Geometry and algorithms to expand 2θ coverage of a 2D detector

2018 ◽  
Vol 33 (2) ◽  
pp. 147-155
Author(s):  
Bob B. He
Keyword(s):  
Intensity Distribution ◽  
Crystal Size ◽  
Structure Refinement ◽  
Phase Identification ◽  
Two Dimensional ◽  
Diffraction Intensity ◽  
2D Pattern ◽  
Multiple Frames ◽  
Scanned Images ◽  
Diffraction Patterns

A two-dimensional (2D) diffraction pattern is an image representing the diffraction intensity distribution over the detected area. For data evaluations of various materials characterization, such as phase identification, stress, texture, and crystal size, this distribution is further converted into the intensity distribution over 2θ or γ angles. For many applications, especially phase analysis and structure refinement, it is crucial for the two-dimensional (2D) pattern to have a large 2θ range sufficient to cover as many diffraction rings as necessary. The 2θ range covered by a 2D detector is determined by the size of the detector active area and the detector distance from the sample. In order to expand the 2θ coverage with a given 2D detector, one may collect several 2D frames at various swing angles and then merge the multiple frames, or scan the 2D detector over the desired 2θ range during the data collection. This paper introduces the geometry and algorithms to produce accurate 2D diffraction patterns with expanded 2θ coverages from multiple images or scanned images.

Materials characterization from diffraction intensity distribution in the γ-direction

2014 ◽  
Vol 29 (2) ◽  
pp. 113-117 ◽  
Author(s):  
Bob B. He
Keyword(s):  
Intensity Distribution ◽  
Crystal Size ◽  
Profile Analysis ◽  
Structure Refinement ◽  
Size Analysis ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
X Ray ◽  
Orientation Relations

Two-dimensional X-ray diffraction (XRD2) pattern can be described by the diffraction intensity distribution in both 2θ and γ-directions. The XRD2 images can be reduced to two kinds of profiles: 2θ-profile and γ-profile. The 2θ-profile can be evaluated for phase identification, crystal structure refinement, and many applications with many existing algorithms and software. In order to evaluate the materials structure associated with the intensity distribution along γ-angle, either the XRD2 pattern should be directly analyzed or the γ-profile can be generated by 2θ-integration. A γ-profile contains information on texture, stress, crystal size, and crystal orientation relations. This paper introduces the concept and fundamental algorithms for stress, texture, and crystal size analysis by the γ-profile analysis.

scholarly journals Gamma Profile Analysis for Stress, Texture and Grain Size

2014 ◽  
Vol 996 ◽  
pp. 209-214
Author(s):  
Bob B. He
Keyword(s):  
Grain Size ◽  
Crystal Size ◽  
Profile Analysis ◽  
Structure Refinement ◽  
Size Analysis ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
X Ray ◽  
2D Pattern

Two-dimensional X-ray diffraction pattern can be described by the diffraction intensity distribution in both 2θ and γ directions. The 2D pattern can be reduced to two kinds of profiles: 2θ-profile and γ-profile. The 2θ-profile can be evaluated for phase identification, crystal structure refinement and many applications with many existing algorithms and software. The γ-profile contains information on texture, stress, and crystal grain size. This article introduces the concept and fundamental algorithms for stress, texture and crystal size analysis by γ-profile analysis.

Algorithms of Two-Dimensional X-Ray Diffraction

MRS Advances ◽  
2016 ◽  
Vol 1 (26) ◽  
pp. 1921-1927
Author(s):  
Bob B. He
Keyword(s):  
Diffraction Pattern ◽  
Intensity Distribution ◽  
Structure Refinement ◽  
Azimuthal Angle ◽  
Bragg Angle ◽  
Phase Identification ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Diffraction Vector ◽  
X Ray

ABSTRACTX-ray diffraction pattern collected with two-dimensional detector contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be integrated to a conventional diffraction pattern and evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through the integration. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern can be expressed either in the laboratory coordinates or in the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation.

