Multiple Bragg Scattering and the Phase Problem in X-Ray Diffraction: Perfect Crystals

Author(s):  
R. Colella
Author(s):  
Н.Л. Лунина ◽  
N.L. Lunina

Advances in the methodology of the X-ray diffraction experiments leads to a possibility to register the rays scattered by large isolated biological particles (viruses and individual cells) but not only by crystalline samples. The experiment with an isolated particle provides researchers with the intensities of the scattered rays for the continuous spectrum of scattering vectors. Such experiment gives much more experimental data than an experiment with a crystalline sample where the information is limited to a set of Bragg reflections. This opens up additional opportunities in solving underlying problem of X-ray crystallography, namely, calculating phase values for the scattered waves needed to restore the structure of the object under study. In practice, the original continuous diffraction pattern is sampled, reduced to the values at grid points in the space of scattering vectors (in the reciprocal space). The sampling step determines the amount of the information involved in solving the phase problem and the complexity of the necessary calculations. In this paper, we investigate the effect of the sampling step on the accuracy of the phase problem solution obtained by the method proposed earlier by the authors. It is shown that an expected improvement of the accuracy of the solution with the reducing the sampling step continues even after crossing the Nyquist limit defined as the inverse of the double size of the object under study.


1987 ◽  
Vol 191 (3) ◽  
pp. L825-L834 ◽  
Author(s):  
Toshio Takahashi ◽  
Shinichiro Nakatani ◽  
Tetsuya Ishikawa ◽  
Seishi Kikuta

2008 ◽  
Vol 64 (a1) ◽  
pp. C109-C109
Author(s):  
P.F. Lyman ◽  
V.L. Shneerson ◽  
R. Fung ◽  
R.J. Harder ◽  
S.S. Parihar ◽  
...  

2021 ◽  
Vol 54 (4) ◽  
Author(s):  
Thomas Tran ◽  
Xiaorong Weng ◽  
Marcel Hennes ◽  
Dominique Demaille ◽  
Alessandro Coati ◽  
...  

It is shown that information on the spatial correlation of nano-objects embedded in a crystalline matrix can be retrieved by analysing the X-ray scattering around the Bragg reflections of the host matrix. Data are reported for vertically aligned Ni and CoNi alloy nanowires (NWs) in an SrTiO3 matrix. When the Bragg condition is fulfilled for the matrix and not for the NWs, the latter can be approximated by voids, and the scattering around the matrix reflections contains information on the self-correlation of the NWs (i.e. on their diameter d) and on the correlation between NWs (interdistance D). Nondestructive synchrotron X-ray diffraction data provide information on these values averaged over large areas, complementing local transmission electron microscopy observations. The measurements show that off-Bragg scattering around the matrix reflections can be exploited to study the spatial correlation and morphology of embedded nano-objects, independently of their crystallinity or strain or the presence of defects.


1994 ◽  
Vol 376 ◽  
Author(s):  
P.S. Pershan

ABSTRACTThe phase problem that troubles x-ray diffraction is also a problem for x-ray and neutron reflectivity; however, there are a range of small angles just beyond the critical angle for which the reflectivity contains information on the phase of the surface scattering amplitude. In principle this phase information can be used to determine the asymmetry of the normal gradient of the scattering amplitude density. We discuss here practical conditions under which this symmetry can, or cannot, be extracted from reflectivity data.


1995 ◽  
Vol 73 (5-6) ◽  
pp. 209-218 ◽  
Author(s):  
J. Katsaras

This brief review of the X-ray diffraction technique used to study oriented lipid bilayer systems is primarily intended to demonstrate to the nonspecialist in the lipid field the amount of detailed information that can be obtained simply by visually inspecting the diffraction pattern and making some measurements with a ruler and protractor. The information that can be extracted from X-ray diffraction data is illustrated by selected examples of our most recent work.Key words: X-ray diffraction, oriented multibilayers, electron density profiles, subgel phase, phase problem.


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