Structure factor contrast

Inclusions with negligible strain fields. Small inclusions which have a negligible strain field can be made visible by several mechanisms. Some contrast may arise simply because these features influence the normal absorption. However, they are usually revealed either by structure factor contrast (Ashby and Brown 1963b) or by phase contrast (Charai and Boulesteix 1983) mechanisms. These will now be discussed. 

Figure 5.20. Schematic diagram illustrating the imaging of small inclusions (voids or bubbles) in a wedge-shaped crystal using structure factor contrast.

Figure 8.55. Facing page. Electron radiation damage in quartz, (a) Damage centers produced within a 1-minute exposure to 100-kV electrons, imaged in BF by structure factor contrast, (b) As the damage centers grow during irradiation, they become visible by the strain they produce in the surrounding matrix, (c) On continued irradiation, the strain fields overlap, (d) Eventually, the crystal becomes amorphous, and the strain contrast disappears. (From McLaren and Phakey 1965a.)...

Microstructural characterisation of RPV embrittiement 217 Structure factor contrast... 

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

Fig. 49a-c. Spectral contributions of the two modes (0, (2)), characterized by T1 and r2, respectively, to the dynamic structure factor for different contrast conditions. (Reprinted with permission from [154]. Copyright 1990 American Chemical Society, Washington)... 

At higher Q, however, where the static structure factor reveals the asymptotic power law behavior S (Q, 0) Q 1/v, the assumption of ideal conformation clearly fails. In particular, this is evident for the core (sample 1) and shell contrast conditions (sample 2). 

TRXRD detects the propagation of coherent acoustic phonons as a transient change in the diffraction angles. In contrast, the atomic motions associated with coherent optical phonons modify only the Bragg peak intensity, because they do not change the barycentric positions of the crystal lattice. The Bragg peak intensity is proportional to the squared modulus of the structure factor [1,3,4] ... 

Performing neutron scattering not on perdeuterated samples but on a single deuterated chain in a protonated matrix (or vice versa both ways provide the same contrast) gives the single-chain structure factor,... 

In HREM images of inorganic crystals, phase information of structure factors is preserved. However, because of the effects of the contrast transfer function (CTF), the quality of the amplitudes is not very high and the resolution is relatively low. Electron diffraction is not affected by the CTF and extends to much higher resolution (often better than lA), but on the other hand no phase information is available. Thus, the best way of determining structures by electron crystallography is to combine HREM images with electron diffraction data. This was applied by Unwin and Henderson (1975) to determine and then compensate for the CTF in the study of the purple membrane. 

Key words HREM, Structure factors, Crystallographic image processing. Contrast transfer... 

As mentioned in section 6, the structure factors F(u) are proportional to the Fourier components lim(u) of the HREM image and the projected potential is proportional to the negative of the image intensity, if the image is taken Scherzer defocus where the contrast transfer function T(u) -1. In general, the Fourier components lim(u) are proportional to the structure factors F(u) multiplied by the contrast transfer function (CTF). The contrast transfer function T(u) = D(u)sinx(u) is not a linear function. It contains two parts an envelope part D(u) which dampens the amplitudes of the high resolution components ... 

Mathematical CTF correction calculating first the mathematical contrast transfer function T(u) from the estimated defocus values. Then the structure factor is calculated from the Fourier transform lim(u) of the image for all u except those with sinx(u) 0 by ... 

Further note that for t=0 Eq. 3.24 does not resemble the Debye function but yields its high Q-limiting behaviour i.e. it is only valid for QR >1. In that regime the form of Dr immediately reveals that the intra-chain relaxation increases in contrast to normal diffusion ocQ, Finally, Fig. 3.2 illustrates the time development of the structure factor. 

If the object is embedded into a matrix with the same average scattering properties as the considered jumping unit, then the scattering contrast from the average size of the object is matched by the matrix and the corresponding forward scattering is suppressed. It can be shown [133] that the dynamic structure factor for an object embedded in a matrix, which performs jumps in a two level system, can be obtained as ... 

In the low Q-regime RPA describes well the static structure factor for the short chain melt, where the ODT is sufficiently far away (kN 7). In the dynamics we would expect the diblock breathing mode to take over around QRg 2 (Q=0.04 A ). Instead, deviations from Rouse dynamics are already observed at Q values as high as QR =5. At QJ g=3 a crossover to a virtually Q-independent relaxation rate about four to five times faster than the predicted breathing mode is found. This phenomenon is only visible under h-d labelUng. Under single chain contrast (see below) these deviations from RPA are not seen. Thus, the observed fast relaxation mode must be associated with the block contrast. 

Figure 8 displays the structure factor S (q) obtained from solutions of dendrimer G4 in deuterated dimethylacetamide by application of Eq. (8) [24]. In this solvent the high contrast between solute and solvent allows one to determine S q) conveniently. For low scattering angles S (q) is considerably smaller than unity whereas at higher q the structure factor S(q) is unity, as expected for dissolved molecules [32, 33]. There is no distinct maximum as in concentrated suspensions of rigid colloidal objects [32, 33]. One reason for this is the rather low volume fraction of the dendrimers. In addition, dendrimers are not expected to... 

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