Diffraction Angle Transformation

The crystalline precipitate, as synthesised, shows in X-ray wide angle powder diffraction which is equivalent to the B-structure of native potato starch. Upon heating in the presence of 18% by weight of water the crystallites transform to the A-structure of native wheat starch. 

Small angle neutron diffraction method permits the observation of large scale structures with clusters (particles) size from 1 nm to 100 nm. From the properties of the Fourier transform, [4], it follows that the diffraction intensity from objects of this size is concentrated in a small angle region, 0.2 < (9 < 10 radians, in the so-called zero peak. In conventional diffractometers the zero peak is inseparable from the instrumental broadening of the incident neutron beam. To make the measurement possible, SANS method applies cold neutron sources and filtration of the incident neutron flux by mirror guides or Be filters. In SANS, the angular interval Q < I sin QR/QR) in (2) is practically constant... 

Yang, A.C.-M. and Kramer, E.J. (1986) Craze microstructure characterization by low-angle electron-diffraction and Fourier-transforms of craze images. J. Mater. Sci., 21, 3601. 

In order to learn about the phase states adopted by LPS and lipid A, Fourier-transform infrared spectroscopy, differential scanning calorimetry, and X-ray small-angle diffraction with CuXa or synchrotron radiation have been applied. In the following section, some recent results are summarized. 

For obvious reasons, Fourier transformations are widely used to solve problems in X-ray crystallography [129]. With innumerable replications of a molecule in a crystal, all being oriented the same way, approximate periodic boundary conditions are given. Periodic functions become discrete when Fourier transformed. In fact, the diffraction pattern of an X-ray shot on a crystal amounts to the Fourier transform of the square of the absolute values of the real space function [130]. The measurements of intensities and different reflection angles from the crystal relate to the Fourier transform of the electron densities in the crystal. 

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