Modeling X-ray diffractomerers using ray tracing and parallel coprocessors

In X-ray powder diffraction, the use of the Rietveld technique to refine crystalline structures requires modeling the diffractometer. Some of the codes using this technique incorporate simple models for it. These codes do not affect the refined parameters only when the X-ray source is a synchrotron with enough X-ray optic to reduce the associated aberrations. When the diffractometer belongs to a standard laboratory, however, the optic associated to it gives rise to large aberrations; for example, asymmetric and shifted peaks that depend on the diffraction angle. When the above codes are used to refine crystalline structures, the refined parameters are non-confident, because they are partially modeling these aberrations. If in the code, the effect of the optical components on the diffraction pattern is modeled correctly, the obtained refined parameters will be more confident. This kind of modeling has been done in the codes that use the fundamental parameters model for the diffractometer. There are two ways to perform this modeling: in one of them the codes use an analytical model for each one of the optical components of the diffractometer; other codes use the ray tracing technique to model the path of the x-rays along the optic. This last technique requires a powerful computer facility. In this work, we present the developing of an open-source code to model the diffractometer by using the ray tracing technique. To reduce the calculation time, the code was written in OpenCL for a computer with a Fermi K20 coprocessor, and for a computer with a Xeon-Phi coprocessor, using the Qt platform for both systems. The device-function generated with this code can be used as input for any other code that models diffraction patterns, or refines crystalline structures. The code can also be used for teaching the effect of the different optical components on an X-ray powder diffraction pattern, including the effect of a wrong alignment of these components.

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Powder X-Ray Data for Synthetic Anhydrous Sodium Zirconium Silicates

Powder Diffraction ◽

10.1017/s0885715600012653 ◽

1987 ◽

Vol 2 (3) ◽

pp. 176-179 ◽

Cited By ~ 1

Author(s):

G. Wilson ◽

F. P. Glasser

Keyword(s):

Solid State ◽

Diffraction Pattern ◽

Powder Diffraction ◽

Solid State Reaction ◽

The Other ◽

X Ray Diffraction ◽

Powder Diffraction File ◽

X Ray ◽

Sodium Zirconium ◽

Diffraction Patterns

AbstractA systematic survey of phase formation in the Na2O-ZrO2-SiO2 system has revealed inconsistencies in the number and identity of ternary phases, and of their X-ray powder data. The phases Na2ZrSiO5, Na4Zr2Si3O12, Na2ZrSi2O7 and Na2ZrSi4O11 were prepared by solid-state reaction and their experimental X-ray diffraction patterns measured. Calculated X-ray diffraction patterns were generated by computer, using published crystallographic data, and critically compared with the experimentally observed values. The unit-cell constants were redefined to a greater accuracy than the presently accepted values published in the Powder Diffraction File. Only Na4Zr2Si3O12 produced an X-ray diffraction pattern which agreed with that previously published; those from the other phases were significantly different in both the intensities and positions of the reflections. Data for synthetic Na2ZrSi4O11 identical to the mineral vlasovite are reported.

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X-ray powder diffraction studies of fibrillar zinc trimolybdates ZnMo3O10·nH2O (n=3.75,5,10)

Powder Diffraction ◽

10.1017/s0885715600010678 ◽

1999 ◽

Vol 14 (4) ◽

pp. 276-279

Author(s):

Wiesław Łasocha ◽

Wiesław Surga ◽

Alicja Rafalska-Łasocha

Keyword(s):

Diffraction Pattern ◽

Powder Diffraction ◽

Diffraction Data ◽

Lattice Parameters ◽

Fiber Axis ◽

Powder Diffraction Data ◽

Parallel Fibers ◽

X Ray ◽

Space Groups ◽

Diffraction Patterns

The X-ray powder diffraction data of polycrystalline fibrillar zinc trimolybdates ZnMo3O10·3.75H2O, ZnMo3O10·5H2O, and ZnMo3O10·10H2O, are reported. An uncommon diffraction pattern was recorded in the case of the “wet fibers” of ZnMo3O10·10H2O, which could be indexed assuming a model of parallel fibers with translation disorder along the fiber axis. The powder diffraction patterns, lattice parameters, space groups, and other data describing these compounds are presented in this paper.© 1999 International Centre for Diffraction Data.

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Full-field energy-dispersive powder diffraction imaging using laboratory X-rays

Journal of Applied Crystallography ◽

10.1107/s1600576715000801 ◽

2015 ◽

Vol 48 (1) ◽

pp. 269-272 ◽

Cited By ~ 5

Author(s):

Christopher K. Egan ◽

Simon D. M. Jacques ◽

Matthew D. Wilson ◽

Matthew C. Veale ◽

Paul Seller ◽

...

