Structure refinement with X-ray powder diffraction data for synthetic calcium hydroxyapatite by Rietveld method

Ca₅(PO₄)₃OH, M_r = 502.3, hexagonal, P 6₃/m, a = 9.4207(3), c = 6.8780(2) Å, V = 528.67 ų, Z = 2, D_x = 3.156 Mg · m⁻³, CuKα, λKα₁ = 1.54051, λKα₂ = 1.54433 Å, μ = 26.25 mm⁻¹, F(000) = 500, T = 294 K. The powder diffraction pattern was analysed by the Rietveld method. The parameters were refined by the program PFSR (DBW2.9) to final R-factors R_p = 0.079, R_wp = 0.081 and R_B = 0.015.     

Synthesis and powder X-ray diffraction of new Schiff-base liquid crystal

Liquid crystals (LCs) are soft materials that combine the fluidity of disordered liquids and the long-range orientational or positional order of crystalline solids, along one or two directions of space. A search for better stationary phases, including highly selective ones, is an important trend in chromatography development. Among the stationary phases under investigation are LC stationary phases that have been recently generated much interest. A variety of isomeric molecules were separated with high accuracy. Successfully, X-ray scattering is widely used to investigate and characterise the microscopic structure of most LCs. In this paper, a new liquid crystalline material that can be used potentially as stationary phase in gas chromatography was synthesised and characterised by means of nuclear magnetic resonance (NMR), infrared (IR) spectra, elemental analysis and X-ray diffraction.     

Structure determination of two asymmetrically substituted oxadiazoles from powder diffraction data

The crystal structures of the 1,3,4 oxadiazole compounds N,N‐dimethyl‐N‐[4‐(1,3,4‐oxadiazol‐2‐yl)phenyl]amine ( 1 ) and 2‐methyl‐5‐phenyl‐1,3,4‐oxadiazole ( 2 ) have been determined. In case of 1 no adequate crystals were available; therefore the structure was solved at room temperature from X‐ray powder diffraction data using the method of simulated annealing. This solution is compared to a second one obtained by applying the molecular replacement method. Subsequent Rietveld refinements combined with the so called two stage method based on the data collected to 1.6 Å resolution yielded an R_wp value of 7.27% for 1 . Compound 1 crystallizes in the orthorhombic space group P2₁2₁2₁ with lattice parameters of a = 7.599(4) Å, b = 6.004(2) Å, c = 21.736(3) Å. The crystal structure of 2 was solved by means of single crystal structure analysis (monoclinic space group P2₁/c, a = 8.010(3) Å, b = 10.783(4) Å, c = 19.234(7) Å, β = 90.794(9)°). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and crystal structure determination of two dispiro compounds from laboratory x‐ray powder diffraction data

The crystal structures of the dispiro compounds 1,3,4,8,10,11‐Hexaphenyl‐13‐methyl‐1,2,8,9,13‐pentaazadispiro[4.1.4.3]tetradeca‐2,9‐dien‐6‐one ( 3a ) and 4,11‐Bis(4‐methoxyphenyl)‐13‐methyl‐1,3,8,10‐tetraphenyl‐1,2,8,9,13‐pentaazadispiro‐[4.1.4.3]tetradeca‐2,9‐dien‐6‐one ( 3b ) have been determined at room temperature from X‐ray powder diffraction data using the method of simulated annealing as implemented in the programs DASH and TOPAS. Subsequent Rietveld refinements using the data collected to 1.5 Å resolution yielded R‐Bragg values of 2.2% for ( 3a ) and 3.7% for ( 3b ). It was found, that both compounds crystallize in the monoclinc space group P 2₁/n with lattice parameters of a = 17.1656(5) Å, b =13.8128(3) Å, c = 16.1016(5) Å, and β = 103.7330(2)° for ( 3a ) and a = 17.2529(8) Å, b = 13.8729(5) Å, c =16.1287(10) Å, and β = 103.6910(3)° for ( 3b ). Both compounds exhibit a distorted hexagonal close type of packing (hcp) of the molecular centers of gravity. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray powder diffraction study of polytetrafluoroethylene

Samples of polytetrafluoroethylene were studied by X-ray diffraction. A quantitative X-ray powder diffraction analysis of three components of the polymer was performed for the first time. All samples of polytetrafluoroethylene were found to be three-phase and consist of one crystalline and two amorphous phases. One of the amorphous phases is composed of low-molecular-weight products. The structure of the latter phase was established for the first time by X-ray diffraction methods and computer simulation.     

The crystal structure of Zr2Se reinvestigated by electron crystallography and X-ray powder diffraction

The metal-rich compound Zr₂Se is of particular interest for electron crystallography, since it was one of the first examples that proved that heavy-atom structures can be solved via quasi-automatic direct methods from selected area electron diffraction intensities [1]. For this reason, Zr₂Se has been chosen as a model to discuss the possibilities and the limits of the quasi-kinematical approach that has been successfully used to determine this and related structures from high-resolution electron microscopy (HREM) images and selected area electron diffraction. In order to quantify the achievable accuracy of the electron crystallography techniques used, the corresponding structures are compared with results from structural analysis with X-ray powder data and with a model received from first-principles calculations. The latter structure was chosen in this study as a reference, since the calculations do not depend on experimental parameters. Analysis of the obtained result from electron diffraction structural analysis (EDSA) shows that the structural model is, on average, only off by 0.08 Å, despite the investigated crystal having an effective thickness of 286 Å. The corresponding result from Rietveld refinement with X-ray powder data agrees to within 0.04 Å with the structure from calculation and within 0.03 Å with the result from an earlier single crystal X-ray study [2].     

