Hydrogen scattering factor

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

Modified Spherical Scattering Factor for the Hydrogen Atom... 

FIG. 3.1 Scattering Factors for the hydrogen atom. IAM, free atom SDS bonded atom as in H2, according to Stewart et al. (1965) k = 1.4, IAM density contracted with a kappa parameter equal to 1.4. 

FIGURE 2.13 (a) X-ray scattering factors for hydrogen, carbon, chloride and ferrous ions (b) the neutron scattering cross sections for several elements, as a function of sinOA. 

Solution and Refinement of the Structure. Scattering factors for the hydrogen (14) and nonhydrogen (15) atoms are those used previously. Anomalous dispersion terms (16) were included in Fc for rhodium and phosphorus atoms. For the processing of the data and solution and refinement of the structure procedures and computer programs standard in this laboratory were used. (See, e.g., Ref. 17).) Trial absorption corrections calculated for a random selection of reflections gave transmission factors in the range 0.71 to 0.73 therefore a full absorption correction was considered to be unnecessary. 

The difference Fourier synthesis, phased by the P, Cl, N, C and O atoms, revealed the hydrogen atoms with their expected locations. Thus, the final refinement could be performed on the entire set of atoms including hydrogens with fixed isotropic thermal parameter factor, BH = 4 A2. Final R and S values are 0.022 and 0.948, respectively. The last difference Fourier map showed no values to be greater than 0.3 eA 3 (Table 15). Atomic scattering factors were corrected for anomalous dispersion from Cromer and WaberS8). 

The reason that neutron diffraction is so much more effective than x-ray diffraction as a means for locating hydrogen atoms can be seen in the atomic scattering amplitudes given in Table 9-II (taken from reference 94, except for the neutron diffraction scattering factor for deuterons). 

The S (Q,ai) are reported in scaled units, which are related to the correct units, bam (cm ), by a linear factor, y. Since the spectra from hydrogenous molecules are dominated by the hydrogen scattering this cross section can be subsumed within y. This practice stems not from a wish to avoid academic rigor but from an acceptance of experimental reality. As with other spectroscopic techniques, neutron spectroscopy is difficult to perform on the basis of absolute measurements and it results in few tangible benefits. Therefore, only the relative strengths of spectral intensities are measured. 

Single-crystal x-ray studies of the contact-ion pair complexes shown in Table II have been completed. The data were measured with a Picker automated diffractometer, and the structures were solved by direct methods. Hydrogen atom positions were included in all the structures but usually not refined. Refinements of the structures were made using a full-matrix, least-squares technique with neutral-atom scattering factors. 

In Figure 1.6, the atomic scattering factors f(s) for hydrogen, carbon, and oxygen are plotted against s = 2(sin 6)/X. In the forward direction (s = 0) the x-ray waves scattered from different parts of the electron cloud in an atom are all in phase, and the wave amplitudes simply add up, rendering /(0) equal to the atomic number Z. As s increases, the waves from different parts of the atom develop more phase differences, and the overall amplitude begins to decrease. The exact shape of the curve f(s) reflects the shape of the electron density distribution in the atom. The... 

Figure 1.6 Atomic scattering factors f(s) for hydrogen, carbon, and oxygen atoms plotted against s = 2(sin 0)/X.

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