Diffraction amplitude

For a zigzag helix the complex diffracted amplitude becomes... 

For a continuous electron distribution p(r), the summation over waves of different phase must be replaced by an integration leading to a diffraction amplitude ... 

Fig. 3 EC derived maps of tubulin, a Pure experimental map Fo from diffraction amplitudes and image derived phases at 3.7 A resolution [6] b Map after crystallographic refinement to 3.5 A using diffraction amplitudes and both image and model derived phases [8]...

A way to get round collecting and processing image sets for each new ligand tested was to use the phases from the original PTX experiment to process the diffraction amplitudes recorded for new drugs in the Zn sheets. As discussed above, this is not a new concept. The techniques molecular replacement (MR) and phase switching are often employed in X-ray crystal structure determination when actual phases aren t known [32], The application and results of these experiments are described herein. 

Thus, for a unit cell containing n atoms that scatter with amplitudes /i /2 "./n and phases v>, v>2. > V n. the resultant diffracted amplitude is given by... 

In addition, there are various technical corrections that must be made to the image data to allow an unbiased model of the structure to be obtained. These include correction for the phase-contrast transfer function (CTF) and, at high resolution, for the effects of beam tilt. For crystals, it is also possible to combine electron diffraction amplitudes with image phases to produce a more accurate structure (7), and in general to correct for loss of high resolution contrast for any reason by "sharpening" the data by application of a negative temperature factor (22). 

L/2 L) is called the shear plane. The reciprocal lattice of the shear structures above may be constructed by multiplying the diffraction amplitudes of a few Cu3 Au cells with the diffraction amplitude of a tetragonal body-centered 4 lattice of 8 functions. The following properties of shear structures have been observed ... 

A. Carlsson, T. Oku, J.O. Bovin, G. Karlsson, Y. Okamoto, N. Ohnishi, and O. Terasaki, The Structure of Iron Oxide Implanted Zeolite Y, Determined by High-resolution Electron Microscopy and Refined with Selected Area Electron Diffraction Amplitudes. Chem. Eur. J., 1999, 5, 244-249. 

Although there is no inherent phase problem in the HREM technique it is replaced by an "instrumental" phase problem arising from the relatively imperfect nature of electromagnetic lenses. Spherical aberration is the chief limitation, and its effect can be coupled with that of deviation from the Qatissian focus into a phase factor which can be considered to act upon the diffracted amplitudes before re-combination by the lens to produce the initial image amplitude, namely ... 

Diffracted amplitude structure factor andform factor... 

Structure factor, we assumed that the atoms had a certain position defined by the vector r. We now see that the positions of these atoms are constantly changing. As a result, the diffracted amplitude is modified. This modification depends in theory on what family of planes considered because each atom is moving inside a potential well with an anisotropic shape, since it depends on the ciystallographic direction. The complete description of this effect will not be given here. We will simply point out that the diffracted intensity is attenuated by a factor, called the Debye or Debye-Waller factor, smaller than 1, and whose value usually depends on which family of planes is being considered. This factor will be denoted by D. Finally, the intensity diffiacted by a polyciystalline sample is therefore written ... 

Figure 5.4a shows a representation of an edge dislocation. This type of defect is very common, particularly in metals, and corresponds to major local deformations of the atomic arrangement. The diffracted amplitude is affected by the displacements of the atoms with respect to their reference positions in the same crystal without defects. 

Let us consider a cell with its initial position with respect to the origin of the lattice specified by the veetor R, which has undergone a displacement characterized by the vector 8. Such a displacement is usually the result of a translation and a rotation. If we consider that the rotation is significant enough, then its effect on the scattered radiation s phase is negligible and will not be taken into account when we calculate the diffracted amplitude. If we denote by Ap the amplitude diffracted by the displaced cell p, we can write ... 

The French mathematician Mathieu investigated this equation in 1868 to describe the vibrations of an elliptical membrane. Mathieu functions are applicable to a wide variety of physical phenomena, e.g problems involving waveguides, diffraction, amplitude distortion, and vibrations in a medium with modulated density. Hill was interested in the motion of planets and was thus engaged in differential equations with periodic integrals [1]. 

Fig. 5.11 Geometry of the parallelepiped discussed (a) and the patterns (b) of the diffraction amplitude (above) and intensity (below)...

Figure 22 The relative difference of the x-ray diffraction amplitude without (1 at f = 0 kV/mm) and with an electric field (E 2.5 kV/mm, 1 j,) of the BaTi03 crystal microspheres with a volume fraction of 31.5%. Reproduced with permission from W. Wen and K. Lu, Appl. Pliys. Lett. 68(1996)1046...

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