scholarly journals Assignment of enantiomorphs for the chiral allotrope β-Mn by diffraction methods

2021 ◽  
Vol 7 (20) ◽  
pp. eabg0868
Author(s):  
Ulrich Burkhardt ◽  
Aimo Winkelmann ◽  
Horst Borrmann ◽  
Andreea Dumitriu ◽  
Markus König ◽  
...  
Keyword(s):  
Quantitative Comparison ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Distribution Maps ◽  
Kikuchi Pattern ◽  
Spatially Resolved ◽  
Pattern Simulation ◽  
Related Phase

The assignment of enantiomorphs by diffraction methods shows fundamental differences for x-rays and electrons. This is particularly evident for the chiral allotrope of β-Mn. While it is not possible to determine the sense of chirality of β-Mn with established x-ray diffraction methods, Kikuchi pattern simulation of the enantiomorphs reveals differences, if dynamical electron diffraction is considered. Quantitative comparison between experimental and simulated Kikuchi patterns allows the spatially resolved assignment of the enantiomorph in polycrystalline materials of β-Mn, as well as the structurally strongly related phase Pt2Cu3B. On the basis of enantiomorph distribution maps, crystals were extracted from enantiopure domains by micropreparation techniques. The x-ray diffraction analyses confirm the assignment of the Kikuchi pattern evaluations for Pt2Cu3B and do not allow to distinguish between the enantiomorphs of β-Mn.

Micro Diffraction Imaging of Bulk Polycrystalline Materials

2006 ◽  
Vol 524-525 ◽  
pp. 273-278
Author(s):  
Thomas Wroblewski ◽  
A. Bjeoumikhov ◽  
Bernd Hasse
Keyword(s):  
High Spatial Resolution ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Short Sample ◽  
X Ray ◽  
Detector Distance ◽  
Transmission Geometry ◽  
Diffraction Imaging ◽  
Position Sensitive

X-ray diffraction imaging applies an array of parallel capillaries in front of a position sensitive detector. Conventional micro channel plates of a few millimetre thickness have successfully been used as collimator arrays but require short sample to detector distances to achieve high spatial resolution. Furthermore, their limited absorption restricts their applications to low energy X-rays of around 10 keV. Progress in the fabrication of long polycapillaries allows an increase in the sample to detector distance without decreasing resolution and the use of high X-ray energies enables bulk investigations in transmission geometry.

2D real space visualization of d values in polycrystalline bulk materials of different hardness

2021 ◽  
Vol 54 (2) ◽  
pp. 597-603
Author(s):  
Mari Mizusawa ◽  
Kenji Sakurai
Keyword(s):  
Lattice Distortion ◽  
Structural Information ◽  
Hardness Test ◽  
Real Space ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
D Values

Conventional X-ray diffraction measurements provide some average structural information, mainly on the crystal structure of the whole area of the given specimen, which might not be very uniform and may include different crystal structures, such as co-existing crystal phases and/or lattice distortion. The way in which the lattice plane changes due to strain also might depend on the position in the sample, and the average information might have some limits. Therefore, it is important to analyse the sample with good lateral spatial resolution in real space. Although various techniques for diffraction topography have been developed for single crystals, it has not always been easy to image polycrystalline materials. Since the late 1990s, imaging technology for fluorescent X-rays and X-ray absorption fine structure has been developed via a method that does not scan either a sample or an X-ray beam. X-ray diffraction imaging can be performed when this technique is applied to a synchrotron radiation beamline with a variable wavelength. The present paper reports the application of X-ray diffraction imaging to bulk steel materials with varying hardness. In this study, the distribution of lattice distortion of hardness test blocks with different hardness was examined. Via this 2D visualization method, the grains of the crystals with low hardness are large enough to be observed by X-ray diffraction contrast in real space. The change of the d value in the vicinity of the Vickers mark has also been quantitatively evaluated.

