Abstract
THE intensity of an X-ray crystal reflection is governed by many factors, such as the state of perfection of the specimen and the electronic structure of the component atoms, but chiefly by the relative arrangement of the atoms in the unit cell. The resultant amplitude obtained by combining simple sine waves emanating from each atom in the structure is known as the geometrical structure amplitude. Dr. K. Lonsdale has carried this summation over the co-ordinates of the general positions hi which the atoms lie (“equivalent points”) for each of the 230 space groups of mathematical crystallography. The general formulae she has already given in the “International Tables for the Determination of Crystal Structures” (see NATTJBE, 137, 927; 1936), but in the present work these equations are reduced to forms in which they can be applied directly for any given combination of indices. In addition, the converse formulae, in which the electron density at any point is expressed as a Fourier series, are given in convenient form, the summation here being taken over the eight quadrants of the reciprocal lattice, so that only positive values of the indices Jikl need be considered, if the axes are orthogonal. For non-centrosymmetrical structures, the way in which the phase constants vary in the different quadrants is also given in every case.
Simplified Structure Factor and Electron Density Formulæ for the 230 Space Groups of Mathematical Crystallography
By Dr. Kathleen Lonsdale. (Published for the Royal Institution.) Pp. vii + 181. (London: G. Bell and Sons, Ltd., 1936.) 10s. net.
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ROBERTSON, J. Structure Factor and Electron Density Formulæ. Nature 138, 627 (1936). https://doi.org/10.1038/138627a0
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DOI: https://doi.org/10.1038/138627a0