010) halved.

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