X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

Standard Deviations in X-Ray Stress and Elastic Constants Due to Counting Statistics

1988 ◽  
Vol 32 ◽  
pp. 377-388 ◽  
Author(s):  
Masanori Kurita
Keyword(s):  
Elastic Constants ◽  
Stress Measurement ◽  
Steel Specimen ◽  
Polycrystalline Materials ◽  
X Rays ◽  
Confidence Limits ◽  
X Ray Diffraction ◽  
X Ray ◽  
Standard Deviations ◽  
Counting Statistics

AbstractX-ray diffraction can be used to nondestructively measure residual stress of polycrystalline materials. In x-ray stress measurement, it is important to determine a stress constant experimentally in order to measure the stress accurately. However, every value measured by x-ray diffraction has statistical errors arising from counting statistics. The equations for calculating the standard deviations of the stress constant and elastic constants measured by x-rays are derived analytically in order to ascertain the reproducibility of the measured values. These standard deviations represent the size of the variability caused by counting statistics, and can be calculated from a single set of measurements by using these equations. These equations can apply Lu any meuhud for x-ray stress ifiesuremenL. The variances of the x-ray stress and elastic constants are expressed in terms of the linear combinations of the variances of the peak position. The confidence limits of these constants of a quenched and tempered steel specimen were determined by the Gaussian curve method. The 95% confidence limits of the stress constant were -314 ± 25 MFa/deg.

Three-Dimensional X-Ray Diffraction Microscopy Using High-Energy X-Rays

MRS Bulletin ◽  
2004 ◽  
Vol 29 (3) ◽  
pp. 166-169 ◽  
Author(s):  
Henning F. Poulsen ◽  
Dorte Juul Jensen ◽  
Gavin B.M. Vaughan
Keyword(s):  
Materials Science ◽  
Three Dimensional ◽  
High Energy ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Reconstruction Methods ◽  
The Individual ◽  
Individual Grains

AbstractThree-dimensional x-ray diffraction (3DXRD) microscopy is a tool for fast and nondestructive characterization of the individual grains, subgrains, and domains inside bulk materials. The method is based on diffraction with very penetrating hard x-rays (E ≥ 50 keV), enabling 3D studies of millimeter-to-centimeter-thick specimens.The position, volume, orientation, and elastic and plastic strain can be derived for hundreds of grains simultaneously. Furthermore, by applying novel reconstruction methods, 3D maps of the grain boundaries can be generated. The 3DXRD microscope in use at the European Synchrotron Radiation Facility in Grenoble, France, has a spatial resolution of ∼5 μm and can detect grains as small as 150 nm. The technique enables, for the first time, dynamic studies of the individual grains within polycrystalline materials. In this article, some fundamental materials science applications of 3DXRD are reviewed: studies of nucleation and growth kinetics during recrystallization, recovery, and phase transformations, as well as studies of polycrystal deformation.

Analysis of stresses and crystal structure in the surface layer of hexagonal polycrystalline materials: a new methodology based on grazing incidence diffraction

2016 ◽  
Vol 49 (1) ◽  
pp. 85-102 ◽  
Author(s):  
Marianna Marciszko ◽  
Andrzej Baczmański ◽  
Chedly Braham ◽  
Mirosław Wróbel ◽  
Wilfrid Seiler ◽  
...  
Keyword(s):  
Synchrotron Radiation ◽  
Stress Gradient ◽  
Grazing Incidence ◽  
Lattice Parameter ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Surface Layers ◽  
X Ray ◽  
Good Agreement

The multireflection grazing-incidence X-ray diffraction (MGIXD) method is commonly used to determine a stress gradient in thin surface layers (about 1–20 µm for metals). In this article, the development of MGIXD to enable the determination not only of stresses but also of thec/aratio and thea0strain-free lattice parameter in hexagonal polycrystalline materials is presented and tested. The new procedure was applied for the results of measurements performed using a laboratory X-ray diffractometer and synchrotron radiation. The evolution of stresses and lattice parameters with depth was determined for Ti and Ti-alloy samples subjected to different mechanical surface treatments. A very good agreement of the results obtained using three different wavelengths of synchrotron radiation as well as classical X-rays (CuKα radiation) was found.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

scholarly journals Spatially Resolved Forming Mechanisms Detection in Single Point Incremental Forming Using Synchrotron Based Texture Analysis

