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.

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.

X-Ray Diffraction Study of Shock-Modified Tetragonal Phases of SnO2 and MnO2

1992 ◽  
Vol 36 ◽  
pp. 595-601
Author(s):  
P. Newcomer ◽  
B. Morosin ◽  
R. A. Graham
Keyword(s):  
Shock Loading ◽  
Crystal Size ◽  
Lattice Strain ◽  
Profile Analysis ◽  
Line Profile Analysis ◽  
X Ray Diffraction ◽  
Pressure Shock ◽  
X Ray ◽  
Diffraction Line Profile ◽  
Coherent Crystal

AbstractX-ray diffraction line-profile analysis on tetragonal forms of SnO2 (cassiterite), MnO2 (pyrolusite), and previously studied TiO2 (rutile), which were subjected to high pressure shock loading, show that residual lattice strain and coherent “crystal” size are a function of shock parameters. An interesting observation on a sample of MnO2 concerns the recovery of cubic Mn2O3 (bixbyite) in the material subjected to 22 GPa, indicating a shock-induced chemical synthesis.

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.

Determination of dispersion and polarization of thermal plane waves in crystals

1971 ◽  
Vol 134 (3-4) ◽  
Author(s):  
P. L. La Fleur
Keyword(s):  
Intensity Distribution ◽  
Phonon Scattering ◽  
Reciprocal Lattice ◽  
Plane Waves ◽  
Lattice Points ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Reciprocal Lattice Point ◽  
X Ray

AbstractThe dispersion of the thermal plane waves (phonons) in crystals can be determined from the x-ray diffraction intensity distribution around a reciprocal lattice point. In the method presented here no higher-order phonon-scattering corrections are necessary. It is shown furthermore that polarizations and dispersion of the phonons can be determined from the intensity distributions around six properly chosen reciprocal lattice points.

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.

scholarly journals Study on the Electrical, Structural, Chemical and Optical Properties of PVD Ta(N) Films Deposited with Different N2 Flow Rates

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 937
Author(s):  
Yingying Hu ◽  
Md Rasadujjaman ◽  
Yanrong Wang ◽  
Jing Zhang ◽  
Jiang Yan ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Optical Properties ◽  
Photoelectron Spectroscopy ◽  
Crystal Size ◽  
Silicon Substrates ◽  
X Ray Diffraction ◽  
Dc Magnetron Sputtering ◽  
Flow Rates ◽  
X Ray ◽  
N2 Flow Rate

By reactive DC magnetron sputtering from a pure Ta target onto silicon substrates, Ta(N) films were prepared with different N2 flow rates of 0, 12, 17, 25, 38, and 58 sccm. The effects of N2 flow rate on the electrical properties, crystal structure, elemental composition, and optical properties of Ta(N) were studied. These properties were characterized by the four-probe method, X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and spectroscopic ellipsometry (SE). Results show that the deposition rate decreases with an increase of N2 flows. Furthermore, as resistivity increases, the crystal size decreases, the crystal structure transitions from β-Ta to TaN(111), and finally becomes the N-rich phase Ta3N5(130, 040). Studying the optical properties, it is found that there are differences in the refractive index (n) and extinction coefficient (k) of Ta(N) with different thicknesses and different N2 flow rates, depending on the crystal size and crystal phase structure.

scholarly journals Mining Wastes of an Albite Deposit as Raw Materials for Vitrified Mullite Ceramics

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 232
Author(s):  
Pedro J. Sánchez-Soto ◽  
Eduardo Garzón ◽  
Luis Pérez-Villarejo ◽  
George N. Angelopoulos ◽  
Dolores Eliche-Quesada
Keyword(s):  
Particle Size ◽  
Raw Materials ◽  
Phase Evolution ◽  
Particle Size Analysis ◽  
Size Analysis ◽  
Mining Wastes ◽  
X Ray Diffraction ◽  
X Ray ◽  
Maximum Value

In this work, an examination of mining wastes of an albite deposit in south Spain was carried out using X-ray Fluorescence (XRF), X-ray diffraction (XRD), particle size analysis, thermo-dilatometry and Differential Thermal Analysis (DTA) and Thermogravimetric (TG) analysis, followed by the determination of the main ceramic properties. The albite content in two selected samples was high (65–40 wt. %), accompanied by quartz (25–40 wt. %) and other minor minerals identified by XRD, mainly kaolinite, in agreement with the high content of silica and alumina determined by XRF. The content of Na2O was in the range 5.44–3.09 wt. %, being associated with albite. The iron content was very low (<0.75 wt. %). The kaolinite content in the waste was estimated from ~8 to 32 wt. %. The particle size analysis indicated values of 11–31 wt. % of particles <63 µm. The ceramic properties of fired samples (1000–1350 °C) showed progressive shrinkage by the thermal effect, with water absorption and open porosity almost at zero at 1200–1250 °C. At 1200 °C, the bulk density reached a maximum value of 2.38 g/cm3. An abrupt change in the phase evolution by XRD was found from 1150 to 1200 °C, with the disappearance of albite by melting in accordance with the predictions of the phase diagram SiO2-Al2O3-Na2O and the system albite-quartz. These fired materials contained as main crystalline phases quartz and mullite. Quartz was present in the raw samples and mullite was formed by decomposition of kaolinite. The observation of mullite forming needle-shape crystals was revealed by Scanning Electron Microscopy (SEM). The formation of fully densified and vitrified mullite materials by firing treatments was demonstrated.

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