The determination of crystal size and disorder from the X-ray diffraction photograph of polymer fibres. 2. Modelling intensity profiles

1991 ◽  
Vol 24 (6) ◽  
pp. 1051-1059 ◽  
Author(s):  
I. H. Hall ◽  
R. Somashekar
Keyword(s):  
Structural Parameters ◽  
Intensity Profile ◽  
Model Parameters ◽  
X Ray Diffraction ◽  
X Ray ◽  
Fourier Cosine ◽  
Lattice Disorder ◽  
Diffraction Photograph ◽  
Diffraction Patterns ◽  
Experimental Values

The intensity profile of the X-ray reflection from a crystalline material is related to the lattice disorder and the distribution of crystal sizes through its Fourier cosine coefficients. However, existing methods of obtaining these structural parameters from the coefficients require more than one order of reflection and this is seldom available with polymer fibres. They also rely heavily on the low-order harmonics which are those determined with least accuracy. The development and testing of a method which overcomes this weakness and which is suitable for use with a single order is described. The coefficients are calculated for a model with paracrystalline disorder and an assumed distribution of crystal sizes and the parameters describing this model are refined to minimize the discrepancy between the calculated and experimental values of the coefficients. Provided the distribution of lengths is asymmetric this discrepancy is no greater than would be expected from experimental error and so the assumed model cannot be rejected on the evidence available. Since a range of model parameters all gave equally good agreement with experiment, it was not possible with a single order to obtain a well defined set of values. Diffraction patterns displaying two orders had been chosen and results from the second order were consistent with the first, only a narrow range satisfying both simultaneously. The method was further developed by calculating the intensity profile from the harmonics and using this in the refinement. There was no advantage over using harmonics; indeed, on occasions the refinement algorithm was unstable producing unreliable results.

The determination of crystal size and disorder from X-ray diffraction photographs of polymer fibres. 1. The accuracy of determination of Fourier coefficients of the intensity profile of a reflection

1989 ◽  
Vol 22 (4) ◽  
pp. 363-371 ◽  
Author(s):  
R. Somashekar ◽  
I. H. Hall ◽  
P. D. Carr
Keyword(s):  
Crystal Size ◽  
Fourier Coefficients ◽  
Intensity Profile ◽  
X Ray Diffraction ◽  
Scattering Angle ◽  
X Ray ◽  
Fourier Cosine ◽  
High Harmonics ◽  
Lattice Planes

Methods which determine the number and disorder of lattice planes in a crystal from the Fourier cosine coefficients of the intensity profile of an X-ray reflection use only the low harmonics and require that the coefficients be normalized so that the zero harmonic is unity. Experimentally, the profiles can only be recorded over a smaller range of scattering angle than required by the theory, and it is necessary to subtract background, which is likely to be estimated with considerable error, before determining the coefficients. It is shown that with polymer fibres this causes serious errors in the normalization, and in the values of those low harmonics used in the size and disorder determination, and prevents reliable values being obtained. Methods which avoid normalization and use only high harmonics are needed. It is shown that disorder may be obtained in such a way, but not size, for which low-order normalized coefficients are essential. A method of extrapolation is described and tested which enables the accurate high harmonics to be used to improve the estimates of the low ones. Whilst this will yield more reliable values of crystal size than are obtainable from existing methods, the accuracy depends entirely on the validity of the extrapolation, which cannot be tested in many cases of interest.

Qualitative and Quantitative Analysis of Stacking Disorder in α-and β-SiC by X-ray Diffraction and Structure Modeling

1995 ◽  
Vol 410 ◽  
Author(s):  
Bogdan Palosz ◽  
Svetlana Stel'makh ◽  
Stanislaw Gierlotka
Keyword(s):  
Quantitative Analysis ◽  
Model Parameters ◽  
Qualitative And Quantitative Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Qualitative And Quantitative ◽  
Poisson Function ◽  
Diffraction Patterns ◽  
Computer Generation ◽  
Stacking Disorder

ABSTRACTA method of analysis of disordering in α- and β-SiC polycrystals by numerical modeling, and a simulation of X-ray diffraction profiles are presented. The diffraction patterns of nonperiodic structures were simulated for models of 2000 layer fragments of the structure. Computer generation of the models was based on the Poisson function describing the size distribution of the domains of basic polytypes and faults. The models were quantified by a set of input probability parameters describing relative frequencies of the occurrence of the domains of polytypes and faults. Implementation of a correlation parameter that characterizes coherence of sequential domains of a given polytype assures a good reproducibility of the simulated diffraction profiles obtained for the same set of the model parameters. Based on this method, a quantitative analysis of disordering in polycrystals of SiC annealed in the temperature range 1100–2200 °C was performed.

