Structure determination from powder data using anomalous scattering: 
difference and partial Patterson densities, and phases of structure factors.


K. Burger, W. Prandl


Institut fuer Kristallographie der Universitaet Tuebingen
Charlottenstrasse 33, D - 72070 Tuebingen, Germany


S. Doyle

HASYLAB, DESY and
TH Darmstadt, FB Strukturforschung,
Petersenstr. 20, D--64287 Darmstadt, Germany

Keywords:
powder, structure determination, Patterson density, anomalous
scattering, dispersion

Oct. 1st, 1996

Abstract

For structure determination from X-ray powder data, anomalous (resonant)
scattering can be used to obtain difference Patterson and partial Patterson 
densities as well as phases of structure factors. Usually tuneable synchrotron
radiation is used, and two ore more powder patterns near and far the 
absorption edge of an atom type contained in the crystal are recorded. 

The algebraic theory together with some novel and efficient approximations 
is given in detail. Also symmetry restrictions, experimental and scaling 
procedures, and the use of the Maximum-Entropy method (MEM) are discussed. 
The application to the structure of an iron garnet Fe2Ca3Ge3O12 is presented.  
This resulted in the first determination of two partial Patterson densities: 
of the iron atoms and of germanium atoms.

From an MEM calculation of the electron-density, using the signed structure 
factors F(H)  together with only the absolute values |F(H)| of the remaining
reflections, all atoms could be localized with good resolution and low
background, whereas the ordinary Fourier calculation failed completely to 
show the oxygen atoms.  This result is based on only 34 unique out of 83 
total reflections in 0 <= sin(theta)/lambda <= 0.494 1/A.  These successful 
applications open up new possibilities in the structure determination of 
unknown compounds.