• DOI:10.1524/zkri.1935.90.1.517
• Corpus ID: 102041995

A Direct Method for the Determination of the Components of Interatomic Distances in Crystals

@article{Patterson1935ADM,
  title={A Direct Method for the Determination of the Components of Interatomic Distances in Crystals},
  author={A. L. Patterson},
  journal={Zeitschrift f{\"u}r Kristallographie - Crystalline Materials},
  year={1935},
  volume={90},
  pages={517 - 542}
}

• A. L. Patterson
• Published 1 October 1935
• Mathematics
• Zeitschrift für Kristallographie - Crystalline Materials

In a recent publication) the author has given a brief account of a new method for the direct determination of the components of interatomic distances in crystals. The method is based on the application of the results of the theory of Four i e r series. I t is the object of the present paper to give a more detailed account of the underlying theory and to describe the application of the method to specific examples. In addition, two new results are presented which promise to increase the usefulness of the method for the investigation of complex structures. The paper is divided into two parts. In Part I, which contains the theory of the method, a Fourier Series whose coefficients are the observed values of F 2 (hkl) is derived. This series is shown to be a weighted average distribution of electrons about any point in the crystal. I t is then shown that the peaks of this distribution occur at points which correspond very closely in direction and magnitude with the interatomic distances in the crystal. A second series is then set up, with coefficients derived from those of the first, which corresponds closely to a weighted average distribution of atomic centres. This gives the interatomic distances with greater resolution than the first. Additional results which are of value in practical applications are also derived. In Part II, several known structures are discussed in terms of the new method.