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Media type:
E-Article
Title:
Structure determination without Fourier inversion. Part I. Unique results for centrosymmetric examples
Contributor:
Fischer, Karl F.;
Kirfel, Armin;
Zimmermann, Helmuth
Published:
Walter de Gruyter GmbH, 2005
Published in:
Zeitschrift für Kristallographie - Crystalline Materials, 220 (2005) 7, Seite 643-656
Language:
English
DOI:
10.1524/zkri.220.7.643.67099
ISSN:
2196-7105;
2194-4946
Origination:
Footnote:
Description:
AbstractA concept is presented for determining a one-dimensional structure ofmindependent point scatterers by mapping into anm-dimensional spacePmat leastmobservations as (m– 1)-dimensional so-called “isosurfaces” defined bys(h) ·g(h) org(h) alone, wheres(h) andg(h) are sign and modulus, respectively, of the geometrical structure factor. Values ofg(h) are derived from the observed |F(h)|. The “solution vector(s)”, (x1, …,xm), representing the coordinatesxjof the point scatterers is (are) found from the “common” intersection(s) ofn≥mdifferent isosurfaces. Homometric and quasi-homometric structures can thus safely be detected from multiple solutions, the latter mainly arising from the experimental uncertainties of theg(h). Spatial resolution is by far higher than that offered by a corresponding Fourier transform. Computer time can be drastically reduced upon consideration of both the symmetry ofPmand the anti-symmetry and self-similarity properties of the isosurfaces, which allow for tayloring of the intersection search routines and/or applying linear approximations. The basic principles of the method are illustrated by various two- and three-atom structure examples and discussed in view of the application potential to real structure problems.