Izlaganje sa skupa

A Concept for Crystal Structure Determination without FOURIER Inversion: Some Steps towards Application

Karl F. Fischer ; Technical Physics, University of Saarbruecken, Saarbruecken, Germany
Armin Kirfel ; Crystallography/Mineralogy, University of Bonn, Bonn, Germany
Helmuth Zimmermann ; Crystallography/Condensed Matter Physics, University of Erlangen, Erlangen, Germany

Sažetak

Determination of a crystal structure without Fourier calculation of the scattering density (thus
also avoiding the phase problem) is achieved in a fractional coordinate parameter space of dimension
3m where m is the number of independent atoms, reduced to equal point scatterers at rest.
For demonstration of the basic ideas, two-dimensional parameter spaces (representing, e. g.,
one-dimensional two-atom structures) are used. "Central reciprocal lattice row" reflections allow
for solving one-dimensional projections of the structure, each requiring less reflections and
simultaneously providing better resolution than does a corresponding Fourier summation. The
projection solution can be obtained either from the common intersection of the hyper-faces in
the m-dimensional parameter space defined by the chosen scattering amplitudes or by exploring
the permitted "solution region(s)" that follow from the mere ranking of these amplitudes. All
possible solutions satisfying the data are found, including "false minima". The reconstruction
of a hypothetical three-dimensional 11 atom structure from the solutions of one-dimensional
projections is illustrated in an example based on "theoretical", i. e. error-free data. Since most
of the theoretical background is laid down in two former, refereed publications, emphasis is put
on different options to cope with the computing demands in practical applications. Advantages
and shortcomings of the concept are discussed.

Ključne riječi

crystal structure analysis; unique solution; homometric solutions; phase problem eliminated; intensity inequalities

Hrčak ID:

28508

URI

https://hrcak.srce.hr/28508

Datum izdavanja:

30.6.2008.

Posjeta: 1.537 *