Lattice and Peak Profile Parameters in GIXD Technique

2007 ◽  
Vol 130 ◽  
pp. 281-286 ◽  
Author(s):  
Tomasz Goryczka ◽  
Grzegorz Dercz ◽  
Lucjan Pająk ◽  
Eugeniusz Łągiewka
Keyword(s):  
Structural Parameters ◽  
Incident Beam ◽  
Half Width ◽  
Diffraction Line ◽  
Beam Angle ◽  
X Ray Diffraction ◽  
Parallel Beam ◽  
X Ray ◽  
Diffraction Patterns ◽  
Α Angle

Grazing incident X-ray diffraction technique was applied to determine the influence of incident beam angle (α angle) on structural parameters as well as peak profile. X-ray diffraction patterns were registered in asymmetrical geometry, in which a parallel beam was formed by Soller and divergence slits. Lowering of the α angle results in accuracy decrease of lattice parameters as well as in significant broadening of a half-width of X-ray diffraction line.

Micro X-ray diffraction on capillary powder samples: a novel and effective technique for overcoming preferred orientation

2001 ◽  
Vol 34 (5) ◽  
pp. 663-665 ◽  
Author(s):  
P. Bergese ◽  
E. Bontempi ◽  
I. Colombo ◽  
L. E. Depero
Keyword(s):  
Structural Parameters ◽  
Preferred Orientation ◽  
X Ray Diffraction ◽  
Rapid Preparation ◽  
X Ray ◽  
Polymeric Carriers ◽  
Powder Samples ◽  
Promising Solution ◽  
Diffraction Patterns ◽  
Analytical Approaches

In past years, both experimental and analytical approaches have been developed for eliminating preferred orientation effects on powder X-ray diffraction patterns. The state of the art does not allow one to face the problem without difficult sample treatments, mechanical randomization, pole-figure study or pattern fitting based on the Rietveld approach. These methods are time consuming or need the knowledge of all the structural parameters, and, moreover, must be managed by specialized operators. Besides, none of the above techniques can be applied to powder samples of drugs loaded into polymeric carriers, the diffraction patterns of which present a structured amorphous halo from which the crystalline drug peaks rise up. In this paper, it is shown that micro X-ray diffraction on capillary powder samples, combined with a two-dimensional detector, is a promising solution to preferred orientation problems, since it provides easy and rapid preparation of randomly oriented powder samples, fast measurements (acquisition times of a few minutes) and correct powder diffraction patterns.

Microstructural evolution of mullites produced from single-phase gels

2007 ◽  
Vol 40 (2) ◽  
pp. 260-276 ◽  
Author(s):  
Marek Andrzej Kojdecki ◽  
Esther Ruiz de Sola ◽  
Francisco Javier Serrano ◽  
Estefanía Delgado-Pinar ◽  
María Mercedes Reventós ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Unit Cell ◽  
Molar Ratio ◽  
Model Parameters ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Transmission Electron ◽  
Diffraction Patterns

The crystalline microstructure of mullites obtained by heating monophasic gels has been investigated. Gels with alumina to silica molar ratio of 3:2 (as in secondary mullite) and 2:1 (as in primary mullite) were prepared by gelling mixtures of aluminium nitrate and tetraethylorthosilicate. Phase transformations were induced by heating the gel precursors, with different final treatment temperatures between 1173 and 1873 K. The mullites formed as a result of thermal treatment were studied by means of X-ray diffraction, scanning electron microscopy and transmission electron microscopy. The crystalline structure (unit-cell parameters) and microstructure were determined from X-ray diffraction patterns. The formation of mullites of homogeneous chemical composition and with unit-cell parameters depending almost linearly on the treatment temperature was found. Their compositions, expressed as alumina to silica molar ratio, were determined from the unit-cell parameters and were in the range of those characterizing primary and secondary mullites. Mullites processed at lower temperatures were accompanied by small amounts of vitreous phase. The crystalline microstructure of the obtained mullites was interpreted by means of a mathematical model of polycrystalline material, involving prevalent crystallite shape, volume-weighted crystallite size distribution and second-order crystalline lattice strain distribution as model parameters. The model parameters were determined for each sample by modelling its X-ray diffraction pattern and fitting it to a measured pattern. Bimodality of the size distribution was observed and explained as a consequence of two crystallite nucleation and growth processes, which started from small alumina-rich and alumina-poor domains, spontaneously formed in a precursor gel at early stages of heating. Images produced by scanning and transmission electron microscopy agreed well with the characteristics obtained from the analysis of the X-ray diffraction patterns.

scholarly journals Variations to Spin Crossover in [FexZn(1−x)(Me1,3bpp)2(ClO4)2] molecular alloys examined by Magnetometry and Single Crystal X-Ray Diffraction

2021 ◽  
Author(s):  
Rosa Diego ◽  
Olivier Roubeau ◽  
Guillem Aromí
Keyword(s):  
Single Crystal ◽  
Spin Crossover ◽  
Structural Parameters ◽  
Structural Data ◽  
X Ray Diffraction ◽  
Chemical Pressure ◽  
X Ray ◽  
Diffraction Patterns ◽  
Gradual Variation ◽  
Composition Changes

