Equatorial streak

The cross-section of the primary X-ray beam is extended and not an ideal point. This fact results in a blurring of the recorded scattering pattern. By keeping the cross-section tiny, modern equipment is close to the point-focus collimation approximation - because, in general, the features of the scattering patterns are relatively broad. Care must be taken, if narrow peaks like equatorial streaks (cf. p. 166) are observed and discussed. The solution is either to desmear the scattering pattern or to correct the determined structure parameters for the integral breadth of the beam profile (Sect. 9.7). 

Distribution of Rod Lengths. If the distribution of rod lengths shall be studied, the smearing of the equatorial streak by the primary beam profile must be eliminated99. After that the ID scattering intensity is computed by means of Eq. (8.56) and fitted to the respective ID model (e.g., Eq. (8.80)) from Sect. 8.7.1.1. Be careful. The rods may, in fact, not be stretched out perfectly but only resemble long worms instead. 

Figure 8.36. SAXS pattern of a thermoplastic elastomer during straining. The thin horizontal line in the center is called an equatorial streak. In this case it is well-separated from the long-period peaks above and below... 

D Streak Analysis. The rod scattering from the equatorial streak, Ir (s), is extracted from the scattering pattern [200] and projected... 

Is this an Uncorrelated Hard-Disc Fluid In order to answer this question we compute a 2D CLD and test, whether the function is positive everywhere. In this case the equatorial streak can be considered pure particle scattering. 

Figure 8.37. Equatorial streak analysis of a poly(ether ester) during straining as a function of elongation, . (a) Intensity projected on the cross-sectional plane (b) 2D CLD computed from the projected intensity... 

Figure 8.37a shows the projected intensity100 as a function of the elongation of the material. The resulting 2D CLDs are presented in Fig. 8.37b. Equatorial streaks are observed from an elongation of e = 1.73. Only at this elongation there are some faint correlations among the microfibrils the CLD becomes slightly negative at r 8 nm. For higher elongation the structure in the fiber cross-section conforms to a hard-disc fluid.

Figure 9.6. Fanning-out of an equatorial streak in a fiber pattern caused from misorienta-tion. Dashed arcs indicate azimuthal scans that are performed in practical measurements. The recorded scattering curves are used to separate the effects of misorientation and extension of the structural entities... 

Let us consider a frequent problem the scattering of elongated voids or of mi-crofibrils is investigated. In such materials an equatorial streak is observed - similar to the one sketched in Fig. 9.6. If the voids were perfectly oriented, its integral breadth measured as a function of s 2... 

Figs. 9 and 10. Enlarged views of the central equatorial streaks of patterns 7 and 8, respectively. See Section IV, 3. 

A difference between hydrated kangaroo tendon and elastoidin is illustrated in Figs. 9 and 10, which shows the central equatorial streaks extending out to the location of the normally prominent 15 A. equatorial... 

A possible crystal structure for poly(p-benzamide) which is in accord with the measured repeat distance is shown in Fig. 8. It has been estimated that about 36 repeat units would have to be involved in one chain fold in this polymer. No obvious spacing corresponding to chain folds was found by low single X-ray measurements on highly oriented poly(p-benzamide) fibre. However, a strong equatorial streak was obtained which is consistent either with a microfibrillar structure having axially oriented fibrils or with axially oriented voids or regions of low density. ... 

The secondary spot-like scattering in PTeOX indicates the formation of lamellar stacking in fibrils of PTeOX similar to the case described by W ner et al. On the equator, both patterns of PTOX and PTeOX show a strong and sharp scattering, though the equatorial streak of PTOX is sharper than that of PTeOX. 

Vertical widths on the equatorial streak of PTOX and PTeOX were measured photographically with a microdensitometer at a desired positions of 26. The half widths of the streak, especially PTOX, were almost constant over the considerably wide range of 26. This finding indicates the possibility of the existence of needle-like voids between fibrils in the specimen with high orientation parallel to the fibre axis. 

The SAXS pattern from the fiber used to illustrate the analyses here is shown in Figure 1. The two features obvious in the data are the lamellar reflections and the equatorial streak. Less obvious is an interfibrillar interference peak along the equator at about 50 A. We will here focus only on the lamellar reflections. The various parameters determined by analyzing the data in Figure 1 are listed in Table 1 and are further elaborated below. 

If the pattern reveals equatorial scattering, the equatorial streak may be extracted from the pattern and analyzed separately. In certain cases (If the streak is clearly separated from other reflections and does not fan out ) it should suffice to mask the measured pattern... 

When dealing with the equatorial streak of a fibo- pattmi, it tqtpears suitable to extract the transverse structure /jj (s ). Through Fourier transformation relation this projection is linked to a two-dimensional two-phase system made ftom needle cross sections in a matrix, as indicated in the bottom row of fig 2. 

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