Splitting, layer line

The layer line spacing is 1.036 nm with a meridional reflection on the fifth layer line. The model proposed by Tadokoro (1) has a pitch of twice the value for the observed layer line spacing which becomes halved by the symmetry related intertwining chain, (b) (bottom) Higher resolution diffraction pattern of the equatorial region of i-PMMA. The equator is tilted to extend the range on the film. Note that the reflections shown in (a) are now split. (Patterns obtained in collaboration... 

Variations of this method can, in some cases, provide other kinds of information about the diffracting particles. For instance, TMV is a helical virus with 49.02 0.01 subunits in the three turns of its helix in its 69 R axial repeat. This deviation from an integral number of units in three turns causes the layer lines to split slightly (6). The first two Bessel function terms that contribute to the first layer line of TMV do not fall at a spacing of 69 R above the equator, but rather, at 67.6 and 71.5 R, which corresponds to a splitting of about 0.15 mm on the film at typical specimen-to-film distances (11 cm). Figure 1... 

The positions, < >, were determined as follows. Since the < > are known approximately, the linear equations (6) were solved assuming no layer line splitting. Then, for each reflection, a limited, one-dimensional search was made for a position which fit the measured intensities better. The angular widths, a, were also allowed to vary, since splitting leads to an apparent increase in the measured angular widths of the layer lines. 

The horizontal lines indicate the position on which the layer lines would fall if there were exactly 49 subunits in three turns in the TMV axial repeat. The circles show the positions the Bessel function terms take assuming 49.02 subunits in three turns. The vertical deviations from the solid lines give an indication of the magnitude of the layer line splitting. The horizontal positions indicate the relative positions of the Bessel function terms along the layer lines each term can only contribute to diffraction further from the meridian than the positions marked. 

The intensities and angular positions of layer lines 1 and 2 are also shown in Figure 2. Again, the noise in the positions calculated is lowest at points corresponding to the peaks of intensity. For these layer lines there are also systematic variations in the position with subsequent peaks falling at different positions relative to that which would be expected if there were exactly 49 subunits in the 69 X axial repeat. This layer line splitting was used to calculate the relative contributions of the Bessel function terms on layer lines 1 and 2. 

The separation of Bessel function terms using layer line splitting is confined to regions where only two terms contribute. At higher diffraction angles, where more terms contribute, the separation of Bessel function terms should, ideally, utilize both heavy atom derivative data and the apparent positions and widths of the layer lines. The combined use of both types of information may be possible using a linear relationship between the layer line position and the relative intensities of the Bessel function terms. 

The circles represent the relative intensities calculated from the observed intensities using the layer line splitting. The solid lines are the results of the analysis of heavy-atom derivative data (7). 

We have extended the treatment of Franklin and Klug (6) to the case in which presence of an incommensurable helix cannot give rise to splitting of layer lines due to the fact that only one order of Bessel function is significant in controlling the amplitude of the structure factor. In this case, the layer line will be displaced slightly from the height calculated for the commensurable helix. Our example is the crystal structure of the... 

The results show that for cases consistent with the Raman spectral response for cells 48 hr after infection in Webb s experiments, there is a maximum energy transfer J (line intensity) rf(l/A) to the cell membrane at approximately 45, 90, 140, and 180 cm This does not appear to be so for the normal cell, where lower levels of energy transfer seem associated with normal behavior. The dielectric structure of layers calculated for normal cells does not affect the shape or frequency of the Raman lines observed for the normal cell. (The dielectric layer model used cannot account for the splitting of lines seen in the spectra of tumor cells.Such splitting is of great importance in terms of the possible degeneracy in the oscillatory modes of molecules—perhaps from breaks in the fibronectin layer.)... 

For the undeformed samples Fig. 6.2 shows the scattering intensities I s 2, Sy) and the absolute values of the corresponding CDFs z(r 12, 3). All samples exhibit a layerline scattering pattern. It is characteristic for a highly oriented structure from slender domains arranged in rows along the fiber axis. The layer lines are not indented or even split into separate peaks. Thus there is only one-dimensional arrangement of domains. This fact is obvious from the CDF data in real space (Fig. 6.2, bottom... 

In the left panel of Figure 8 we show the band structure calculation of graphite in the repeated zone scheme, together with a drawing of the top half of the first Brillouin zone. The band structure is for the 1 -M direction. As the dispersion is very small along the c-axis we would find a similar result if we add a constant pc component to the line along which we calculate the dispersion [17]. The main difference is that the splitting of the a 1 and % band, caused by the fact that the unit cell comprises two layers, disappears at the Brillouin zone boundary (i.e. if the plot would correspond to the A-L direction). 

The material (DMET)2FeBr4 consists of electric quasi-ID chain-based donor layers and magnetic Fe3+ square lattices. The absorption line was observed73 to split at 130 GHz and from the splitting the exchange interaction between (/-electrons and Jt-electrons could be estimated. 

---