Crystal truncation rod X-ray scattering: exact dynamical calculation

2008 ◽  
Vol 41 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Václav Holý ◽  
Paul F. Fewster
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Lattice Points ◽  
Space Distribution ◽  
Matrix Formalism ◽  
X Ray ◽  
Transmission Coefficients ◽  
X Ray Scattering ◽  
Crystal Truncation Rod ◽  
Scattering Geometry

A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a non-coplanar scattering geometry.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
V. V. Lizunov
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Three Dimensions ◽  
X Ray ◽  
X Ray Scattering ◽  
Diffraction Geometry ◽  
Lattice Space ◽  
Integrated Intensities ◽  
Ray Scattering

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

Fundamentals of Kinematical X-Ray Scattering Theory

2014 ◽  
pp. 1-14
Keyword(s):  
Scattering Theory ◽  
Profile Analysis ◽  
Reciprocal Lattice ◽  
Line Profile Analysis ◽  
X Ray ◽  
X Ray Scattering ◽  
Basic Concepts ◽  
Lattice Planes ◽  
The Relationship ◽  
Ray Scattering

The broadening of X-ray line profiles is usually described by the kinematical scattering theory. In this chapter, the basic concepts and equations of the kinematical X-ray scattering are presented in order to better understand the theory of line profile analysis. The correlation between the crystal structure and the diffracted intensity distribution is shown. The scattering angles of the diffracted peak maxima are given by the Ewald construction in the reciprocal space. The correspondence between the reciprocal lattice vectors and the lattice planes is also presented, and the relationship between the scattering angle and the lattice plane spacing is given by Bragg’s law.

Protein crystals can be incommensurately modulated

2008 ◽  
Vol 41 (3) ◽  
pp. 600-605 ◽  
Author(s):  
Jeffrey J. Lovelace ◽  
Cameron R. Murphy ◽  
Lee Daniels ◽  
Kartik Narayan ◽  
Clarence E. Schutt ◽  
...  
Keyword(s):  
Diffraction Pattern ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Chemical Crosslinking ◽  
X Ray Diffraction ◽  
X Ray ◽  
Periodic State ◽  
Orientation Matrix ◽  
Aperiodic Crystals ◽  
Future Work

For a normal periodic crystal, the X-ray diffraction pattern can be described by an orientation matrix and a set of three integers that indicate the reciprocal lattice points. Those integers determine the spacing along the reciprocal lattice directions. In aperiodic crystals, the diffraction pattern is modulated and the standard periodic main reflections are surrounded by satellite reflections. The successful indexing and refinement of the main unit cell andqvector usingTWINSOLVE, developed by Svensson [(2003). Lund University, Sweden], are reported here for an incommensurately modulated, aperiodic crystal of a profilin:actin complex. The indexing showed that the modulation is along thebdirection in the crystal, which corresponds to an `actin ribbon' formed by the crystal lattice. Interestingly, the transition to the aperiodic state was shown to be reversible and the diffraction pattern returned to the periodic state during data collection. It is likely that the protein underwent a conformational change that affected the neighbouring profilin:actin molecules in such a way as to produce the observed modulation in the diffraction pattern. Future work will aim to trap the incommensurately modulated crystal state, for example using cryocooling or chemical crosslinking, thus allowing complete X-ray data to be collected.

scholarly journals X-ray scattering from a plane parallel slab using radiation transfer considerations

2020 ◽  
Vol 53 (5) ◽  
pp. 1236-1242
Author(s):  
Stanislav Stoupin
Keyword(s):  
Radiation Transfer ◽  
Slab Thickness ◽  
X Ray ◽  
Total Attenuation ◽  
Plane Parallel ◽  
X Ray Scattering ◽  
Scattering Geometry ◽  
Transfer Equations ◽  
Intensity Transfer ◽  
Ray Scattering

The X-ray scattering power of a plane parallel homogeneous slab of material is derived using radiation intensity transfer equations. The scattering power scales with the ratio of the scattering coefficient of interest to the total attenuation coefficient. The results can be used to guide the choice of slab thickness, scattering geometry and photon energy to maximize the scattering power in both elastic and inelastic X-ray scattering experiments.

X-Ray Investigation of Strain Relaxation in Short-Period SimGen Superlattices using Reciprocal Space Mapping

1993 ◽  
Vol 298 ◽  
Author(s):  
P. Hamberger ◽  
E. Koppensteiner ◽  
G. Bauer ◽  
H. Kibbel ◽  
H. Presting ◽  
...  
Keyword(s):  
Strain Relaxation ◽  
Reciprocal Lattice ◽  
Reciprocal Space ◽  
Lattice Points ◽  
Reciprocal Space Mapping ◽  
Double Crystal ◽  
X Ray ◽  
Short Period ◽  
Integrated Intensity ◽  
Strained Layer Superlattices

