Systematic Errors in X-ray Diffractometer Stress Measurements Due to Specimen Geometry and Beam Divergence

1970 ◽  
Vol 14 ◽  
pp. 360-376 ◽  
Author(s):  
Harry Zantopulos ◽  
Chester F. Jatczak
Keyword(s):  
Tensile Stress ◽  
Systematic Errors ◽  
Beam Divergence ◽  
Convex Shape ◽  
Computer Data ◽  
X Ray ◽  
Stress Measurements ◽  
Beam Focusing ◽  
Horizontal Beam ◽  
Beam Geometry

AbstractA method is described for determining the magnitude and sense of systematic errors in x-ray diffractometer stress measurements produced by focusing aberrations during diffraction from imperfect specimen contours and wide horizontal beam divergences. Corrections for such systematic errors are presently not made. However, if the highest accuracy and/or absolute values of stress are desired, these must be either taken into account or minimized by control of beam geometry. Equations and computer data are presented to indicate the errors in 2θ and stress (σ) resulting from use of flat, various convex and concave curvatures for primary beam divergences of 1° to 3°, Stress errors are calculated for both the parafocus technique of beam focusing and the stationary or non-focusing method.The results show that convex and flat specimens always produce negative 2θ deviations from the condition of perfect focus and thus a net positive or tensile stress error. The magnitude of this error increases as the radius of the convex shape decreases and/or the ψangle and beam divergence is increased. Concave specimens with curvatures less than the radius of the concave shape required for perfect focus (see body of report) produce positive 2θ deviations and, therefore, negative or com-pressive stress errors.The stationary or non-focusing technique produced systematic errors which were 1/3 of those produced by focusing aberrations with the parafocus technique. Fortunately, in both cases the actual errors are not very large (less than ±7.5 ksi), even with divergent beams as large as 3° and convex radii as small as 125”.

The adaptation of a Philips PW1050 X-ray diffractometer system to incorporate an incident beam focusing monochromator: Design, assembly and characterisation

1996 ◽  
Vol 11 (4) ◽  
pp. 290-296
Author(s):  
I. C. Madsen ◽  
R. J. Hill ◽  
G. Stereff
Keyword(s):  
High Resolution ◽  
Incident Beam ◽  
Base Plate ◽  
Knife Edge ◽  
Beam Path ◽  
X Ray ◽  
Beam Focusing ◽  
Horizontal Beam ◽  
Structure Solution ◽  
Resolution Single

A conventional vertical powder diffractometer has been adapted to allow the collection of high-resolution, single-wavelength diffraction data using Co, Cu or Mo radiation. The major modifications are (i) incorporation of an incident beam focusing monochromator attached to the tube shield, (ii) a variable tilt angle of the tube shield to provide a horizontal beam path through the diffractometer (for ease of alignment), (iii) mounting of the entire diffractometer on a single, very stable base-plate, with micrometer-controlled adjustment of the orientation, (iv) inclusion of a knife-edge, micrometer-controlled focusing slit, and (v) use of a range of Soller slits with acceptance angles down to 1.5° 2φ. The performance of the instrument compares favourably with conventional non-monochromated diffractometer data collected from SRM660 LaB6 and monoclinic ZrO2. In particular, the peaks are more symmetric and have narrower widths, and the peak-to-background ratio is much higher, leading to much superior resolution and profile shapes for structure solution and Rietveld refinement.

Application of a single-reflection collimating multilayer optic for X-ray diffraction experiments employing parallel-beam geometry

2008 ◽  
Vol 41 (1) ◽  
pp. 124-133 ◽  
Author(s):  
M. Wohlschlögel ◽  
T. U. Schülli ◽  
B. Lantz ◽  
U. Welzel
Keyword(s):  
Incident Beam ◽  
Grazing Incidence ◽  
Photon Flux ◽  
Data Sets ◽  
Parallel Beam ◽  
X Ray ◽  
Beam Focusing ◽  
Beam Geometry ◽  
Parallel Beam Geometry ◽  
Diffraction Patterns

Instrumental aberrations of a parallel-beam diffractometer equipped with a rotating anode X-ray source, a single-reflection collimating multilayer optic and a parallel-plate collimator in front of the detector have been investigated on the basis of standard measurements (i.e.employing stress- and texture-free isotropic powder specimens exhibiting small or negligible structural diffraction line broadening). It has been shown that a defocusing correction, which is a major instrumental aberration for diffraction patterns collected with divergent-beam (focusing) geometries, is unnecessary for this diffractometer. The performance of the diffractometer equipped with the single-reflection collimating multilayer optic (single-reflection mirror) is compared with the performance of the diffractometer equipped with a Kirkpatrick–Baez optic (cross-coupled Göbel mirror) on the basis of experimental standard measurements and ray-tracing calculations. The results indicate that the use of the single-reflection mirror provides a significant gain in photon flux and brilliance. A high photon flux, high brilliance and minimal divergence of the incident beam make the setup based on the single-reflection mirror particularly suitable for grazing-incidence diffraction, and thus for the investigation of very thin films (yielding low diffracted intensities) and of stress and texture (requiring the acquisition of large measured data sets, corresponding to the variation of the orientation of the diffraction vector with respect to the specimen frame of reference). A comparative discussion of primary optics which can be used to realise parallel-beam geometry shows the range of possible applications of parallel-beam diffractometers and indicates the virtues and disadvantages of the different optics.

