The Effects of Using Long Soller Slits as “Parallel Beam Optics” for Gixrd on Diffraction Data

AbstractGrazing incidence x-ray diffraction (GIXRD) using long soller slit assemblies and a flat crystal monochromator, sometimes referred to as thin film optics, are used to study poly crystal line thin films, polymers, metals, etc. The unique ability of GIXRD to characterize crystalline materials as function of depth and provide accurate strain measurements has lead to the growing popularity of this technique. This non-focusing pseudo-parallel beam geometry can produce various effects on diffraction data which can make interpretation difficult Artifacts such as peak splitting, kα2 distortion, and peaks which shift dramatically as a function of grazing incidence angle are observed when using GIXRD. These artifacts can be related to grazing incidence angle, the divergence of the soller plates, the thickness of the soller plates, the substrate material, and the type of monochromator used. This paper briefly describes some of the topics discussed at the 1992 & 1993 Denver Conferences workshops on parallel beam optics.

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

Journal of Applied Crystallography ◽

10.1107/s0021889807050005 ◽

2008 ◽

Vol 41 (1) ◽

pp. 124-133 ◽

Cited By ~ 24

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.

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The Sensitivity of Focusing, Parallel Beam and Mixed Optics to Alignment Errors in XRD Residual Stress Measurements

Materials Science Forum ◽

10.4028/www.scientific.net/msf.490-491.131 ◽

2005 ◽

Vol 490-491 ◽

pp. 131-136 ◽

Cited By ~ 5

Author(s):

Arnold C. Vermeulen

Keyword(s):

Residual Stress ◽

Incident Beam ◽

Peak Position ◽

Beam Optics ◽

Parallel Beam ◽

Stress Measurements ◽

Beam Geometry ◽

Position Sensitivity ◽

Parallel Beam Geometry ◽

Alignment Errors

The sensitivity of various combinations of optics to alignment errors is investigated. A large number of tests with varying specimen displacements and incident beam misalignments are performed for both line and point focus residual stress optics combinations. This investigation includes experiments with mixed combinations of typical “focusing beam optics” and “parallel beam optics”. It is verified if the peak positions are either sensitive to height errors like for the focusing beam geometry or insensitive like for the parallel beam geometry. The peak position sensitivity is classified for all combinations of incident beam and diffracted beam optics modules.

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Effects of Misalignment of Parallel Beam Optics on Thin Film Stress Analysis

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.996.141 ◽

2014 ◽

Vol 996 ◽

pp. 141-146

Author(s):

Nicholas Norberg ◽

Arnold C. Vermeulen

Keyword(s):

Significant Error ◽

Film Stress ◽

Alignment Error ◽

Beam Optics ◽

X Ray Diffraction ◽

Parallel Beam ◽

X Ray ◽

Thin Film Stress ◽

Beam Geometry ◽

Parallel Beam Geometry

Collecting reliable data is crucial in the research of residual stresses in thin films using X-ray diffraction. The parallel beam geometry has advantage of reliability compared to focusing beam geometry. Though care must be taken to the alignment. A small alignment error may cause a significant error in the stress value. We will show the sensitivity for the misalignment of the parallel beam optics, discuss requirements on hardware alignment and demonstrate a software correction for the presence of remaining hardware errors.

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Interface-sensitive imaging by an image reconstruction aided X-ray reflectivity technique

Journal of Applied Crystallography ◽

10.1107/s160057671700509x ◽

2017 ◽

Vol 50 (3) ◽

pp. 712-721 ◽

Cited By ~ 5

Author(s):

Jinxing Jiang ◽

Keiichi Hirano ◽

Kenji Sakurai

Keyword(s):

Ultrathin Films ◽

Incidence Angle ◽

Grazing Incidence ◽

Two Dimensional ◽

Plane Angle ◽

Pixel Size ◽

Parallel Beam ◽

X Ray ◽

Area Detector ◽

Grazing Incidence Angle

Recently, the authors have succeeded in realizing X-ray reflectivity imaging of heterogeneous ultrathin films at specific wavevector transfers by applying a wide parallel beam and an area detector. By combining in-plane angle and grazing-incidence angle scans, it is possible to reconstruct a series of interface-sensitive X-ray reflectivity images at different grazing-incidence angles (proportional to wavevector transfers). The physical meaning of a reconstructed X-ray reflectivity image at a specific wavevector transfer is the two-dimensional reflectivity distribution of the sample. In this manner, it is possible to retrieve the micro-X-ray reflectivity (where the pixel size is on the microscale) profiles at different local positions on the sample.

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The Effects of Using Long Soller Slits as “Parallel Beam Optics” for GIXRD on Diffraction Data

Advances in X-Ray Analysis ◽

10.1007/978-1-4615-2528-8_22 ◽

1994 ◽

pp. 167-173 ◽

Cited By ~ 4

Author(s):

Michael O. Eatough ◽

Raymond P. Goehner

Keyword(s):

Diffraction Data ◽

Beam Optics ◽

Parallel Beam

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X-ray Diffraction Studies of Polycrystalline Thin Films Using Glancing Angle Diffractometry

Advances in X-ray Analysis ◽

10.1154/s0376030800020620 ◽

1988 ◽

Vol 32 ◽

pp. 311-321 ◽

Cited By ~ 2

Author(s):

R.A. Larsen ◽

T.F. McNulty ◽

R.P. Goehner ◽

K.R. Crystal

Keyword(s):

Thin Films ◽

Deep Penetration ◽

X Ray Diffraction ◽

Parallel Beam ◽

X Ray ◽

Beam Geometry ◽

Polycrystalline Thin Films ◽

Glancing Angle ◽

Parallel Beam Geometry

AbstractThe use of conventional θ/2θ diffraction methods for the characterization of polycrystalline thin films is not in general a satisfactory technique due to the relatively deep penetration of x-ray photons in most materials. Glancing incidence diffraction (GID) can compensate for the penetration problems inherent in the θ/2θ geometry. Parallel beam geometry has been developed in conjunction with GID to eliminate the focusing aberrations encountered when performing these types of measurements. During the past yearwe developed a parallel beam attachment which we have successfully configured to a number of systems.

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Inverse Fourier Transform in the Gamma Coordinate System

International Journal of Biomedical Imaging ◽

10.1155/2011/285130 ◽

2011 ◽

Vol 2011 ◽

pp. 1-16

Author(s):

Yuchuan Wei ◽

Hengyong Yu ◽

Ge Wang

Keyword(s):

Fourier Transform ◽

Coordinate System ◽

Inverse Fourier Transform ◽

Rotation Axis ◽

General Scheme ◽

Weight Functions ◽

Projection Data ◽

Parallel Beam ◽

Beam Geometry ◽

Parallel Beam Geometry

This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.

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