Abstract
THE method of Fourier synthesis from observed X-ray reflexion intensities has been widely used as a means of determining interatomic bond-lengths and bond-angles. Alternative methods of deriving accurate atomic co-ordinates from X-ray diffraction data have been suggested by Hughes1 and by Booth2. Their methods are similar in that the co-ordinates are chosen so as to minimize some function of the observed and calculated structure amplitudes, F0 and Fc Hughes, for example, chooses co-ordinates which minimize Σw(F0 — Fc)2. The weighting factors w are introduced to allow for the fact that the F0‘s are not all measurable with the same accuracy. An obvious weakness of the Fourier method is that all F0‘s, including those few likely to be systematically in error because of extinction, etc., are included as coefficients in the Fourier series and must therefore influence the result. The omission of certain coefficients from the series because they cannot be observed experimentally except with radiation of very short wave-length also leads to ’finite summation‚ errors3.
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References
Hughes, J. Amer. Chem. Soc., 63, 1737 (1941).
Booth, Nature, 160, 196 (1947).
Booth, Proc. Roy. Soc., A, 188, 77 (1946).
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COCHRAN, W. The Fourier Method of Crystal Structure Analysis. Nature 161, 765 (1948). https://doi.org/10.1038/161765a0
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DOI: https://doi.org/10.1038/161765a0
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