scholarly journals Development of a crystal collimation system for high-resolution ultra-small-angle X-ray scattering applications

2019 ◽  
Vol 26 (2) ◽  
pp. 439-444 ◽  
Author(s):  
Michael Sztucki ◽  
Joachim Leonardon ◽  
Pierre Van Vaerenbergh ◽  
Jacques Gorini ◽  
Peter Boesecke ◽  
...  
Keyword(s):  
High Resolution ◽  
Small Angle ◽  
Polystyrene Latex ◽  
Beam Divergence ◽  
X Ray ◽  
Horizontal Beam ◽  
X Ray Scattering ◽  
Collimation System ◽  
Set Up ◽  
Ray Scattering

Crystal collimation offers a viable alternative to the commonly used pinhole collimation in small-angle X-ray scattering (SAXS) for specific applications requiring highest angular resolution. This scheme is not affected by the parasitic scattering and diffraction-limited beam broadening. The Darwin width of the rocking curve of the crystals mainly defines the ultimate beam divergence. For this purpose, a dispersive Si-111 crystal collimation set-up based on two well conditioned pseudo channel-cut crystals (pairs of well polished, independent parallel crystals) using a higher-order reflection (Si-333) has been developed. The gain in resolution is obtained at the expense of flux. The system has been installed at the TRUSAXS beamline ID02 (ESRF) for reducing the horizontal beam divergence in high-resolution mesurements. The precise mechanics of the system allows reproducible alignment of the Bragg condition. The high resolution achieved at a sample–detector distance of 31 m is demonstrated by ultra-small-angle X-ray scattering measurements on a model system consisting of micrometre-sized polystyrene latex particles with low polydispersity.

Spatial resolution of X-ray microanalysis in thin foils

1978 ◽  
Vol 36 (1) ◽  
pp. 544-545
Author(s):  
R. Hutchings ◽  
I.P. Jones ◽  
M.H. Loretto ◽  
R.E. Smallman
Keyword(s):  
Spatial Resolution ◽  
Electron Probe ◽  
Beam Divergence ◽  
Inelastic Interaction ◽  
Specimen Thickness ◽  
High Current ◽  
Beam Spreading ◽  
X Ray ◽  
Thin Foils ◽  
Complex Calculation

There is increasing interest in X-ray microanalysis of thin specimens and the present paper attempts to define some of the factors which govern the spatial resolution of this type of microanalysis. One of these factors is the spreading of the electron probe as it is transmitted through the specimen. There will always be some beam-spreading with small electron probes, because of the inevitable beam divergence associated with small, high current probes; a lower limit to the spatial resolution is thus 2αst where 2αs is the beam divergence and t the specimen thickness.In addition there will of course be beam spreading caused by elastic and inelastic interaction between the electron beam and the specimen. The angle through which electrons are scattered by the various scattering processes can vary from zero to 180° and it is clearly a very complex calculation to determine the effective size of the beam as it propagates through the specimen.

Synchrotron X-Ray Topography Study on the Relationship between Local Basal Plane Bending and Basal Plane Dislocations in PVT-Grown 4H-SiC Substrate Wafers

2020 ◽  
Vol 1004 ◽  
pp. 393-400
Author(s):  
Tuerxun Ailihumaer ◽  
Hongyu Peng ◽  
Balaji Raghothamachar ◽  
Michael Dudley ◽  
Gilyong Chung ◽  
...  
Keyword(s):  
Basal Plane ◽  
Local Strain ◽  
Grazing Incidence ◽  
Peak Shift ◽  
Linear Mapping ◽  
Incidence Geometry ◽  
Convex Shape ◽  
X Ray ◽  
Black And White ◽  
Plane Bending

Synchrotron monochromatic beam X-ray topography (SMBXT) in grazing incidence geometry shows black and white contrast for basal plane dislocations (BPDs) with Burgers vectors of opposite signs as demonstrated using ray tracing simulations. The inhomogeneous distribution of these dislocations is associated with the concave/convex shape of the basal plane. Therefore, the distribution of these two BPD types were examined for several 6-inch diameter 4H-SiC substrates and the net BPD density distribution was used for evaluating the nature and magnitude of basal plane bending in these wafers. Results show different bending behaviors along the two radial directions - [110] and [100] directions, indicating the existence of non-isotropic bending. Linear mapping of the peak shift of the 0008 reflection along the two directions was carried out using HRXRD to correlate with the results from the SMBXT measurements. Basal-plane-tilt angle calculated using the net BPD density derived from SMBXT shows a good correlation with those obtained from HRXRD measurements, which further confirmed that bending in basal plane is caused by the non-uniform distribution of BPDs. Regions of severe bending were found to be associated with both large tilt angles (95% black contrast BPDs to 5% white contrast BPDs) and abrupt changes in a and c lattice parameters i.e. local strain.

