Molecular scattering intensity

The scattering of electrons by an atom pair separated by a rigid distance, r, averaged over all possible orientations in space, gives rise to a molecular scattering intensity function which can be represented in the following way1 ... 

Me,N-GaH3 molecule, molecular scattering intensity pattern, 41 186-187 [Me NlPhlC-Li], 37 76-77 Mercaptans, reactions with hexafluoroacetone, 30 274... 

Fig. 3. The molecular scattering intensity pattern for the Me3N-GaH3 molecule related by Fourier transformation to the corresponding radial distribution curve. The difference between the observed and calculated radial distribution curves is also shown (adapted from Ref. 51).

FIGURE 7.7 Diffraction data for a neutral beam. At the top, the total scattering intensity Vi s is shown and the independent scattering contribution is indicated by the dashed curve. At the bottom, the experimental (solid curve) and theoretical (dashed curve) molecular scattering intensity, sM(s), are compared. The difference AsM(s) is shown in with the uncertainty of lo (grey band) displayed at each data point. 

If we were to predict the structure of a compound that has three equal substituents bound to a central phosphorus atom, we could be forgiven for assuming that it would have threefold symmetry. The structures of several compounds containing PN3 skeletons have been determined, and an early structure determination in 1969 of one of the simplest examples, P(NMe2)3, by gas electron diffraction was interpreted under this assumption. But the fit between the stmctural model and the observed molecular scattering intensities was not particularly convincing. 

If equation (5) is substituted into equation (4), the molecular scattering intensity becomes... 

Figure 2. togular distribution of the relative scattered intensity of hydrogm molecules scattered from a) Ni(110) b) M(111). The angle of incidenoe of the molecular beam and ibe azimuthal orlentaticn of the surface are indicated in the figure. 

Absolute calibration is of critical importance for the determination of molecular weights by the light-scattering method. The scattered intensity is so low compared with the incident beam at a distance of a few cm. being of the order of 10 lo) that a reliable direct comparison of the two beams using the same photocell is impractical. Several methods have been used, with results which are not always comparable, however. 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Theoretical work on inhomogeneous molecular distributions is as yet incomplete, but McNulty et al 6) have made some calculations on adsorbed molecules on the surface of particles. Their conclusion was that the angular distributions have structure and that the inelastic scattering intensity in the forward and backward directions is particularly sensitive to particle size. 

Rayleigh ratio of scattering intensity at scattering angle 0 particle scattering factor = normalized molecular structure factor... 

Fig. 34. Plot of the scaled forward scattering intensity (see Eq. 89) as a function of X=A2-M c for some selected molecular architectures [165]. linear polyester O, A cross-linked polyesters near the ge-point, V weakly cross-linked polyester (see Table 5)...

This expression is given here, without derivation, for the molecular contribution to the total electron scattering intensities (molecular intensities) ... 

However, at that time it was not possible to carry out a quantitative evaluation of the electron scattering intensity distribution. The positions of maxima and minima of the molecular interference pattern could be determined surprisingly well against the steeply falling background of atomic scattering intensity, due to the exaggerating... 

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