# A modified Patterson function

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- International Union of Crystallography
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## Abstract

A modified Patterson function 397 Acta Cryst. (1956). 9, 397 A Modified Patterson Function BY J. M. COWLEY Chemical Physics Section, Division of Industrial Chemistry, Commonwealth Scientific and Industrial Research Organization, Box 4331, G. P. 0., Melbourne, Victoria, Australia (Received 30 September 1955) If the Fourier coefficients [Fh] 2 of a Patterson function are replaced by a power series in I/:h[ ~, which is approximately proportional to IFhl over a limited range, the resulting modified Patterson function is sharpened and the smaller vector peaks are emphasized. This facilitates the interpreta- tion of the Patterson function in some cases. As an example, modified and unmodified Patterson projections of basic lead carbonate are compared. It has been observed that, in two-dimensional Patter- son projections calculated from X-ray or electron diffraction intensities, the map is frequently dominated by the few largest terms of the Fourier summation to such an extent that it appears to contain little of the information associated with the smaller inten- sities. This is noticeable when the range of intensities is large, as in patterns from crystals of relatively high symmetry. It is most striking when the unit cell or its projection is, to a first approximation, made up by the repetition of a sub-cell. The reflexions corre- sponding to the sub-cell are then much stronger than the rest. The larger number of weaker reflexions con- tain the information on the deviations from the sub- cell, but this information is largely submerged beneath the large sub-cell vector peaks in the Patterson projec- tion. The interpretation of the detail observed, more- over, is often uncertain because the errors in measure- ment of the greater intensities are of the same order as the magnitudes of the smaller intensities. 0.3 / / / 0.2 /I/I// 0.1 . " /~ '~- .-~'h ! i 0.2 ' o J4 IFhi 0~6 0'.8 Fig. 1. P lo t of o~-h ---- IFhl~--31Fh:+4:'hle--IFhl 8

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