The Angular Shift of the Transmitted X‐Ray Beam near the Bragg Angle

Different structural [Formula: see text] coatings were designed and deposited on WC-Co cemented carbide by the technology of multiarc ion plating. Monolayered [Formula: see text] coating was deposited using cathode of [Formula: see text]. Multilayered (Ti,Al)N/[Formula: see text] coating and [Formula: see text] coating with gradual silicon content were deposited using two cathodes of [Formula: see text] and [Formula: see text] simultaneously. The surface and cross-section morphology, compositions, and phase structure were characterized by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The dense [Formula: see text] coatings with droplets on the surface and without obvious columnar structure on the cross-sections were obtained. All coatings had the strong peaks of (200) orientation. The different angular shift occurred with different combination of cathodes and processes. The introduction of multilayered and gradient structure effectively reduced the lattice distortion of coatings. Meanwhile, the coating-substrate adhesion strength increased from 38.57 N to 60.17 N with a coating thickness of approximately 3.5 [Formula: see text]m by scratch tests. The highest hardness of [Formula: see text] coating obtained in this paper were [Formula: see text] GPa by nanoindentation. The multilayered coating showed better toughness.

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Nonlinear Equations for High Accuracy X-Ray Crystal Orientation

Advances in X-ray Analysis ◽

10.1154/s0376030800009411 ◽

1991 ◽

Vol 35 (A) ◽

pp. 681-685 ◽

Cited By ~ 1

Author(s):

Danut Dragoi

Keyword(s):

Nonlinear Equations ◽

Crystal Orientation ◽

High Accuracy ◽

Bragg Angle ◽

Large Area ◽

X Ray ◽

Linear System Of Equations ◽

Several Variables ◽

Points Of View ◽

Non Linear System

AbstractNonlinear equations are given for determining the crystallographic orientation of surfaces of single crystals. The equations are solved by an iterative method in several variables. The angle ϕ between the surface plane and the lattice plane in question is decomposed into two components α and β. These two components are obtained from the solution of a non-linear system of equations using two measurements and the Bragg angle. The diffractometric system considered is the well known θ/2θ with a sufficiently large area of x-ray detection and the capability of holding single crystal samples. The results obtained are discussed from experimental and theoretical points of view.

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X-Ray Spectrographic Analysis of the 3-d Transition Metal Corrosion Products Using Potassium Bromide Disks*

Advances in X-ray Analysis ◽

10.1154/s0376030800002834 ◽

1963 ◽

Vol 7 ◽

pp. 590-597

Author(s):

L. A. Schluter

Keyword(s):

Pulse Height ◽

Weight Ratio ◽

Internal Standard ◽

Corrosion Products ◽

Metal Corrosion ◽

Small Samples ◽

Bragg Angle ◽

X Ray ◽

Calibration Curves ◽

Intensity Ratios

AbstractA technique has been developed for quantitative analysis of the major constituents in small samples (less than 0.1 g) of corrosion products found On various missile parts. The technique was developed primarily to aid in interpretation of X-ray diffraction patterns of multicomponent corrosion products. The corrosion sample is mixed with KBr and the mixture is pressed into a disk in the same fashion commonly used in infrared work. The Br Kβ1 line serves as an internal standard. Intensities of the element's Kα line and the internal standard are established by scanning through the appropriate Bragg angle and recording peak heights on a strip-chart recorder. A xenon-filled proportional detector and a pulse-height analyzer were used.The percent of an element is determined by references to calibration curves which relate intensity ratios to weight ratios for the 3-d transition metals. The oxides of the metals were used in the preparation of the calibration curves. The weight ratio vs. intensity ratio relationship is linear over the weight ratio range 0.01 to 0.11. Data were collected using an air path and a helium path; the higher intensity ratios obtained with, the helium path, and the dependence of intensity on atomic number are illustrated. A comparison is made between the intensity ratios in a KBr matrix and in a NaBr matrix. The technique developed requires about 15 min sample preparation time.

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An Area-Imaging Proportional Counter for X-Ray Diffraction

Advances in X-ray Analysis ◽

10.1154/s0376030800007278 ◽

1980 ◽

Vol 24 ◽

pp. 161-166 ◽

Cited By ~ 1

Author(s):

C. Richard Desper ◽

Ronald Burns

Keyword(s):

Data Acquisition ◽

Proportional Counter ◽

Orientation Angle ◽

Polymeric Materials ◽

Bragg Angle ◽

Acquisition Time ◽

Time Interval ◽

X Ray Diffraction ◽

Oriented Polymers ◽

X Ray

Slow data acquisition rates have, in the past, limited the use of X-ray diffraction for characterization of polymeric materials. Photon counting techniques yield quantitative data in digital form for computer analysis. However, a great deal of data acquisition time is required when data is taken sequentially; i.e., when each intensity determination (at a particular goniometer setting) requires a separate time interval, during which intensity at other angle values is ignored. The problem is particularly acute for oriented polymers since two or more diffraction angles are involved: The Bragg angle along with at least one orientation angle. For this reason, an area-imaging (two-dimensional) proportional counter has been developed for use with a four-circle X-ray diffraction system. Although basically a single-crystal unit, this goniometer has been used in this laboratory and others for studies of oriented polymers. The receiving pinhole collimator and aperture have been removed, and the area-imaging counter has been mounted on the detector arm track. The original receiving aperture is still used for alignment, and the area detector Is positioned with its center at the receiving aperture center position.

