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The maximum-entropy method in superspace

Title data

van Smaalen, Sander ; Palatinus, Lukas ; Schneider, Martin:
The maximum-entropy method in superspace.
In: Acta Crystallographica Section A. Vol. 59 (2003) Issue 5 . - pp. 459-469.
ISSN 1600-5724
DOI: https://doi.org/10.1107/S010876730301434X

Official URL: Volltext

Abstract in another language

One of the applications of the maximum-entropy method (MEM) in crystallography is the reconstruction of the electron density from phased structure factors. Here the application of the MEM to incommensurately modulated crystals and incommensurate composite crystals is considered. The MEM is computed directly in superspace, where the electron density in the (3+\it d)-dimensional unit cell (\it d>0) is determined from the scattering data of aperiodic crystals. Periodic crystals (\it d=0) are treated as a special case of the general formalism. The use of symmetry in the MEM is discussed and an efficient algorithm is proposed for handling crystal symmetry. The method has been implemented into a computer program \it BayMEM and applications are presented to the electron density of the periodic crystal NaV\sb 2O\sb 5 and the electron density of the incommensurate composite crystal (LaS)\sb 1.14NbS\sb 2. The MEM in superspace is shown to provide a model-independent estimate of the shapes of the modulation functions of incommensurate crystals. The discrete character of the electron density is found to be the major source of error, limiting the accuracy of the reconstructed modulation functions to approximately 10 of the sizes of the pixels. MaxEnt optimization using the Cambridge and Sakata—Sato algorithms are compared. The Cambridge algorithm is found to perform better than the Sakata—Sato algorithm, being faster, always reaching convergence, and leading to more reliable density maps. Nevertheless, the Sakata—Sato algorithm leads to similar density maps, even in cases where it does not reach complete convergence.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: maximum-entropy method; aperiodic crystals; electron density
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography > Chair Crystallography - Univ.-Prof. Dr. Sander van Smaalen
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 530 Physics
Date Deposited: 17 Mar 2016 07:55
Last Modified: 17 Mar 2016 07:55
URI: https://eref.uni-bayreuth.de/id/eprint/31880