# The use of structural information in the phase probability of a triple product

The use of structural information in the phase probability of a triple product A derivation is given of the probability distribution of the phase of a triple product = h1 + = h2 + = h3 with h1 + h2 + h3 = 0, employing a priori structural information. This derivation is valid if normalized group scattering factors are small and certain conditions for h1, h2, h3 are fulfilled. To derive this distribution it is necessary to regard the atomic position vectors as primitive random variables, not all independent in view of the structural information. It is also shown that if no structural information is available the expression for the probability distribution of the phase of a triple product, where the atomic position vectors are regarded as the primitive random variables, is identical to the one where h1, h2, h3 are regarded as the primitive random variables. In the first case certain conditions for h1, h2, h3 must be fulfilled; in the second the atomic position vectors are subject to certain conditions. 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 use of structural information in the phase probability of a triple product

, Volume 33 (1): 100 – Jan 1, 1977

## The use of structural information in the phase probability of a triple product

, Volume 33 (1): 100 – Jan 1, 1977

### Abstract

A derivation is given of the probability distribution of the phase of a triple product = h1 + = h2 + = h3 with h1 + h2 + h3 = 0, employing a priori structural information. This derivation is valid if normalized group scattering factors are small and certain conditions for h1, h2, h3 are fulfilled. To derive this distribution it is necessary to regard the atomic position vectors as primitive random variables, not all independent in view of the structural information. It is also shown that if no structural information is available the expression for the probability distribution of the phase of a triple product, where the atomic position vectors are regarded as the primitive random variables, is identical to the one where h1, h2, h3 are regarded as the primitive random variables. In the first case certain conditions for h1, h2, h3 must be fulfilled; in the second the atomic position vectors are subject to certain conditions.

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Publisher
International Union of Crystallography
Copyright (c) 1977 International Union of Crystallography
ISSN
0567-7394
DOI
10.1107/S0567739477000217
Publisher site
See Article on Publisher Site

### Abstract

A derivation is given of the probability distribution of the phase of a triple product = h1 + = h2 + = h3 with h1 + h2 + h3 = 0, employing a priori structural information. This derivation is valid if normalized group scattering factors are small and certain conditions for h1, h2, h3 are fulfilled. To derive this distribution it is necessary to regard the atomic position vectors as primitive random variables, not all independent in view of the structural information. It is also shown that if no structural information is available the expression for the probability distribution of the phase of a triple product, where the atomic position vectors are regarded as the primitive random variables, is identical to the one where h1, h2, h3 are regarded as the primitive random variables. In the first case certain conditions for h1, h2, h3 must be fulfilled; in the second the atomic position vectors are subject to certain conditions.

### Journal

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

Published: Jan 1, 1977

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