Layer lines indexing

A fiber diffraction pattern of the potassium salt is shown in Figure 2 ( 8). Sharp Bragg reflections extend to approximately 3.0 A resolution with meridional intensities on the 6th and 9th layer lines. The diffraction pattern can be indexed on the basis of a... 

Fig. 13a and b. Intensity contour maps around the 5.9-nm and 5.1-nm actin layer lines (indicated by arrows) a resting state b contracting state. Z is the reciprocal-space axial coordinate from the equator. M5 to M9 are myosin meridional reflections indexed to the fifth to ninth orders of a 42.9-nm repeat, (c) intensity profiles (in arbitrary units) of the 5.9- and 5.1-nm actin reflections. Dashed curves, resting state solid curves, contracting state. Intensity distributions were measured by scanning the intensity data perpendicular to the layer lines at intervals of 0.4 mm. The area of the peak above the background was adopted as an integrated intensity and plotted as a function of the reciprocal coordinate (R) from the meridian... 

For the spots on layer lines above and below the equator, one index (l) is given by inspection. It should be remembered that the indices of reflections represent phase-differences between waves diffracted by neighbouring units aloiig the three axial directions (see p. 141). The spots on the first layer line above the equator lie oh a cone for which n in the equation nX = c cos (see p. 149) is 1 this means that waves coming from any one diffracting unit are one wavelength behind those from the next diffracting unit above it in fact, n in the cone equation is Z, the third index number. Thus, all spots on the fourth layer line (fourth cone) above the equator are from hk4 planes (those on the fourth layer line below the equator are from hk4 planes), and so on. 

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. 

The X-ray diffraction pattern obtained from the dry, annealed fibre (see Materials and Methods) is shown in Figure 3. The reflections index on a hexagonal unit cell with dimensions a = b = 1.438 nm, c (fibre axis) = 0.582 nm with meridional reflections occurring only on layer lines with 1 = 2 n, where n is an integer. These constraints on the Miller indices hkl are in accordance with... 

Figure 15. Cylindrically averaged transforms of the two models illustrated in Figures 6 and 7 (a) intensity distribution on successive layer lines for the triple-stranded 7, helix (b) intensity distribution on successive layer lines for the triple-stranded 6, helix. Note layer lines with index 1 = 1,2, 4, and 5 are absent.

The cylindrically averaged Fourier transform of the sevenfold and six-fold triple-stranded structures are shown in Figure 15. The Fourier transform of the six-fold triple-stranded model illustrates the symmetry of the system by the total absence of intensity on layer lines with index i 3 n, where n is an integer. The Fourier transform of the seven-fold triple-stranded structure shows that in destroying this precise symmetry relationship intensity occurs on all layer lines which are orders of the 2.27 nm spacing. This reinforces the concept of an indigenous triple-stranded structure which is perturbed slightly by the interaction of solvent. 

Fig. 11. (a) FOM t 0, in % W-1cm-2 and (b) conversion efficiency FOM rj0 in % W-1cm-2 as a function of core thickness with the same nonlinearity din each case. Here the dashed line identifies the perfectly phasematched case, the solid lines identify the and the dotted lines the +/0 QPM structures respectively. The individual symbols relate to the MDPM structures with (solid) and +/0 (open). , MDPM, TM0(co)—>TM1(2co) , O -MDPM, TM0(co) T, V QPM maximum and , A QPM optimum. Calculation done for DANS d=6 pm V"1 with a second harmonic loss of 40 dB cm4 and a fundamental loss of 5 dB cnr1 for a sample length of 2 mm. The MDPM structures are calculated assuming two layers perfectly index matched to the DANS parameters... 