scholarly journals Algorithms for Two-dimensional XRD Data Evaluation

2014 ◽  
Vol 70 (a1) ◽  
pp. C1130-C1130
Author(s):  
Bob He
Keyword(s):  
Diffraction Pattern ◽  
Intensity Distribution ◽  
Profile Analysis ◽  
Bragg Angle ◽  
Phase Identification ◽  
Two Dimensional ◽  
Diffraction Vector ◽  
Diffraction Profile ◽  
X Ray ◽  
2D Pattern

The diffracted x-rays from a polycrystalline (powder) sample form a series diffraction cones in space since large numbers of crystals oriented randomly in the space are covered by the incident x-ray beam. Each diffraction cone corresponds to the diffraction from the same family of crystalline planes in all the participating grains. When a two-dimensional (2D) detector is used for x-ray powder diffraction, the diffraction cones are intercepted by the 2D detector and the x-ray intensity distribution on the sensing area is converted to an image-like diffraction pattern. The 2D pattern contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be analyzed directly or by data reduction to the intensity distribution along γ or 2θ. The γ-integration can reduce the 2D pattern into a diffraction profile analogs to the conventional diffraction pattern which is the diffraction intensity distribution as a function of 2θ angles. This kind of diffraction pattern can be evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through γ-integration. The intensity distribution and 2θ variations along γ contain more information, such as the orientation distribution, strain states, crystallite size and shape distribution. In order to understand and analyze 2D diffraction data, new approaches and algorithms are necessary. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern measured in the laboratory coordinates can be transformed to the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation by γ-profile analysis. The unit diffraction vector is also used in polarization and absorption correction.

Kinematical two-dimensional multiple-diffraction intensity profiles. Application to ω–ψ scans of silicon and diamond obtained with synchrotron radiation

2001 ◽  
Vol 34 (2) ◽  
pp. 157-165 ◽  
Author(s):  
E. Rossmanith ◽  
A Hupe ◽  
R. Kurtz ◽  
H. Schmidt ◽  
H.-G. Krane
Keyword(s):  
Synchrotron Radiation ◽  
Incident Beam ◽  
Mosaic Structure ◽  
Two Dimensional ◽  
Diffraction Intensity ◽  
Multiple Diffraction ◽  
Crystal Sample ◽  
Diffraction Patterns ◽  
Kinematical Theory

In a previous paper by Rossmanith [J. Appl. Cryst.(2000),33, 1405–1414], expressions for the calculation of multiple-diffraction patterns observed in ω–ψ scans of Bragg reflections were derived within the framework of the kinematical theory, taking into account the divergence and wavelength spread of the incident beam, as well as the mosaic structure of the crystal sample. Agreement with CuKα experiments was demonstrated. In this paper, it is shown that the theoretical expressions are also suitable for synchrotron radiation experiments.

scholarly journals Determination of crystal size distribution by two-dimensional X-ray diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C1131-C1131
Author(s):  
Alejandro Rodriguez-Navarro ◽  
Krzysztof Kudłacz
Keyword(s):  
Size Distribution ◽  
Crystal Size ◽  
High Sensitivity ◽  
Crystal Size Distribution ◽  
Polycrystalline Materials ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Area Detector ◽  
Diffraction Patterns

Polycrystalline materials properties and behaviour are ultimately determined by their crystallinity, phase composition and microstructure (i.e., crystal size, preferential orientation). Two-dimensional (2D) diffraction patterns collected with an area detector (i.e., CDD), available in modern X-ray diffractometers, contain detailed information about all these important material characteristics. Furthermore, recent advances in detector technologies permits the collection of high resolution diffraction patterns in which the microstructure of the material can be directly imaged. If the size of beam relative to the crystal size in the sample is adequately choosen, the diffraction pattern produced will have spotty rings in which the spots are the diffracted images of individual grains. The resolution of the image is mainly dependent on the characteristics of the X-ray beam (i.e., diameter, angular divergence), which can be modulated by X-ray optics, sample to detector distance, the pixel size of the detector and the sharpness of the point spread function. From these patterns, the crystal size distribution of different crystalline phases present in the sample can be independently determined using specialized software capable of extracting and combining the information contained in these patterns. This technique is applicable to materials with crystal sizes ranging from submicron to mm sizes and is complementary to techniques based on peak profile analyses (i.e., Scherrer method) which are applicable only to nanocrystalline materials. Finally, given the high sensitivity of current detectors, crystal size evolution can be followed in real-time to study important transformation processes such as crystallization, annealing, etc. The use of 2D X-ray diffraction as applied to microstructure characterization will be illustrated through several examples.

