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.     

A precision X-ray method for the determination of the orientation of single crystal surfaces

A precision method for the determination of the orientation of single crystal surfaces is describes enabling us to ascertain the orientation data from an indexed Laue photograph by precise measurement of lengths and angles, without the necessity of knowing the exact single crystal - film distance. An example shows the individual steps of the procedure.     

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.     

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.     

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.     

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.     

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.     

Assembly models for zeolite crystal structures according to the data of topological analysis by the tiling method

Cluster analysis of 194 tetrahedral T structures of zeolites has been performed by the tiling method using the TOPOS program package. An algorithm of the complete expansion of T structures in tiles (complementarily bound polyhedral clusters, which are responsible for the normal (face-to-face) partition of crystal space) and an algorithm for selecting nonintersecting tiles were used. Primary tiles, which number no more than two for any zeolite studied and have packing that completely determines the topology of the entire zeolite structure, have been determined for 41 zeolites. It is established that 24 zeolites are characterized by a single assembly version, 15 have two alternative versions, and IWR and TSC zeolites are characterized by 3 and 4 assembly versions. Isolated zeolites contain 2?C11 topologically different T _n tiles, where n is the number of tetrahedral T sites per tile; n = 4?C168 and the diameter is 6?C35 ?. The most numerous group of zeolites is characterized by n values of 4?C18. This group contains no tiles with the odd values n = 7?C17 and even value n = 6. The other group includes zeolites with large n values: 24, 30, 32, 36, 42, 48, 64, 72, 96, and 168.     

X-ray mapping in heterocyclic design: IV. Crystal structure determination of 3-(p-nitrobenzoyl)-2-oxooxazolo[3,2-a]pyridine from powder diffraction data

The structure of 3-(p-nitrobenzoyl)-2-oxooxazolo[3,2-a]pyridine is determined by the powder diffraction technique. The crystals are monoclinic, a = 13.642(2) Å, b = 22.278(3) Å, c = 3.917(1) Å, β = 90.63(2)°, Z = 4, and space group P2₁/n. The structure is solved by a modified Monte Carlo method and refined by the Reitveld method. The six-membered heterocycle is characterized by the alternation of partially single and partially double bonds. The system of two conjugated heterocycles is planar and forms a dihedral angle of 46.1(1)° with the plane of the phenyl ring. The nitro group is virtually coplanar with the phenyl fragment. An extensive system of intramolecular and intermolecular contacts involving hydrogen, oxygen, and nitrogen atoms is observed in the crystal.     

Algorithm for crystal-profile control in automated crystal growth by the Czochralski method

Growth setups of the new generation should provide crystal growth in the automated mode. One of the necessary conditions for growing quality crystals is the rigorous maintenance of the given boule profile. In the systems with weight control, the model weight is compared with the weight measured by the weight sensor. Below, we describe an algorithm for calculating the model weight based on the numerical solution of the Bardsley equation. The algorithm allows one to set the crystal profile either by a function or a point set.