Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

The Fourier Method of Crystal Structure Analysis

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(F0Fc)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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

COCHRAN, W. The Fourier Method of Crystal Structure Analysis. Nature 161, 765 (1948). https://doi.org/10.1038/161765a0

Download citation

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/161765a0

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing