Equatorial reflections

The occurrence of the mesophase in the fiber is confirmed by x-ray diffraction examination. The occurrence of three equatorial reflections 010, 110, and 100, the absence of layer and meridional reflections, and the manifestation of the intensity maximum of diffusively scattered radiation at 20 = 19 in the fiber diffraction pattern are the criterion for the presence of the mesophase. The... 

When using the procedure with equatorial reflections, the value of fc is determined from the relationship deduced by Gupta and Kumar [22] ... 

The quantitative assessment of the degree of crystallite orientation by x-ray examination is not free of ambiguity. From a comparative analysis [23] in which results obtained from the consideration of (105) and from three different variations of equatorial reflection were compared, the conclusion was that the first procedure can lead to underrated results, i.e., to the underestimation of the orientation. However, it can be assumed that this does not result from an incorrect procedure, but from ignoring the fact that the adjacent (105) reflex can overlap. The absence of the plate effect of the orientation is characteristic of the orientation of crystallites in PET fibers. The evidence of this absence is the nearly identical azimuthal intensity distributions of the diffracted radiation in the reflexes originating from different families of lattice planes. The lack of the plate effect of orientation in the case of PET fiber stretching has to do with the rod mechanism of the crystallite orientation. 

Figure 8. (Continued). As described above, the packing of myosin molecules into the thick filament is such that a layer of heads is seen every 14.3 nm, and this reflection is thought to derive from this packing. Off the meridian the 42.9 nm myosin based layer line is shown. This arises from the helical pitch of the thick filament, due to the way in which the myosin molecules pack into the filament. The helical pitch is 42.9 nm. c) Meridional reflections from actin. Actin based layer lines can be seen at 35.5 nm, 5.9 nm and 5.1 nm (1st, 6th, and 7th layer lines)and they all arise from the various helical repeats along the thin filament. Only the 35.5 nm layer line is shown here.The 5.9 nm and 5.1 nm layer lines arise from the monomeric repeat. The 35.5 nm layer line arises from the long pitch helical repeat and is roughly equivalent to seven actin monomers. A meridional spot at 2.8 nm can also be seen, d) The equatorial reflections, 1,0 and 1,1 which arise from the spacings between crystal planes seen in cross section of muscle.

For a unimodal equatorial reflection the treatment is more involved. If the distribution is narrow, it follows from Fig. 9.5 an approximation

approximative solution, in turn (Ruland cited by Thunemann [257], P- 28)... 

On each side of the meridian, only a distorted image of the orientation distribution is observed. Nevertheless, even equatorial reflections can generally be used for the purpose of orientation-desmearing if we make assumptions concerning the analytical type of the orientation distribution. The corresponding method is demonstrated in the following section. 

The unit cell of cellulose from Chaetomorpha melagonium is monoclinic, with a = 16.43 A (1.643 nm), b(fiber axis) = 10.33 A (1.033 nm), c = 15.70 A (1.570 nm), and /3 = 96.97°. In base-plane projection, each of the Meyer-Misch subcells that make up the super-lattice are identical. All equatorial reflections can be indexed by using a one-chain unit-cell, meaning that every single chain has... 

Fig. 1. Cross-/] structure of amyloid fibrils. (A) Cartoon representation of a cross-/] X-ray diffraction pattern. The defining features are a meridional reflection at 4.7 A and an equatorial reflection on the order of 10 A. The 4.7-A reflection is generally much brighter and sharper than the reflection at 10 A. (B) The cross-/] core structure of amyloid fibrils. Parallel /(-sheets are depicted, but the structure could equivalendy be composed of antiparallel /(-sheets or a mix of parallel and antiparallel. The 4.7-A spacing of /(-strands within each /(-sheet is parallel to the long fibril axis. The depicted 10-A sheet-to-sheet spacing actually ranges from about 5 to 14 A (Fandrich and Dobson, 2002), depending on the size and packing of amino acid side chains. Amyloid fibrils have diameters on the order of 100 A.

In a later publication, Kishimoto et al. (2004) proposed the water-filled nanotube as a model for the fibrillar N-terminal domain of the yeast prion Sup35p. The authors find that hydrated Sup35p fibrils show no 10-A equatorial reflection in the fiber diffraction pattern, but that dried fibrils... 

Parts a c of Fig. 5 show 3-D plots of the changes in the 14.5 nm layer line and equatorial reflections measured during an activation cycle at 100 ms time resolution, and are to be compared with the tension transient shown in Fig. 5 b. Clearly active tension production is associated with a large depression of the intensity of the 14.5 nm... 

Calculate the values of d for all observed equatorial reflections for the bulk polymer and the stretched polymer sample (Notes 2 and 3). 

Tabulate Miller indices, 26, and for all identified equatorial reflections. 

Indexing rotation photographs. Preliminary consideration. The spots on the equator of a rotation photograph are obviously reflections from atomic planes which were vertical during the exposure. In Plate VII the equatorial spots are reflections from planes parallel to the c axis, that is, hkO planes the third or l index for these reflections is 0 by inspection. The other two indices, h and k, of all the equatorial reflections may be found from the spacings of the planes, which are worked out from the reflection angles 6 by the Bragg equation. 

Consider first the equatorial reflections. For a crystal rotated round its c axis, the equatorial reflections are those of hkO planes. To assign correct indices it is only necessary to make a diagram (Fig. 87 b) of the zero level of the reciprocal lattice (the dimensions being already known from layer-line spacings on other photographs), and to measure with a ruler the distance f of each point from the origin it is then obvious which reciprocal lattice point corresponds to each spot on the rotation diagram. 

If the crystal is rotated round its b axis (Fig. 89) the equatorial spots are reflections from hOl planes. The values for these spots are found as before by measuring the distance from the origin to each point of the (non-rectangular) hOl net plane (Fig. 88). Note that the indexing of equatorial reflections in this case cannot be done by a log d chart, since there are three variables, a, c, and / the reciprocal lattice method is essential. Once the indices for the equatorial reflections have been found, those of the reflections on upper and lower layer lines follow at once, since all reciprocal lattice points having the same h and l indices (such a set as 201, 211, 221, 231, and so on) are at the same distance from the axis of rotation and thus form row lines. 

Fig. 91. Graphical method for determining values for non-equatorial reflections of monoclinic crystal rotated round c.

Assuming that the equatorial reflections have been shown to fit a rectangular reciprocal lattice net, attention may be turned to the upper and lower layer lines. The values for all the spots are read off on Bernal s chart, and the reciprocal lattice rotation diagram is constructed from these values if the values for the upper and lower layer lines correspond with those of the equator—that is, row7 lines as well as layer lines are exhibited as in Fig. 80—then the unit cell must be orthorhombic. It should be noted that some spots may be missing from the equator, and it may be necessary to halve one or both of the reciprocal axes previously found to satisfy the equatorial reflections. The dimensions of the unit cell, and the indices of all the spots, follow immediately from the reciprocal lattice diagrams. 

Suppose, however, that although the equatorial reflections fit a rectangular projected cell-base—that is, a rectangular zero-level reciprocal lattice net—the rest of the spots do not fall on row lines. This must mean that the remaining axis of the reciprocal lattice is (as in Fig. 90) not normal to the zero level in other words, the unit cell is monoclinic,... 

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