2021 ◽  
Author(s):  
Mateus Dobecki ◽  
Alexander Poeche ◽  
Walter Reimers
Keyword(s):  
Texture Analysis ◽  
Incremental Forming ◽  
Single Point ◽  
High Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Forming Mechanism ◽  
Spatially Resolved ◽  
Step Down ◽  
Stress States

AbstractDespite the ongoing success of understanding the deformation states in sheets manufactured by single-point incremental forming (SPIF), the unawareness of the spatially resolved influence of the forming mechanisms on the residual stress states of incrementally formed sheet metal parts impedes their application-optimized use. In this study, a well-founded experimental proof of the occurring forming mechanisms shear, bending and stretching is presented using spatially resolved, high-energy synchrotron x-ray diffraction-based texture analysis in transmission mode. The measuring method allows even near-surface areas to be examined without any impairment of microstructural influences due to tribological reactions. The depth-resolved texture evolution for different sets of forming parameters offers insights into the forming mechanisms acting in SPIF. Therefore, the forming mechanisms are triggered explicitly by adjusting the vertical step-down increment Δz for groove, plate and truncated cone geometries. The texture analysis reveals that the process parameters and the specimen geometries used lead to characteristic changes in the crystallites’ orientation distribution in the formed parts due to plastic deformation. These forming-induced reorientations of the crystallites could be assigned to the forming mechanisms by means of defined reference states. It was found that for groove, plate and truncated cone geometries, a decreasing magnitude of step-down increments leads to a more pronounced shear deformation, which causes an increasing work hardening especially at the tool contact area of the formed parts. Larger step-down increments, on the other hand, induce a greater bending deformation. The plastic deformation by bending leads to a complex stress field that involves alternating residual tensile stresses on the tool and residual compressive stresses on the tool-averted side incrementally formed sheets. The present study demonstrates the potential of high-energy synchrotron x-ray diffraction for the spatially resolved forming mechanism research in SPIF. Controlling the residual stress states by optimizing the process parameters necessitates knowledge of the fundamental forming mechanism action.

Phase composition depth profiles using spatially resolved energy dispersive X-ray diffraction

2004 ◽  
Vol 37 (6) ◽  
pp. 967-976 ◽  
Author(s):  
Andrew C. Jupe ◽  
Stuart R. Stock ◽  
Peter L. Lee ◽  
Nikhila N. Naik ◽  
Kimberly E. Kurtis ◽  
...  
Keyword(s):  
Phase Composition ◽  
Spatial Resolution ◽  
Zinc Coating ◽  
High Energy ◽  
Sulfate Attack ◽  
Energy Dispersive ◽  
X Ray Diffraction ◽  
X Ray ◽  
Spatially Resolved ◽  
Composition Profiles

Spatially resolved energy dispersive X-ray diffraction, using high-energy synchrotron radiation (∼35–80 keV), was used nondestructively to obtain phase composition profiles along the radii of cylindrical cement paste samples to characterize the progress of the chemical changes associated with sulfate attack on the cement. Phase distributions were acquired to depths of ∼4 mm below the specimen surface with sufficient spatial resolution to discern features less than 200 µm thick. The experimental and data analysis methods employed to obtain quantitative composition profiles are described. The spatial resolution that could be achieved is illustrated using data obtained from copper cylinders with a thin zinc coating. The measurements demonstrate that this approach is useful for nondestructively visualizing the sometimes complex transformations that take place during sulfate attack on cement-based materials. These transformations can be spatially related to microstructure as seen by computed microtomography.

Investigation of the phase shift in X-ray forward diffraction using an X-ray interferometer

1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose
Keyword(s):  
Phase Shift ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bragg Geometry

The phase shift of forward-diffracted X-rays by a perfect crystal is discussed on the basis of the dynamical theory of X-ray diffraction. By means of a triple Laue-case X-ray interferometer, the phase shift of forward-diffracted X-rays by a silicon crystal in the Bragg geometry was investigated.

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