Kinematical two-dimensional multiple-diffraction intensity profiles. Application to ω–ψ scans obtained with CuKα radiation

2000 ◽  
Vol 33 (6) ◽  
pp. 1405-1414 ◽  
Author(s):  
Elisabeth Rossmanith
Keyword(s):  
Synchrotron Radiation ◽  
Incident Beam ◽  
Two Dimensional ◽  
Diffraction Intensity ◽  
Multiple Diffraction ◽  
Crystal Sample ◽  
X Ray ◽  
Diffraction Patterns ◽  
Kinematical Theory ◽  
Theoretical Results

Expressions for the calculation of multiple-diffraction patterns observed in ω–ψ scans of Bragg reflections are derived within the framework of the kinematical theory, taking into account the divergence and wavelength-spread of the incident beam as well as the mosaicity of the crystal sample. The theoretical results can be applied to X-ray tube radiation as well as synchrotron radiation experiments. A 189.9° experimental CuKα \bar2\bar2\bar2 ω–ψ scan of diamond is compared with the corresponding theoretical multiple-diffraction pattern.

Fast microstructure and phase analyses of nanopowders using combined analysis of transmission electron microscopy scattering patterns

2014 ◽  
Vol 70 (5) ◽  
pp. 448-456 ◽  
Author(s):  
P. Boullay ◽  
L. Lutterotti ◽  
D. Chateigner ◽  
L. Sicard
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Electron Diffraction ◽  
Structure Refinement ◽  
Pattern Search ◽  
Phase Identification ◽  
Combined Analysis ◽  
Transmission Electron ◽  
Diffraction Patterns

The full quantitative characterization of nanopowders using transmission electron microscopy scattering patterns is shown. This study demonstrates the feasibility of the application of so-called combined analysis, a global approach for phase identification, structure refinement, characterization of anisotropic crystallite sizes and shapes, texture analysis and texture variations with the probed scale, using electron diffraction patterns of TiO2and Mn3O4nanocrystal aggregates and platinum films. Electron diffraction pattern misalignments, positioning, and slight changes from pattern to pattern are directly integrated and refined within this approach. The use of a newly developed full-pattern search–match methodology for phase identification of nanopowders and the incorporation of the two-wave dynamical correction for diffraction patterns are also reported and proved to be efficient.

Polymorphic phase transition of a membrane protein - analysis of continuous diffuse electron diffraction intensity

1986 ◽  
Vol 44 ◽  
pp. 166-167
Author(s):  
Douglas L. Dorset ◽  
Andrew K. Massalski
Keyword(s):  
Molecular Sieve ◽  
Three Dimensional ◽  
Pore Geometry ◽  
Two Dimensional ◽  
Diffraction Intensity ◽  
Polymorphic Phase Transition ◽  
E Coli ◽  
Crystallographic Study ◽  
Hexagonal Form ◽  
Polymorphic Forms

Matrix porin, the ompF gene product of E. coli, has been the object of a electron crystallographic study of its pore geometry in an attempt to understand its function as a membrane molecular sieve. Three polymorphic forms have been found for two-dimensional crystals reconstituted in phospholipid, two hexagonal forms with different lipid content and an orthorhombic form coexisting with and similar to the hexagonal form found after lipid loss. In projection these have been shown to retain the same three-fold pore triplet geometry and analyses of three-dimensional data reveal that the small hexagonal and orthorhombic polymorphs have similar structure as well as unit cell spacings.

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