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.

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.

Introduction to two-dimensional X-ray diffraction

2003 ◽  
Vol 18 (2) ◽  
pp. 71-85 ◽  
Author(s):  
Bob Baoping He
Keyword(s):  
Diffraction Pattern ◽  
Diffraction Data ◽  
Data Reduction ◽  
Data Interpretation ◽  
Phase Identification ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Texture Measurement ◽  
One Dimensional ◽  
X Ray

Two-dimensional X-ray diffraction refers to X-ray diffraction applications with two-dimensional detector and corresponding data reduction and analysis. The two-dimensional diffraction pattern contains far more information than a one-dimensional profile collected with the conventional diffractometer. In order to take advantage of two-dimensional diffraction, new theories and approaches are necessary to configure the two-dimensional X-ray diffraction system and to analyze the two-dimensional diffraction data. This paper is an introduction to some fundamentals about two-dimensional X-ray diffraction, such as geometry convention, diffraction data interpretation, and advantages of two-dimensional X-ray diffraction in various applications, including phase identification, stress, and texture measurement.

scholarly journals Comment on ‘Multilayered Stable 2D Nano-Sheets of Ti2NTx MXene: Synthesis, Characterization, and Anticancer Activity’

2020 ◽  
Author(s):  
Yitong Guo ◽  
Qianku Hu ◽  
Libo Wang ◽  
Aiguo Zhou
Keyword(s):  
Anticancer Activity ◽  
Diffraction Pattern ◽  
Hydrofluoric Acid ◽  
Recent Article ◽  
Room Temperature ◽  
Max Phase ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray

<p>A recent article entitled “Multilayered stable 2D nano-sheets of Ti<sub>2</sub>NT<sub>x</sub> MXene: synthesis, characterization, and anticancer activity” published in this journal, claimed that two-dimensional Ti<sub>2</sub>NT<sub>x</sub> MXene could be synthesized by selectively etching Ti<sub>2</sub>AlN in concentrated hydrofluoric acid at room temperature. However, the X-ray diffraction pattern of Ti<sub>2</sub>NT<sub>x</sub> MXene reported in that paper is completely different with those of other MXenes. In this comment, it is argued that the samples synthesized in that paper were NOT Ti<sub>2</sub>NT<sub>x</sub> MXene at all. Although carbide MXenes can be made by selectively etching A layers from MAX phase, it is very difficult or impossible to make nitride MXenes (Ti<sub>2</sub>NT<sub>x</sub>) by the same way.</p>

A computer-based method of measuring the integrated intensities of the reflections on the X-ray diffraction photograph of an oriented crystalline polymer

1987 ◽  
Vol 20 (3) ◽  
pp. 246-255 ◽  
Author(s):  
I. H. Hall ◽  
J. Z. Neisser ◽  
M. Elder
Keyword(s):  
Intensity Distribution ◽  
Statistical Tests ◽  
Structure Refinement ◽  
Intensity Variation ◽  
Crystalline Polymer ◽  
Background Intensity ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Photograph ◽  
Integrated Intensities

The method is designed to be used with a batch-processing computer system and will determine the integrated intensities of the spots on an X-ray diffraction photograph of an oriented fibre of a partially crystalline synthetic polymer. It is necessary to assume that the spot boundary is elliptical, that the intensity distribution along any line through the centre of this ellipse is Gaussian, and that the background intensity variation is linear over the region of a spot; these are justified experimentally, although, in the radial direction, the choice of a Gaussian intensity distribution is probably theoretically unsound. The computational procedures correct for minor differences between users in the choice of input parameters and reject bad choices. The method was applied to determine the intensities of the 30 visible spots in the diffraction photograph of oriented poly(trimethyleneterephthalate) which were used in a subsequent structure refinement. successful integrations were obtained for 22 spots, the failures being (1) pairs of similar intensity just resolved by eye, (2) better resolved pairs of which one member is stronger than the other, or (3) very weak. Statistical tests indicated very much better internal consistency of data than is usually obtained with these materials, and enabled a rational weighting scheme to be used in the structure refinement. The R factor of 7.9% obtained is unusually low, indicating much improved accuracy over earlier methods.

scholarly journals Comment on ‘Multilayered Stable 2D Nano-Sheets of Ti2NTx MXene: Synthesis, Characterization, and Anticancer Activity’

2020 ◽  
Author(s):  
Yitong Guo ◽  
Qianku Hu ◽  
Libo Wang ◽  
Aiguo Zhou
Keyword(s):  
Anticancer Activity ◽  
Diffraction Pattern ◽  
Hydrofluoric Acid ◽  
Recent Article ◽  
Room Temperature ◽  
Max Phase ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray

<p>A recent article entitled “Multilayered stable 2D nano-sheets of Ti<sub>2</sub>NT<sub>x</sub> MXene: synthesis, characterization, and anticancer activity” published in this journal, claimed that two-dimensional Ti<sub>2</sub>NT<sub>x</sub> MXene could be synthesized by selectively etching Ti<sub>2</sub>AlN in concentrated hydrofluoric acid at room temperature. However, the X-ray diffraction pattern of Ti<sub>2</sub>NT<sub>x</sub> MXene reported in that paper is completely different with those of other MXenes. In this comment, it is argued that the samples synthesized in that paper were NOT Ti<sub>2</sub>NT<sub>x</sub> MXene at all. Although carbide MXenes can be made by selectively etching A layers from MAX phase, it is very difficult or impossible to make nitride MXenes (Ti<sub>2</sub>NT<sub>x</sub>) by the same way.</p>

X-ray diffraction with a Bragg angle near π/2 and its applications

1998 ◽  
Vol 5 (3) ◽  
pp. 670-672 ◽  
Author(s):  
S. Kikuta ◽  
Y. Imai ◽  
T. Iizuka ◽  
Y. Yoda ◽  
X.-W. Zhang ◽  
...  
Keyword(s):  
High Resolution ◽  
Diffraction Pattern ◽  
Thin Plate ◽  
Bragg Angle ◽  
Lattice Plane ◽  
X Ray Diffraction ◽  
X Ray ◽  
Face To Face ◽  
Very High ◽  
Diffraction Condition

X-ray dynamical diffraction phenomena at a Bragg angle near π/2 are studied. The X-ray transmissivity as well as the reflectivity from the (991) lattice plane of a silicon thin plate is observed. It agrees fairly well with the diffraction pattern calculated on the basis of the Darwin approach. The possibility is discussed whether a set of two crystal plates arranged face to face, in which the diffraction condition with a Bragg angle near π/2 is satisfied, may be used as a very high resolution monochromator.

scholarly journals Texture and Lamellae Distribution Functions in Lamellar Eutectics

1986 ◽  
Vol 6 (4) ◽  
pp. 265-287 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
X Rays ◽  
Two Dimensional ◽  
Absorption Factor ◽  
X Ray Diffraction ◽  
Diffraction Vector ◽  
X Ray ◽  
Pole Figures

The crystallographic orientation distribution and the geometrical lamellae orientation distribution in lamellar eutectics are, in general, not independent of each other. The combined orientation-lamellae distribution function depends on five angular parameters. X-ray diffraction in such eutectics may exhibit an anisotropic macroscopic absorption factor if the penetration depth of the X-rays is large compared with their planar size. As a consequence, the reflected X-ray intensity may depend on a third angle γ, i.e. a rotation of the sample about the diffraction vector s additionally to the usual pole figure angles α, β which describe the orientation of the diffraction vector s with respect to the sample coordinate system. It is thus necessary to measure three-dimensional generalized pole figures instead of conventional two-dimensional ones.

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