Absent reflections glide planes

It is seen for this structure that (100) is a reflection plane, (010) a glide plane with translation a/2, and (001) a glide plane with translation a/2 + bj2. The space group is accordingly Y h—Pman. The absent reflections required by V h are (hOl), h odd, and (M0), h- -k odd. Hassel and Luzanski report no reflections of the second class. However, they list (102) in Table V as s.s.schw. This reflection, if real, eliminates this space group and the suggested structure I believe, however, in view of the reasonableness of the structure and the simple and direct way in which it has been derived, as well as of the fact that although thirty reflections of the type (hOl), h even, were observed, only one apparently... 

Thus, while screw axes and glide planes can be detected and distinguished from each other by observing which types of reflections are absent, ordinary rotation axes and reflection planes cannot be detected in this way, since neither type leads to any systematic absences of reflections. 

Consider now a 2 -axis parallel to the b axis. As shown in Fig. 9.4.4, the coordinates x and z are irrelevant for the (OkO) planes, and the systematic absences (OkO) absent with k odd implies the presence of a 2i-axis parallel to b. Note that this is a very weak condition as compared to those for lattice centering and glide planes, and is already covered by them. Since the (OkO) reflections are few in number, some may be too weak to be observable, and hence the determination of a screw axis from systematic absences is not always reliable. 

Refers to the Miller indices (Shkl) values) that are absent from the diffraction pattern. For instance, a body-centered cubic lattice with no other screw axes and glide planes will have a nonzero intensity for all reflections where the sum oi Qi + k + 1) yields an odd number, such as (100), (111), etc. other reflections from planes in which the sum of their Miller indices are even, such as (110), (200), (211), etc. will be present in the diffraction pattern. As these values indicate, there are three types of systematic absences three-dimensional absences (true for all hkl) resulting from pure translations (cell centering), two-dimensional absences from glide planes, and one-dimensional absences from screw axes.[261... 

In Table 6.1, tbe four rows teU us tbe following N is tbe number of independent reflections that should be absent if the respective symmetry element is present. The second row describes how many of those N reflections are stronger than three times their own standard uncertainty. < l > in the third row is the average intensity of the N reflections and in the last row describes the average I/a value of the reflections that should be absent in the presence of the respective symmetry element. The systematic absences clearly indicate the presence of a glide plane in the direction of n and the absence of an a or c glide plane. The situation for the twofold screw axis is less clear. Half of the 33 reflections 0 0 with k 2n that should be absent for a monoclinic 2i -axis are observed, however those observed are significantly weaker than the rest of the data. 

The structure of polyethylene, shown in fig. 4.17, has glide planes perpendicular to the b- and a-axes, which means that reflection in these planes followed by translation by /2 or bj2, respectively, leaves the structure unchanged. Explain why, for any crystal with such glide planes, it follows that the QiQl) and (Ok/) reflections have zero intensity, i.e. the (AO/) and (Ok/) spots are absent, unless h and k are even. 

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