Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The Phase Problem in Structure Analysis and its One-Dimensional Solution

The Phase Problem in Structure Analysis and its One-Dimensional Solution In a preceding paper, the author has developed a new method of phase determination using latent lattices. The structure is generated by a shift function which displaces the atoms from their idealized position into the correct one. As a consequence, the number of phases to be determined in reciprocal shift space is reduced to m/2 (M = number of atoms in the unit cell). The application of the new method is subject to a transformation of conventional Fourier coefficients to those of the shift function. This is greatly facilitated by some known conventional phases. In the case of little phase information, a rough proposal may suffice to start the solution of certain sets of linear equations. Each atomic distance in the unit defines a system of M - 1 independent equations. In spite of their interdependence, each system yields just one solution of the phase problem. Two different methods may be applied: (i) (M - 1)/2 exact independent pieces of information on distances may be used to evaluate the corresponding system of linear equations; or (ii) a rough model of the structure with averaged atomic distances or coordinates may serve to apply certain sets of `joker' equations, providing displacements of atoms into the correct direction. In this way, a refined model can be proposed for a repeated use of the joker equations. At the end of this process, a conventional refinement of the structure should be performed. The principles of the new method are explained with the aid of a simple one-dimensional model structure containing one kind of atom only. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

The Phase Problem in Structure Analysis and its One-Dimensional Solution

The Phase Problem in Structure Analysis and its One-Dimensional Solution


Abstract

In a preceding paper, the author has developed a new method of phase determination using latent lattices. The structure is generated by a shift function which displaces the atoms from their idealized position into the correct one. As a consequence, the number of phases to be determined in reciprocal shift space is reduced to m/2 (M = number of atoms in the unit cell). The application of the new method is subject to a transformation of conventional Fourier coefficients to those of the shift function. This is greatly facilitated by some known conventional phases. In the case of little phase information, a rough proposal may suffice to start the solution of certain sets of linear equations. Each atomic distance in the unit defines a system of M - 1 independent equations. In spite of their interdependence, each system yields just one solution of the phase problem. Two different methods may be applied: (i) (M - 1)/2 exact independent pieces of information on distances may be used to evaluate the corresponding system of linear equations; or (ii) a rough model of the structure with averaged atomic distances or coordinates may serve to apply certain sets of `joker' equations, providing displacements of atoms into the correct direction. In this way, a refined model can be proposed for a repeated use of the joker equations. At the end of this process, a conventional refinement of the structure should be performed. The principles of the new method are explained with the aid of a simple one-dimensional model structure containing one kind of atom only.

Loading next page...
 
/lp/international-union-of-crystallography/the-phase-problem-in-structure-analysis-and-its-one-dimensional-7gqm0AcN7L

References (0)

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
International Union of Crystallography
Copyright
Copyright (c) 1996 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S010876739600431X
Publisher site
See Article on Publisher Site

Abstract

In a preceding paper, the author has developed a new method of phase determination using latent lattices. The structure is generated by a shift function which displaces the atoms from their idealized position into the correct one. As a consequence, the number of phases to be determined in reciprocal shift space is reduced to m/2 (M = number of atoms in the unit cell). The application of the new method is subject to a transformation of conventional Fourier coefficients to those of the shift function. This is greatly facilitated by some known conventional phases. In the case of little phase information, a rough proposal may suffice to start the solution of certain sets of linear equations. Each atomic distance in the unit defines a system of M - 1 independent equations. In spite of their interdependence, each system yields just one solution of the phase problem. Two different methods may be applied: (i) (M - 1)/2 exact independent pieces of information on distances may be used to evaluate the corresponding system of linear equations; or (ii) a rough model of the structure with averaged atomic distances or coordinates may serve to apply certain sets of `joker' equations, providing displacements of atoms into the correct direction. In this way, a refined model can be proposed for a repeated use of the joker equations. At the end of this process, a conventional refinement of the structure should be performed. The principles of the new method are explained with the aid of a simple one-dimensional model structure containing one kind of atom only.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Sep 1, 1996

There are no references for this article.