X-ray diffraction studies of protein crystal disorder

Protein crystals contain many kinds of disorder, but only a small fraction of these are likely to be important in limiting the diffraction properties of interest to crystallographers. X-ray topography, high-angular-resolution reciprocal space measurements, and standard crystallographic data collection have been used to probe three factors that may produce diffraction-limiting disorder: (1) solution variations during crystal growth, (2) macromolecular impurities, and (3) post-growth crystal treatments. Variations in solution conditions that occur in widely used growth methods may lead to variations in equilibrium protein conformation and crystal packing as a crystal grows, and these may introduce appreciable disorder for sensitive proteins. Tetragonal lysozyme crystals subjected to abrupt changes in temperature, pH, or salt concentration during growth show increased disorder, consistent with this mechanism. Macromolecular impurities can have profound effects on protein crystal quality. A combination of diffraction measurements provides insight into the mechanisms by which particular impurities create disorder, and this insight leads to a simple approach for reducing this disorder. Substantial degradation of diffraction properties due to conformation and lattice constant changes can occur during post-growth crystal treatments such as heavy-atom compound and drug binding. Measurements of the time evolution of crystal disorder during controlled crystal dehydration – a simple model for such treatments – suggest that structural metastability conferred by the constraints of the crystal lattice plays an important role in determining the extent to which the diffraction properties degrade.     

Intensities of overlapping peaks in X-ray powder diffraction

Separation of overlapping peaks in X-ray powder diffraction is investigated by means of fitting a modified Lorentzian function to experimental profiles of reflexions. Application of the new type of analytical function and simultaneous refinement of background level parameters are described and discussed with respect to the accurate determination of integrated intensities of reflexions.     

The X-ray method for the determination of damaged layer thickness of the Si crystal surface

In this paper the X-ray section topograph method was used for determination of damaged layer thickness of silicon crystal surface. For measurements such reflections should be chosen for which the “margine” effect is very sharp. It was used the fact that in the ranges of strong perturbances the approximation of kinematic theory could be applied.     

A method for implementing the diffraction of a widely divergent X-ray beam

A method for implementing the diffraction of a widely divergent characteristic X-ray beam from a standard X-ray tube with a linear focal spot was improved. X rays, passing through a diaphragm 30 μm in diameter, diffract from a crystal adjacent to the diaphragm. The crystal, together with a photographic plate, rotates around the axis perpendicular to the plate. It is shown that the diffraction image is a set of hyperbolas in this case. The equations of the hyperbolas are obtained and investigated. A method for interpreting the diffraction images in the case of small crystal asymmetry is proposed.     

A Czochralski crystal puller automated by the weighing method

The automated crystal growing equipment makes use of a commercial electronic balance equipped with a microprocessor. The mode of operation is explained and experiences got on the occasion of crystal growth experiments are presented.     

Grazing-incidence dynamic X-ray diffraction from a crystal with a shaped surface

The dynamic grazing-incidence X-ray diffraction from a crystal with a shaped surface in the form of one-dimensional submicron grating has been investigated. The interaction between the specularly reflected and diffracted waves and grating harmonics is taken into account for noncoplanar diffraction under the conditions of total external reflection. It is shown that this approximation exhibits good convergence in the number of harmonics taken into account. The influence of the angular divergence of the incident beam on the rocking-curve shape is shown.     

X-ray crystal orientation determination for semiconductor single crystals

An improved method to measu reorientation angles of flat single crystals was developed taking Buerger precession technique. The method is described and compared with Laue- and goniometer techniques. Advantages are low costs and short measuring time. An easy evaluation of the records allows to take this method as a routine angle determination for semiconductor manufacturing.     

Theory of X-ray diffraction from a nonideal crystal with a trapezoidal cross section

The theory of X-ray diffraction from a nonideal lateral crystal with a trapezoidal cross section in the Born (kinematical) approximation has been developed. Distortions of the crystal structure are caused by continuous (nonrandom) lattice strains and randomly distributed defects. Continuous lattice strain is a combination of elastic bending of atomic planes and a linear variation in the interplanar spacing with increasing distance from the crystal surface. Within the method of triple-crystal X-ray diffraction, numerical simulation of the angular intensity distribution of coherent and diffuse scattering has been performed for different continuous and random lattice strains in the lateral and vertical directions.     

An X-ray diffraction refinement of the crystal structure of natural apophyllite

The crystal structure of apophyllite (Andersberg — GDR), with a = 8.966(2), c = = 15.767(1) Å, P4/mnc, z = 2, Q = 2.35 gm · cm⁻³, has been refined (R = 0.035) by least squares with 976 reflections collected with a diffractometer. Apophyllite is a sheet structure with the bringing Si O bond lengths 1.6236 Å, while the non-bridging bond length Si O(3) is 1.5843 Å. The two independent Si O Si angles are 140.09, 140.76 degrees. The mean Si O bond length is 1.6138 Å. As it was not possible to locate unequivocally the H-atoms with the X-ray data, the interpretation of the of water in the structure was based on the charge balance approach of DONNAY and ALLMAN . Assuming that the fluorine ion is bonded to calcium ion (Ca-F = = 2.416 Å) and to H3 atom (F-H3 = 0.9145(1) Å) and water molecule hydrogen bonded to silicate framework. The average bond distances O-H are 0.962(2) Å and angle 105.24(1)°.     

Determination of the parameters of a rough surface from the dynamical X-ray diffraction data

A new method is proposed for determining the roughness parameters from X-ray diffraction data. The method is based on a controllable displacement of reflecting planes under an external tangential pressure. It is shown that the displacement of atomic planes near the rough surface upon sample compression increases in proportion to the applied stress and strongly depends on the roughness parameters. Rough surfaces with determinate periodic and random reliefs are considered together with the corresponding features of X-ray rocking curves.