scholarly journals Radiation dose estimation for pencil beam X-ray luminescence computed tomography imaging

2021 ◽  
pp. 1-12
Author(s):  
Ignacio O. Romero ◽  
Changqing Li
Keyword(s):  
Computed Tomography ◽  
Radiation Dose ◽  
Small Animal ◽  
Pencil Beam ◽  
Computed Tomography Imaging ◽  
Step Size ◽  
Imaging Protocol ◽  
X Ray ◽  
Beam Geometry ◽  
Muscle Tissues

BACKGROUND: Pencil beam X-ray luminescence computed tomography (XLCT) imaging provides superior spatial resolution than other imaging geometries like sheet beam and cone beam geometries. However, the pencil beam geometry suffers from long scan times, resulting in concerns overdose which discourages the use of pencil beam XLCT. OBJECTIVE: The dose deposited in pencil beam XLCT imaging was investigated to estimate the dose from one angular projection scan with three different X-ray sources. The dose deposited in a typical small animal XLCT imaging was investigated. METHODS: A Monte Carlo simulation platform, GATE (Geant4 Application for Tomographic Emission) was used to estimate the dose from one angular projection scan of a mouse leg model with three different X-ray sources. Dose estimations from a six angular projection scan by three different X-ray source energies were performed in GATE on a mouse trunk model composed of muscle, spine bone, and a tumor. RESULTS: With the Sigray source, the bone marrow of mouse leg was estimated to have a radiation dose of 44 mGy for a typical XLCT imaging with six angular projections, a scan step size of 100 micrometers, and 106 X-ray photons per linear scan. With the Sigray X-ray source and the typical XLCT scanning parameters, we estimated the dose of spine bone, muscle tissues, and tumor structures of the mouse trunk were 38.49 mGy, 15.07 mGy, and 16.87 mGy, respectively. CONCLUSION: Our results indicate that an X-ray benchtop source (like the X-ray source from Sigray Inc.) with high brilliance and quasi-monochromatic properties can reduce dose concerns with the pencil beam geometry. Findings of this work can be applicable to other imaging modalities like X-ray fluorescence computed tomography if the imaging protocol consists of the pencil beam geometry.

Service Loading Analysis of Wind Turbine Gearbox Rolling Bearings Based on X-Ray Diffraction Residual Stress Measurements

2013 ◽  
Vol 768-769 ◽  
pp. 723-732 ◽  
Author(s):  
Jürgen Gegner ◽  
Wolfgang Nierlich
Keyword(s):  
Residual Stress ◽  
Wind Turbine ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
X Ray Diffraction ◽  
Rolling Bearings ◽  
Wind Turbine Gearbox ◽  
X Ray ◽  
Stress Measurements

Rolling bearings in wind turbine gearboxes occasionally fail prematurely by so-called white etching cracks. The appearance of the damage indicates brittle spontaneous tensile stress induced surface cracking followed by corrosion fatigue driven crack growth. An X-ray diffraction based residual stress analysis reveals vibrations in service as the root cause. The occurrence of high local friction coefficients in the rolling contact is described by a tribological model. Depth profiles of the equivalent shear and normal stresses are compared with residual stress patterns and a relevant fracture strength, respectively. White etching crack failures are reproduced on a rolling contact fatigue test rig under increased mixed friction. Causative vibration loading is evident from residual stress measurements. Cold working compressive residual stresses are an effective countermeasure.

scholarly journals Semi-automated protein crystal mounting device for the sulfur single-wavelength anomalous diffraction method

2010 ◽  
Vol 43 (2) ◽  
pp. 341-346 ◽  
Author(s):  
Yu Kitago ◽  
Nobuhisa Watanabe ◽  
Isao Tanaka
Keyword(s):  
Diffraction Method ◽  
Systematic Errors ◽  
Protein Crystal ◽  
X Rays ◽  
Anomalous Diffraction ◽  
X Ray ◽  
Frozen Solution ◽  
Custom Made ◽  
Protein Molecules ◽  
X Ray Absorption

Use of longer-wavelength X-rays has advantages for the detection of small anomalous signals from light atoms, such as sulfur, in protein molecules. However, the accuracy of the measured diffraction data decreases at longer wavelengths because of the greater X-ray absorption. The capillary-top mounting method (formerly the loopless mounting method) makes it possible to eliminate frozen solution around the protein crystal and reduces systematic errors in the evaluation of small anomalous differences. However, use of this method requires custom-made tools and a large amount of skill. Here, the development of a device that can freeze the protein crystal semi-automatically using the capillary-top mounting method is described. This device can pick up the protein crystal from the crystallization drop using a micro-manipulator, and further procedures, such as withdrawal of the solution around the crystal by suction and subsequent flash freezing of the protein crystal, are carried out automatically. This device makes it easy for structural biologists to use the capillary-top mounting method for sulfur single-wavelength anomalous diffraction phasing using longer-wavelength X-rays.

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