Symmetry equivalent reflections

The Laue symmetry of the diffraction pattern is now reduced to the symmetry of the non-centrosymmetric point group to which the crystal belongs (see Table 2 a listing of symmetry-equivalent reflections in the non-centrosymmetric point groups is available26). Under these circumstances, it is possible to determine different manifestations of non-centrosymmetry in a crystal, such as ... 

The previously determined unit-cell and space-group data were confirmed from precession photographs, the 6/wtnwt diffraction symmetry being further confirmed by careful intensity measurements with scintillation counters of several sets of symmetry-equivalent reflections. 

A crystal was mounted on an Enraf-Nonius CAD-4 four-circle diffractometer, and accurate cell dimensions were obtained by a least-squares fit to three sets of eight symmetry-equivalent reflections with 26 between 25 and 29°. The cell dimensions and data collection parameters are summarized in Table I. 

Now, one might think that this should not be a serious problem, the scaling of reflections, but it is, and furthermore it often serves as one of the most serious sources of error in the creation of a data set when it is done improperly or carelessly. If we consider, for example, the hkl and —hk — l symmetry equivalent reflections from a monoclinic crystal, or the hkl and —h — k — l reflections from any crystal (again ignoring anomalous dispersion) we would expect any measured intensity hu to be exactly equal to its symmetry or Friedel mate. They seldom are, however, and we may consider the reasons why. 

The reflections (2) are called symmetry equivalent reflections the set eontains both the Friedel opposites (Chapter 3). If the space group is non-eentrosymmetric, the reflections (2) and their Friedel opposites, say ... 

GTP hydrolysis occurs with a half-life of about 40 min at room temperature. This is the same rate as encountered in solution. The synchrotron Laue data were recorded on photographic film at EMBL, Hamburg (X31 beam line). The data were processed using the Daresbury Laue software where the A-curve was explicitly determined from symmetry equivalent reflections (Campbell et al 1986) Helliwell et al 1989b). 

This is assuming that all symmetry-equivalent reflections are merged (except Friedel pairs for non-centrosymmetric structures) and not treated as independent for the calculation of the data-parameter ratio. 

In the case of the powder method, all the symmetry equivalent reflections superimpose because they all have the same spacing (Section 3.5.3). Thus, this method does not allow us to observe the Laue symmetry, only the metric of the unit cell. For the same reason, the rotation method is also poorly adapted for the determination of the symmetry. There are other diffraction methods, which are not described in this work, by which all the reflections may be individually observed without superposition from which it is also possible to determine the Laue class of a crystal and consequently the crystal system. Is it possible to obtain other information about the symmetry and, in particular, the Bravais class and the space group ... 

Using this averaging procedure, the full list of structure factors derived from all scans in an experiment is reduced to a list of nonequivalent reflections with appropriate error bars. In bulk crystallography, one often uses a so-called J -factor (reliability factor) to describe the average discrepancy of symmetry-equivalent reflections... 

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