Keyword(s):

Powder Diffraction ◽

Texture Mapping ◽

Friction Stir Weld ◽

Field Energy ◽

X Rays ◽

Full Field ◽

X Ray ◽

Friction Stir ◽

Diffraction Imaging ◽

Diffraction Patterns

A laboratory instrument with the ability to spatially resolve energy-dispersed X-ray powder diffraction patterns taken in a single snapshot has been developed. The experimental arrangement is based on a pinhole camera coupled with a pixelated spectral X-ray detector. Collimation of the diffracted beam is defined by the area of the footprint of a detector pixel and the diameter of the pinhole aperture. Each pixel in the image, therefore, contains an energy-dispersed powder diffraction pattern. This new X-ray imaging technique enables spatial mapping of crystallinity, crystalline texture or crystalline phases from within a sample. Validation of the method has been carried out with a back-to-back comparison with crystalline texture mapping local to a friction stir weld in an aluminium alloy taken using synchrotron radiation.

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Crystal structure of copper(ii) citrate monohydrate solved from a mixture powder X-ray diffraction pattern

Powder Diffraction ◽

10.1017/s0885715613001267 ◽

2013 ◽

Vol 29 (1) ◽

pp. 28-32 ◽

Cited By ~ 1

Author(s):

Ana Palčić ◽

Ivan Halasz ◽

Josip Bronić

Keyword(s):

Crystal Structure ◽

Diffraction Pattern ◽

Rietveld Refinement ◽

Powder Diffraction ◽

X Ray Diffraction ◽

X Ray ◽

Indexing Structure ◽

Pattern Approach ◽

Structure Solution ◽

Diffraction Patterns

The crystal structure of copper(ii) citrate monohydrate (C6H4O7Cu2·H2O) has been solved from a mixture powder diffraction pattern. Approach to indexing, structure solution and Rietveld refinement of multiphase diffraction patterns is discussed. Rietveld refinement is carried out employing free-atom refinement and rigid body refinement.

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The Far Infrared Spectra and X-Ray Powder Diffraction Patterns of the Structure I Hydrates of Cyclopropane and Ethylene Oxide at 100 °K

Canadian Journal of Chemistry ◽

10.1139/v75-009 ◽

1975 ◽

Vol 53 (1) ◽

pp. 71-75 ◽

Cited By ~ 16

Author(s):

John E. Bertie ◽

Frances E. Bates ◽

David K. Hendricksen

Keyword(s):

Infrared Spectrum ◽

Ethylene Oxide ◽

Diffraction Pattern ◽

Powder Diffraction ◽

Low Frequency ◽

Far Infrared ◽

Lattice Parameter ◽

X Ray ◽

Oxide Hydrate ◽

Diffraction Patterns

This paper presents the far-infrared spectrum and X-ray powder diffraction pattern of the structure I hydrate of cyclopropane at 100 °K, and the powder diffraction pattern of the isostructural ethylene oxide hydrate at 100 °K. Between 360 and 100 cm−1 the absorption by cyclopropane hydrate is essentially identical to that by ethylene oxide hydrate, but is shifted to low frequency by about 2%. This shift is undoubtedly related to the hydrogen bonds being slightly longer in cyclopropane hydrate, whose cubic lattice parameter is 11.98 ± 0.02 Å compared to 11.89 ± 0.02 Å for ethylene oxide hydrate, both at 110 ± 20 °K. The absorption by cyclopropane hydrate below 100 cm−1 decreases rapidly with decreasing frequency; this confirms that the absorption plateau observed for ethylene oxide hydrate between 100 and about 50 cm−1 is due to primarily rotational vibrations of ethylene oxide. A recent statement, that the orientational disorder of the water molecules need not be invoked to explain the far infrared spectrum of ice 1 h, is disputed.

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X-ray powder diffraction and electron diffraction studies of the thortveitite-related L phase, (Zn,Mn)2V2O7

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768108042444 ◽

2009 ◽

Vol 65 (2) ◽

pp. 160-166 ◽

Cited By ~ 2

Author(s):

Kevin M. Knowles ◽

Mary E. Vickers ◽

Anjan Sil ◽

Yung-Hoe Han ◽

Périne Jaffrenou

Keyword(s):

Electron Diffraction ◽

Powder Diffraction ◽

System Analysis ◽

Bravais Lattice ◽

Second Phase ◽

X Rays ◽

X Ray ◽

The Difference ◽

Diffraction Patterns ◽

A Minor

The phase designated γ-Zn3(VO4)2 reported as a minor second phase in zinc oxide-based varistor materials doped with vanadium oxide and manganese oxide is shown to be the L phase, (Zn1 − x Mn x )2V2O7 (0.188 < x < 0.538), in the pseudo-binary Mn2V2O7–Zn2V2O7 system. Analysis of X-ray powder diffraction patterns and electron diffraction patterns of this phase shows that the previously published a, c and β values for this thortveitite-related phase are incorrect. Instead, Rietveld refinement of the X-ray powder pattern of the L phase shows that it has a monoclinic C lattice with Z = 6, with a = 10.3791 (1), b = 8.5557 (1), c = 9.3539 (1) Å and β = 98.467 (1)°. Although prior convergent-beam electron diffraction work of `γ-Zn3(VO4)2' confirmed the C Bravais lattice, the space group was found to be Cm rather than C2/m, the difference perhaps arising from the inability of the X-rays to detect small displacements of oxygen. Attempts to refine the structure in Cm did not produce improved R factors. The relationship between the crystal structure of the L phase and the high-temperature C2/m β′-Zn2V2O7 thortveitite-type solid solution is discussed.