Spin crossover (SCO) active solid solutions with formula [FexZn1-x(Me1,3bpp)2](ClO4)2 (x = 0.10, 0.15, 0.22, 0.33, 0.41, 0.48, 0.56 and 0.64, Me1,3bpp is a bis-pyrazolylpyridine) and the complex [Zn(Me1,3bpp)2](ClO4)2 have been prepared and characterized by single crystal X-ray diffraction. The structural data and the powder diffraction patterns of all the compounds have been compared with the reported isostructural molecular crystal [Fe(Me1,3bpp)2](ClO4)2. Increasing amounts of Zn diminishes monotonically the cooperativity of the SCO of the parent Fe(II) complex (T1/2=183 K) and cause a decrease of T1/2 in line with the negative chemical pressure exerted by the Zn(II) complexes on the Fe(II) lattice. The gradual variation of the magnetic properties as the composition changes are paralleled by the evolution of the structural parameters at the molecular, intermolecular and crystal lattice scales. Thermal trapping of a portion of the Fe(II) centers of these alloys by quenching the crystals to 2 K unveils that, upon warming, the temperature of relaxation of the metastable states is almost constant for all compositions.

Relationships between Structural Parameters and Chemical Composition of Micas

Clay Minerals ◽  
1993 ◽  
Vol 28 (4) ◽  
pp. 603-624 ◽  
Author(s):  
B. B. Smoliar-Zviagin
Keyword(s):  
Chemical Composition ◽  
Structural Parameters ◽  
Regression Equations ◽  
X Ray Diffraction ◽  
Cell Parameters ◽  
Octahedral Cation ◽  
Structural Details ◽  
Diffraction Patterns ◽  
Experimental Values ◽  
Atomic Coordinates

AbstractRegression analysis of high-precision structural and chemical data on trioctahedral and dioctahedral micas yielded interrelationships between unit-cell parameters, chemical composition and structural details. Regression equations relating b and csinβ parameters of micas to composition were used for estimating composition from cell data in order to analyse P-T conditions of rock formation. Algorithms for computing atomic coordinates for 2M1 37' and 1M dioctahedral micas having either centrosymmetric or non-centrosymmetric layers and 1M trioctahedral micas are presented. Deviations of computed atomic coordinates from experimental values are, on average, 0·002 Å for octahedral cations and 0·005-0·010 Å for other atoms. Discrepancies between calculated and experimental individual interatomic distances seldom exceed 0·01 Å. Computed atomic coordinates were used to calculate X-ray diffraction patterns for glauconite and illite. Results indicate a close fit between the calculated and experimental patterns. The local structure around an octahedral cation of interest can be determined.

scholarly journals Enhancing the Visualization of Laue Diffraction for Analyzing Strength Model Parameters

2020 ◽  
Author(s):  
Ayan Biswas ◽  
David Walters ◽  
Devin Francom ◽  
Sky Sjue ◽  
Earl Lawrence ◽  
...  
Keyword(s):  
Ground Truth ◽  
Surrogate Models ◽  
Model Parameters ◽  
Fast Time ◽  
Domain Expert ◽  
X Ray Diffraction ◽  
X Ray ◽  
System P ◽  
Diffraction Patterns ◽  
Output Domain

X-ray diffraction is important for analyzing crystals and their structures. Since the simulated diffraction patterns are costly, surrogate models are developed to enable fast time-to-solution. However, surrogate models produce slightly different output from the ground truth (simulation). Understanding and exploring these differences easily is an important topic for materials scientists. Visual comparison of these differences is difficult because diffraction spots are often very sparse and occupy few pixels in the images. In this work, we propose to use Voronoi-based tessellations to enhance visualizations of diffraction patterns. We propose to use this method for exploration of individual images as well as for visualizing the differences between the emulated and simulated outputs. We use Cinema-based viewers for exploration of the analyzed output. Domain expert feedback is provided to validate the utility of the proposed visualization and exploration system.

Evaluation of Freezing Methods by Low Temperature X-Ray Diffraction

1977 ◽  
Vol 35 ◽  
pp. 330-333
Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello
Keyword(s):  
Biological Materials ◽  
Molecular Organization ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Rate Dependent ◽  
Before And After ◽  
Freeze Etching ◽  
Diffraction Patterns ◽  
Set Up

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.

Examination of Rabbit Fc Crystals

1968 ◽  
Vol 26 ◽  
pp. 140-141
Author(s):  
J. P. Robinson ◽  
P. G. Lenhert
Keyword(s):  
Molecular Weight ◽  
Flat Plate ◽  
Phosphate Buffer ◽  
Asymmetric Unit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutral Ph ◽  
Small Crystals ◽  
Carbon Coated ◽  
Diffraction Patterns

Crystallographic studies of rabbit Fc using X-ray diffraction patterns were recently reported. The unit cell constants were reported to be a = 69. 2 A°, b = 73. 1 A°, c = 60. 6 A°, B = 104° 30', space group P21, monoclinic, volume of asymmetric unit V = 148, 000 A°3. The molecular weight of the fragment was determined to be 55, 000 ± 2000 which is in agreement with earlier determinations by other methods.Fc crystals were formed in water or dilute phosphate buffer at neutral pH. The resulting crystal was a flat plate as previously described. Preparations of small crystals were negatively stained by mixing the suspension with equal volumes of 2% silicotungstate at neutral pH. A drop of the mixture was placed on a carbon coated grid and allowed to stand for a few minutes. The excess liquid was removed and the grid was immediately put in the microscope.

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