AbstractThe optoelectronic properties of SimGen strained layer superlattices (SLS's) depend strongly on the structural perfection. We used double crystal and triple axis x-ray diffractometry to characterize the structural properties of short period Si9Ge6 SLS's grown on about lμm thick step-graded SiGe alloy buffers. As grown SLS's and samples annealed subsequently at 550°C, 650°C and 780°C for 60 mmn were investigated. Precise strain data were extracted from two-dimensional reciprocal space maps around (004) and (224) reciprocal lattice points. These data were used as refined input parameters for the dynamical simulation of the integrated intensity along the qll[004] direction. Annealing causes interdiffusion as indicated by the decreasing superlattice (SL)-satellite peak intensities and by the change of the Si/Ge thickness ratio. However, the full width at half maximum of the SL satellite peaks does not change significantly with annealing up to 650°C. The in-plane SL lattice constant in both samples is increased only slighty by annealing (< 9×10−3 Å). Consequently the interface intermixing due to interdiffusion is the main cause for the shift of the luminescence energy to higher values in these annealed samples.

High-pressure developments for resonant X-ray scattering experiments at I16

2020 ◽  
Vol 27 (2) ◽  
pp. 351-359
Author(s):  
I. Povedano ◽  
A. Bombardi ◽  
D. G. Porter ◽  
M. Burt ◽  
S. Green ◽  
...  
Keyword(s):  
High Pressure ◽  
Low Temperature ◽  
The Body ◽  
X Ray ◽  
X Ray Scattering ◽  
Scattering Geometry ◽  
Diamond Anvil ◽  
Membrane Cell ◽  
Ray Scattering

An experimental setup to perform high-pressure resonant X-ray scattering (RXS) experiments at low temperature on I16 at Diamond Light Source is presented. The setup consists of a membrane-driven diamond anvil cell, a panoramic dome and an optical system that allows pressure to be measured in situ using the ruby fluorescence method. The membrane cell, inspired by the Merrill–Bassett design, presents an asymmetric layout in order to operate in a back-scattering geometry, with a panoramic aperture of 100° in the top and a bottom half dedicated to the regulation and measurement of pressure. It is specially designed to be mounted on the cold finger of a 4 K closed-cycle cryostat and actuated at low-temperature by pumping helium into the gas membrane. The main parts of the body are machined from a CuBe alloy (BERYLCO 25) and, when assembled, it presents an approximate height of 20–21 mm and fits into a 57 mm diameter. This system allows different materials to be probed using RXS in a range of temperatures between 30 and 300 K and has been tested up to 20 GPa using anvils with a culet diameter of 500 µm under quasi-cryogenic conditions. Detailed descriptions of different parts of the setup, operation and the developed methodology are provided here, along with some preliminary experimental results.

Spin and Orbital Magnetic Moment of Pd3Co Evaluated by X-Ray Magnetic Diffraction Experiment

2010 ◽  
Vol 459 ◽  
pp. 3-6
Author(s):  
Masahisa Ito ◽  
Yoshiaki Oba ◽  
Ayako Sato ◽  
Kosuke Suzuki ◽  
Tatsuki Tadenuma ◽  
...  
Keyword(s):  
Magnetic Moment ◽  
Reciprocal Lattice ◽  
Form Factors ◽  
Dipole Approximation ◽  
Magnetization Measurement ◽  
Lattice Points ◽  
Diffraction Experiment ◽  
X Ray ◽  
Orbital Magnetic Moment ◽  
Magnetic Form Factors

We have measured spin and orbital magnetic form factors of Pd3Co for various reciprocal lattice points by the X-ray magnetic diffraction. Observed spin and orbital magnetic form factors are fitted by theoretical curves of the isolated atomic model under the dipole approximation. By the fitting analysis we have evaluated separately the spin and orbital component of the magnetic moment of Pd3Co alloy as 2.19 µB/f.u. and 0.83 µB/f.u., respectively. The total magnetic moment 3.02 µB/f.u. is comparable to the value of 2.93 µB/f.u. obtained by the magnetization measurement.

scholarly journals Grazing-Transmission Scattering for Measuring Nano-structured Thin Films

2014 ◽  
Vol 70 (a1) ◽  
pp. C876-C876
Author(s):  
Kevin Yager
Keyword(s):  
Thin Films ◽  
Data Analysis ◽  
Small Angle ◽  
Three Dimensional ◽  
Object Size ◽  
X Ray ◽  
X Ray Scattering ◽  
Lattice Symmetry ◽  
Scattering Geometry ◽  
Nanoscale Order

We describe a new scattering geometry which can be used to quantify three-dimensional nanoscale order in thin films: Grazing-Transmission Small-Angle X-ray Scattering (GTSAXS). This technique collects sub-horizon scattering which exits from the edge of the sample, and does not suffer from the large refraction-distortions and multiple-scattering terms that complicate GISAXS data analysis. We also present a new modelling formalism applicable to superlattices of nano-objects, where lattice symmetry and nano-object size/shape can be arbitrarily defined.

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