Direct Structure Determination by Optical-Transform Methods

Nature ◽  
1957 ◽  
Vol 180 (4583) ◽  
pp. 431-432
Author(s):  
M. M. CROWDER ◽  
K. A. MORLEY ◽  
C. A. TAYLOR
1960 ◽  
Vol 4 ◽  
pp. 1-18
Author(s):  
Arnold Hargreaves

AbstractOptical transforms are of particular value In the earlier stages of crystal-structure determination; they enable trial structures to be tested rapidly and may indicate the nature of changes which will improve a postulated structure. The optical transforms are produced in a simple instrument called an optical diffractometer. The projected positions of the atoms in a postulated structure are represented by a set of holes punched in a mask, and the diffractometer produces the Fraunhofer diffraction pattern of the mask. The distribution of intensity in the optical transform is comparable, when sampled at suitable Intervals, with the distribution of intensity among the observed intensities in a particular zone of X-ray reflections. The use of optical transforms in the determination of crystal structures and in the study of imperfect structures will be illustrated by examples.


1970 ◽  
Vol 26 (2) ◽  
pp. 194-196
Author(s):  
G. Harburn ◽  
C. A. Taylor

Sir Lawrence Bragg's flair for identifying the essential physical principles underlying the most complex phenomena is exemplified by his introduction of optical diffraction studies as a means of solving X-ray diffraction problems. This paper reviews briefly some of the many developments that have stemmed from his original idea.


The analogy between the diffraction of light by a set of holes, and the diffraction of X -rays by a set of atoms can be exploited in solving many different types of X -ray diffraction problem . A special instrument has been built to obtain diffraction patterns rapidly, making possible several different approaches to the determination of crystal structures. Of particular importance is that involving the ‘optical transform’ of a molecular representation. Consideration of the optical transform, which is closely related to the Fourier transform, can, for simple space groups, lead directly to the crystal structure. For more complicated space groups, optical transforms of molecules in different orientations have to be combined, and some rules governing their combination are given. The discussion includes several examples of structures which have been determined by optical-transform methods. These methods require the presentation of the X -ray data in the form of a weighted reciprocal lattice, from which information can often be obtained directly. For several new structures such information as the separation of two similarly oriented molecules, or the orientation of hexagonal arrangements of atoms, has been deduced by considering the weighted reciprocal lattice alone. In some cases this led to the complete structure; in others it was a valuable supplement to the optical transform method. Despite the lack of quantitative accuracy, optical methods can be of use in refining approximate structures by ordinary Fourier methods. Examples are given of the deter­mination of the relative phase angles of the reflexions of both centrosymmetric and non-centrosymmetric structures. The relationships between optical methods and more conventional methods of structure determination are discussed.


Author(s):  
Douglas L. Dorset ◽  
Anthony J. Hancock

Lipids containing long polymethylene chains were among the first compounds subjected to electron diffraction structure analysis. It was only recently realized, however, that various distortions of thin lipid microcrystal plates, e.g. bends, polar group and methyl end plane disorders, etc. (1-3), restrict coherent scattering to the methylene subcell alone, particularly if undistorted molecular layers have well-defined end planes. Thus, ab initio crystal structure determination on a given single uncharacterized natural lipid using electron diffraction data can only hope to identify the subcell packing and the chain axis orientation with respect to the crystal surface. In lipids based on glycerol, for example, conformations of long chains and polar groups about the C-C bonds of this moiety still would remain unknown.One possible means of surmounting this difficulty is to investigate structural analogs of the material of interest in conjunction with the natural compound itself. Suitable analogs to the glycerol lipids are compounds based on the three configurational isomers of cyclopentane-1,2,3-triol shown in Fig. 1, in which three rotameric forms of the natural glycerol derivatives are fixed by the ring structure (4-7).


Author(s):  
William Krakow

Tilted beam dark-field microscopy has been applied to atomic structure determination in perfect crystals, several synthesized molecules with heavy atcm markers and in the study of displaced atoms in crystals. Interpretation of this information in terms of atom positions and atom correlations is not straightforward. Therefore, calculated dark-field images can be an invaluable aid in image interpretation.


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