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Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern

Powder Diffraction ◽

10.1017/s0885715600012409 ◽

1987 ◽

Vol 2 (2) ◽

pp. 73-77 ◽

Cited By ~ 92

Author(s):

Deane K. Smith ◽

Gerald G. Johnson ◽

Alexandre Scheible ◽

Andrew M. Wims ◽

Jack L. Johnson ◽

...

Keyword(s):

Diffraction Pattern ◽

Powder Diffraction ◽

Diffraction Method ◽

Weight Fraction ◽

Reference Database ◽

Weighted Sum ◽

X Ray ◽

Unique Approach ◽

Diffraction Patterns ◽

Best Fit

AbstractA new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns.The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

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Method of Simulation of Diffraction Pattern for Nanosize Crystalline Systems

Siberian Journal of Physics ◽

10.54362/1818-7919-2008-3-4-47-51 ◽

2008 ◽

Vol 3 (4) ◽

pp. 47-51

Author(s):

Dmitriy A. Yatsenko ◽

Sergey V. Tsybulya

Keyword(s):

Diffraction Pattern ◽

Powder Diffraction ◽

X Ray ◽

Original Algorithm ◽

Diffraction Peaks ◽

Diffraction Patterns ◽

Definition Of ◽

Integrated Intensities

The original algorithm and the software for calculation of x-ray powder diffraction patterns from ensemble of nanocrystal particles are developed. Test calculations are carried out. Errors in definition of positions, integrated intensities and halfwidth of diffraction peaks are estimated.

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Sub-nanosecond X-ray powder diffraction

Journal of Applied Crystallography ◽

10.1107/s0021889890008500 ◽

1990 ◽

Vol 23 (5) ◽

pp. 441-443 ◽

Cited By ~ 13

Author(s):

N. C. Woolsey ◽

J. S. Wark ◽

D. Riley

Keyword(s):

Powder Diffraction ◽

Laser Light ◽

Polycrystalline Materials ◽

Spectral Brightness ◽

X Rays ◽

Single Exposure ◽

Time Resolved ◽

X Ray ◽

Titanium Target ◽

Diffraction Patterns

The X-rays emitted from a laser-produced plasma have been used to obtain powder diffraction patterns with exposures of less than a nanosecond. The X-rays were produced by focusing approximately 50 J of 0.53 μm laser light in a 600 ps (FWHM) pulse to a tight (~100 μm diameter) spot on a solid titanium target. The spectral brightness of the resonance line of the helium-like titanium thus produced was sufficient to record diffraction from LiF powder in a single exposure using the Seemann–Bohlin geometry. These results indicate that time-resolved measurements of the lattice parameters of polycrystalline materials can be made with sub-nanosecond temporal resolution.

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The Value of X-ray Powder Diffraction Patterns, and the Structure of the Manganese-Aluminum Alloys with Apparent Icosahedral Symmetry

Powder Diffraction ◽

10.1017/s0885715600011210 ◽

1986 ◽

Vol 1 (1) ◽

pp. 14-15 ◽

Cited By ~ 2

Author(s):

Linus Pauling

Keyword(s):

Powder Diffraction ◽

Bragg Reflection ◽

Icosahedral Symmetry ◽

X Rays ◽

X Ray ◽

California Institute Of Technology ◽

Tetragonal Crystal ◽

Institute Of Technology ◽

Diffraction Patterns ◽

Angle Of Reflection

I have made use of X-ray powder diffraction patterns for over sixty years. In the summer of 1922, in anticipation of my becoming a graduate student in chemistry, I read the book “X-Rays and Crystal Structure,” by W. H. and W. L. Bragg. Then in September 1922 I arrived in Pasadena, and immediately began to learn how to determine the structure of a crystal by a study of the X-ray diffraction pattern from Roscoe Gilkey Dickinson, who was the first person to have received a Ph.D. degree from the California Institute of Technology (1920). The procedure in use in Pasadena started with the preparation of a photograph showing lines obtained by Bragg reflection from a developed face of a large crystal with monochromatic radiation, usually molybdenum K alpha and beta. Measurement of the angle of reflection gave a set of possible values for the length of the edges of the unit of structure, usually of a cubic, hexagonal, or tetragonal crystal, since the methods were not powerful enough to permit the evaluation of more than two or three parameters. The next step was the preparation of Laue photographs, and their analysis. This was a powerful method, which often led to the correct structures.

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