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On the Maxima of the Patterson Functions

On the Maxima of the Patterson Functions For the case of a one-dimensional crystal (and, therefore, in three dimensions as well) it is possible to construct a counter-example, realizing the following situation: the electron density is the sum of two monatomic distributions, but the number of peaks in Patterson's diagram exceeds three, whereas the standard rule would claim at most three such peaks. Consequently, the usual "addition rule of peaks" is false as a general mathematical theorem. It follows that the explanation of the empirical success of this rule in crystallography lacks to date a mathematical basis, that is, a non-empirical foundation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review American Physical Society (APS)

On the Maxima of the Patterson Functions

Hartman, Philip; Wintner, Aurel
Physical Review , Volume 81 (2) – Jan 15, 1951
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1951 The American Physical Society
ISSN
1536-6065
DOI
10.1103/PhysRev.81.271
Publisher site
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Abstract

For the case of a one-dimensional crystal (and, therefore, in three dimensions as well) it is possible to construct a counter-example, realizing the following situation: the electron density is the sum of two monatomic distributions, but the number of peaks in Patterson's diagram exceeds three, whereas the standard rule would claim at most three such peaks. Consequently, the usual "addition rule of peaks" is false as a general mathematical theorem. It follows that the explanation of the empirical success of this rule in crystallography lacks to date a mathematical basis, that is, a non-empirical foundation.

Journal

Physical Review – American Physical Society (APS)

Published: Jan 15, 1951

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