Angle of scattering

Streuungswinkel, m. angle of scattering. Streu-vermbgen, n. scattering power, -wachs,... 

The simplest experimental set-up used for X-ray diffraction, and an example of the diffraction pattern obtained, are shown in Fig. 1.6. A collimated (i.e. parallel) beam of X-rays hits a powdered sample, and X-rays scattered at different angles are detected. Only certain angles of scattering are found, as at these angles, and not otherwise, the X-rays scattered from different atoms are in phase, giving constructive interference. A simple analysis is based on Fig. 1.7, which shows the scattering of X-rays from two successive planes of atoms in a crystal. The difference in path length for the two beams shown is... 

Imagine now a sample, such as a powder or solution, in which all the molecules are randomly oriented. Diffraction by such amorphous samples is usually called scattering. The diffraction pattern is averaged in all directions, spherically, because the X-ray beam encounters all possible orientations of the molecules in the sample. But the diffraction pattern still contains information about how electron density varies with distance from the center of the molecules that make up the sample. Obviously, for complex molecules, this information would be singularly uninformative. But if the molecule under study contains only a few atoms, or only a few that dominate diffraction (like metal atoms in a protein), then it may be possible to extract useful distance information from the way that scattered X-ray intensity varies with the angle of scattering from the incident beam of radiation. As usual, when we try to extract information from intensity measurements, we work without knowledge of phases. 

In simple collision theory, if the impact parameter 6 < rA + rB, then collision will occur if 6 > rA + rB collision cannot occur. In molecular beam studies a collision is still defined in terms of a distance apart of the trajectories, but this is no longer rA + rB, but is a distance 6,nax. If the impact parameter b < 6max, collision occurs, and the numerical value of 6max is found from scattering experiments and is closely related to the minimum angle of scattering able to be detected. 

Just made it as a collision minimum angle of scattering observed. 

Figure 4.3 The relation between impact parameter and angle of scattering...

As Chylek et al. (2003) noted, the maximum permissible error in outgoing radiation flux determination from satellite data Afr = 0.5Wm-2 determines the necessity to retrieve the atmospheric optical thickness, r, with an error not more than At = 0.015 on land and 0.010 over the oceans. However, this level of error has still not been achieved. Using AVHRR data, the MSD of r values varies within 0.06-0.15, whereas in the case of MODIS data over land, At = 0.05-0.2t, which corresponds to the interval of At values from 0.07 to 0.21, with t varying from 0.1 to 0.8. The use of the extra-nadir data of multi-spectral thermal video-radiometer MTI for intermediate angles of scattering provides the level of error At = 0.03. 

Consider the schematic illustration of a coherent scatter experiment illustrated in Fig. 6. A well-collimated beam of X-rays strikes a scatter sample initiating coherent scatter events that are recorded at a full angle of scatter, 9, in a detector. 

There are hence two fundamentally analogous ways of probing a crystal lattice by varying the momentum transfer. In the first (classical) case the wave vector, k, is held constant and the angle of scatter, 0, is varied (angular-dispersive). Alternatively, it is possible to hold 9 constant and to allow k to vary (energy-dispersive). 

The well-known Bragg diffraction formula (Eq. 4) relates the angle of scatter at which a diffraction peak may occur to the spacing, d, of the lattice planes. 

The photon energy range chosen for XDI influences the angle of scatter required to probe a certain momentum transfer value, x, implicitly through Eq. 3. As indicated in... 

Consider a central primary beam ( = 0). The angle of scatter, 6, will have components 0Y in the Y direction and 9Z in Z. Assuming 9 and its components are small and measured in radians, then ... 

The final data set is a collection of angles of scatter, 9(Sy, Sz, Cy, Cz, Px, Py, Pz, Dy, Dz), where the independent variables refer to the source coordinates (.S ), the primary collimator exit coordinates (C), the object point coordinates (P) and the detector coordinates (D), respectively. 

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