Form factor scattering defined

Clearly, the structure factor dominates the SAXS patterns. It is relevant to ask whether the cylinder form factor, depending on the pore radius, also plays a significant role in the scattering distribution. The calculated cylinder form factor is defined by a Bessel function [12,15,17] which has zeroes at specific k-values. As shown in Fig 4, the experimental profiles for 40 V membranes (pore diameter 48nm) do not display a clear link to this pattern. The predicted first minimum is close to the broad third-order structure factor peak. It is consequently impossible to derive a value for the pore radius directly from the resuhs without a more detailed analytic treatment. This is disappointing, as the pore size is fundamentally important in the use of AAO membranes in filtration or as templates. Electron microscopy studies show that for the synthetic conditions employed, pore diameters above 12mn are linearly related to anode voltage (1.2 nnW) and so are approximately half the mean pore separation [7,15]. 

The simulations shown in Figs. 3 and 4 correspond to a typical scenario in polymer nano-structures. The nanodots exhibit a rather broad distribution of the diameter oR/R = 0.25. As a consequence basically no form factor contribution is visible in the two-dimensional scattering pattern, which is purely dominated by the structure factor contribution. This can be understood as a well defined template with rather well arranged positions but ill defined individual sizes of the nano-dots. 

For anisotropic samples, the space correlation function will depend on the orientation imposed to the vector and P(q) will vary both with the scattering angle 6 and azimuthal angle [Pg.72]

The dependence of the scattered intensity on the size and the shape of the polymer is usually described by the form factor defined as the ratio of intensity scattered at angle 9 (scattering wavevector to that extrapolated to zero angle ( —>0) and therefore, zero scattering wavevector (1 1 - 0) ... 

The form factor in Eq. (2.139) is defined for a specific orientation of the molecule with respect to the scattering wavevector q. Often (but not always ), the system is isotropic with equal probabilities of all molecular... 

Here the structure factor signifies the vectorial sum of the waves scattered by the single atoms which show amplitude f and phase y. Every atom contributes a scattered wave to the whole diffraction effect, the amplitude of which is proportional to the so-called form factor. The phase is thus defined by the position of the atom in the elementary cell, whilst the form factor is a characteristic constant for every sort of atom which represents a measure of its scattering power. Hence no special differences exist in the positions of the diffracted beams, which in both X-ray and electron diffraction cases satisfy the geometric relations between lattice constant and X-ray or material wavelengths, according to the Bragg equation. However, there are definitely differences in their intensities. 

Here we describe the qualitative variation of the form factor with the scattering vector q (of modulus 1 1 = q) and the duration of relaxation t. The covered time range must also be defined, which is usually achieved by referring to the viscoelastic behaviour. Furthermore, different possibilities of data interpretation are suggested. 

When we come to deal with neutrino scattering we shall have a current that is not conserved and the F3 type form factor will appear. The form factors Fi,F2 are defined in such a way that for q = 0, which physically corresponds to the proton interacting with a static electro-magnetic field, one has... 

For US and USe no sharp excitations have been found. A number of experimental scans were presented by Buyers and Holden (1985), but are all somewhat similar to those shown in fig. 21. The peak in the USe spectra at 6THz (=25 meV) is the optic phonon. There is a further broad peak at [220], which is assumed to be magnetic. On going from [220] to [440] the square of the magnetic form factor drops from 0.51 to 0.07, thus rendering the magnetic scattering invisible at [440]. The excitation is very broad in USe, and a similar situation exists in US. In this latter material the excitation is so broad (see lower panel of fig. 21) that it is even difficult to define Ep,. 

---