The chemical structure was deduced to involve mainly (1 —> 4)-linked 2-deoxy-2-(sulfoamino)-a-D-glucose 6-sulfate and (1 —> 4)-linked 2-sulfated a-L-idopyranosyluronic acid residues. The X-ray patterns from sodium salts of hog-mucosal heparin index with a triclinic unit-cell, having a = 1.30 nm, b = 1.02 nm, c = 1.65 nm, a = 104°, /3 = 96°, and y = 116°, containing one chain. The macromo-lecular heparin from rat skin, at 84% relative humidity (r.h.), gives a pattern consistent with a highly oriented version of the hog-mucosal heparin. On lowering the r.h. to 76%, the repeat distance along the fiber axis increases to 1.73 nm, with meridional reflections on the even layer-lines. 

The patterns from the calcium salts of heparin are different from those from the sodium salt form. The layer-line spacing is 1.68 nm, with meridional reflections on even layer-lines. The unit cell is orthorhombic. The same pattern also occurs in the calcium salt of heparin sulfate,23 which indexes with an orthorhombic unit cell having a = 1.70 nm, b = 1.27 nm, and c = 1.68 nm. 

The close correspondence in size between the hexagonal unit cells of poly(y-methyl-L-glutamate) and poly(L-methionine) implies a similarity in the intensity expected in the observed strong reflections. In particular those on the flfth layer line associated with the pitch of the helix (or on the corresponding layer Une of a higher order helix) indexed as 105 and 115 are normally very strong (18, 24) in poly(y-methyl-L-glutamate). But the 105 reflection is much weaker than the 115 reflection... 

The third type of disorder, related to the variability of the unit cell, is relatively less common. Usually, it is caused by the fact that polymer chains, although packed in good order laterally, are able to slip along their axes relative to one another. This occurrence is manifested by streaks on layer lines other than the equator if there are streaks on the equator also, some disorder in the lateral packing, as well, is indicated. The most severe type of unit-cell disorder, that of the simultaneous presence of more than one type of unit cell in the same specimen, is rather rare. It would be indicated by spots that appear where they do not belong, as, for example, between layer lines, or by layer lines of variable separation. In its milder cases, some reflections on a diagram otherwise proper-looking would not be indexed satisfactorily. 

On either type of diffraction pattern the individual diffraction spots can be used to calculate spadngs between planes of equivalent structure in the specimen. The spots often occur in row or layer lines as shown in Fig. 2. Particular importance attaches to the layer lines, which are expected to cross the central row line (meridian) at regular intervals and may be numbered (indexed) according to their distance from the central layer line (equator). The separation between layer lines usually permits unequivocal establishment of the size of the axial period of the fibril s structure, i.e. the distance between equivalent locations along the fibril. Row lines can be used to determine structure transverse to the fibril axis, but unless a large number of row lines are available the study of transverse structure is limited. 

The difficulties facing theoretical attempts to relate intense layer lines of small index with the distribution of individual amino-acid residues are similar to those which are encountered in calculations of apparent protein molecular weights from chemical composition. In both cases reliance is largely placed on the least frequent residues, which are the ones whose data are, in fact, least reliable. 

Figure 1.36. (a) Schematic of the diftraction pattern of PPV film (b) intensity profiles (molecular transform) of the first six layer lines predicted for a perfectly oriented, randomly shifted PPV molecular system (c) reciprocal net for the (a, b ) equatorial plane ( ) observed reflection, (O) predicted reflection (d) indexing of the (a, b ) plane shown in (c). (Reproduced from ref 266 with kind permis.sion. Copyright (1986) John Wiley Sons, Inc., New York.)... 

The fibre pattern obtained for a particular sample of polyoxymethy-lene -fCH2—using X-rays of wavelength 0.154 nm exhibits equatorial reflections at angles of 21.9°, 37.7° and 23.2°. Show that these spots may be consistently indexed as the (110), (200) and (020) reflections, respectively, of an orthorhombic unit cell. The first layer line corresponds to the angle 25.6° and the unit cell contains four repeat units. Calculate the density of the crystalline material. 

Fig. 24) the reflections are easily indexed and the pattern is easily interpreted [9, pp. 15-68]. The cone pattern of Figure 25, which shows the layer lines measurable with a given crystal setting, corresponds to the rotating crystal pattern. 

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