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Estimating the structure factors in X-ray diffraction

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273318007593 ◽

2018 ◽

Vol 74 (5) ◽

pp. 481-498 ◽

Cited By ~ 2

Author(s):

Paul F. Fewster

Keyword(s):

Diffraction Theory ◽

Bragg Angle ◽

Enhancement Effect ◽

Diffraction Effect ◽

X Ray Diffraction ◽

Acta Cryst ◽

X Ray ◽

Background Removal ◽

Structure Factors ◽

Path Lengths

This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.

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On the dilatation of synthetic type Ib diamond by substitutional nitrogen impurity

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1991.0135 ◽

1991 ◽

Vol 337 (1648) ◽

pp. 497-520 ◽

Cited By ~ 46

Keyword(s):

Infrared Absorption ◽

Infrared Absorption Spectrum ◽

Internal Standard ◽

Optical Microscope ◽

Lattice Parameter ◽

Bragg Angle ◽

Growth Sector ◽

Double Crystal ◽

X Ray ◽

Nitrogen Impurity

Sequences of high Bragg-angle (0 B = 74°) double-crystal X-ray topographs taken at the SRS (Daresbury, U.K.) have yielded precise measurements of lattice parameter differences between growth sectors of different crystallographic forms in a large undoped synthetic diamond whose type Ib infrared absorption spectrum (principal peak at 1130 cm -1 ) indicated atomically dispersed nitrogen, singly substituting for carbon, as the only detectable impurity. The plate-shaped specimen, polished parallel to (110), 5.0 x 3.2 mm 2 in area, 0.7 mm thick, possessed an unusually well developed (110) growth sector containing nitrogen impurity concentration of only ca. 10 -6 , which served as an internal standard of pure-diamond lattice parameter with which lattice parameters of nitrogen-containing growth sectors were compared. The specimen’s suitability for precision diffractometry was checked by comprehensive tests using optical microscope techniques, cathodoluminescence and single-crystal X-ray topography. The double-crystal combination was silicon reference crystal, asymmetric 175 reflection, with diamond specimen symmetrical 440 reflection. The principal measurement was the increase of the lattice parameter, a 0 , of the (111) growth sector (nitrogen content 88 + 7 parts per 10 6 atomic) relative to that of the (110) sector: Aa 0 / a 0 = 1.18 + 0.07 x 10 -5 . In terms of measured infrared absorption coefficient at 1130 cm -1 , this gives Aa 0/a 0 = (2.95 + 0.27) x 10 -6 [p(1130 cm -1 )/cm -1 ], which is believed to hold for growth sectors of all crystallographic forms. Combination with the nitrogen assay findings of Woods, van Wyk & Collins ( Phil. Mag. B 62. 589-595 (1990)) provides a direct relation to c N , the fractional atomic concentration of substitutional nitrogen, as A a 0 / a 0 = (0.14 + 0.02) c N , which indicates that the effective volume of a single substitutional nitrogen atom in diamond is 1.41 +0.06 times that of the carbon atom it replaces. This substantial dilatation conflicts with several models for the substitutional nitrogen structure.

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X-ray backscattering (diffraction at a Bragg angle of π/2): A review

Crystallography Reports ◽

10.1134/s1063774512050094 ◽

2012 ◽

Vol 57 (5) ◽

pp. 628-647 ◽

Cited By ~ 2

Author(s):

V. V. Lider

Keyword(s):

Bragg Angle ◽

X Ray

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Diffraction studies under in situ electric field using a large-area hybrid pixel XPAD detector

Journal of Applied Crystallography ◽

10.1107/s0021889813013903 ◽

2013 ◽

Vol 46 (4) ◽

pp. 1151-1161 ◽

Cited By ~ 24

Author(s):

Pierre Fertey ◽

Paul Alle ◽

Emmanuel Wenger ◽

Bernard Dinkespiler ◽

Olivier Cambon ◽

...

Keyword(s):

Electric Field ◽

Single Crystals ◽

Operation Mode ◽

Bragg Angle ◽

Weak Electric Field ◽

Structural Variations ◽

Large Area ◽

X Ray ◽

Off Pump

A new experimental approach to perform in situ electric field diffraction on single crystals using an on-then-off pump–probe mode in situ (i.e. the field-switching method) with a synchrotron or a laboratory X-ray source is presented. Taking advantage of the fast readout of the XPAD hybrid pixel two-dimensional detector and its programmable functionalities, the operation mode of the detector has been customized to significantly increase the efficiency of the method. The very weak electric field-induced structural response of a piezoelectric crystal can be accurately measured. This allows the piezoelectric tensor to be precisely obtained from Δθ shifts while the structural variations can be modelled using a full set of ΔI/I data. The experimental method and methodology are detailed and tested as a case study on pure piezoelectric compounds belonging to the α-quartz family (SiO2 and GaAsO4 single crystals). Using the two scan modes developed, it is demonstrated that tiny Bragg angle shifts can be measured as well as small field-induced Bragg intensity variations (<1%). The relevance of measurements performed with an X-ray laboratory source is demonstrated: partial data sets collected at synchrotrons can be completed, but more interestingly, a large part of the study can now be realized in the laboratory (medium to strong intensity reflections) in a comparable data collection time.

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