# The application of phase relationships to complex structures. VlI. Magic integers

The application of phase relationships to complex structures. VlI. Magic integers With phases expressed in cycles so that 0 < 1 it is possible with a single symbol x, in the range 0 to 1, to represent several phases, say m, by = nix mod (1) where i runs from 1 to m and the integers, ni, are referred to as 'magic integers'. A starting set of phases may consist of some which fix the origin and enantiomorph, some known by 1 relationships for example and others given magic-integer representation in terms of x, y and z. Relationships between the starting-set phases then appear in the form Hx + Ky + Lz + b 0, and maxima of the function, = |E1rE2rE3r| cos {2(Hrx + Kry + Lrz + b)} , lead to sets of possible values of the unknown phases in the starting set of reflexions. By means of the magic-integer process complex structures requiring very large starting sets may be tackled. Examples of the application of the method are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography International Union of Crystallography

# The application of phase relationships to complex structures. VlI. Magic integers

, Volume 31 (1): 53 – Jan 1, 1975

## The application of phase relationships to complex structures. VlI. Magic integers

, Volume 31 (1): 53 – Jan 1, 1975

### Abstract

With phases expressed in cycles so that 0 < 1 it is possible with a single symbol x, in the range 0 to 1, to represent several phases, say m, by = nix mod (1) where i runs from 1 to m and the integers, ni, are referred to as 'magic integers'. A starting set of phases may consist of some which fix the origin and enantiomorph, some known by 1 relationships for example and others given magic-integer representation in terms of x, y and z. Relationships between the starting-set phases then appear in the form Hx + Ky + Lz + b 0, and maxima of the function, = |E1rE2rE3r| cos {2(Hrx + Kry + Lrz + b)} , lead to sets of possible values of the unknown phases in the starting set of reflexions. By means of the magic-integer process complex structures requiring very large starting sets may be tackled. Examples of the application of the method are given.

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Publisher
International Union of Crystallography
Copyright (c) 1975 International Union of Crystallography
ISSN
0567-7394
DOI
10.1107/S0567739475000095
Publisher site
See Article on Publisher Site

### Abstract

With phases expressed in cycles so that 0 < 1 it is possible with a single symbol x, in the range 0 to 1, to represent several phases, say m, by = nix mod (1) where i runs from 1 to m and the integers, ni, are referred to as 'magic integers'. A starting set of phases may consist of some which fix the origin and enantiomorph, some known by 1 relationships for example and others given magic-integer representation in terms of x, y and z. Relationships between the starting-set phases then appear in the form Hx + Ky + Lz + b 0, and maxima of the function, = |E1rE2rE3r| cos {2(Hrx + Kry + Lrz + b)} , lead to sets of possible values of the unknown phases in the starting set of reflexions. By means of the magic-integer process complex structures requiring very large starting sets may be tackled. Examples of the application of the method are given.

### Journal

Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General CrystallographyInternational Union of Crystallography

Published: Jan 1, 1975

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