Adapting the charge-flipping algorithm to powder diffraction data
Lukas Palatinus, EPFL Lausanne
The charge-flipping structure-solution algorithm introduced by Oszlányi
and Sütő for single crystals in 2004 has been adapted to accommodate
powder diffraction data in the computer program Superflip.
A flow diagram of the algorithm showing these modifications is given
on the right (click on the image to get a higher resolution picture).
A routine for repartitioning the intensities of overlapping reflections (righthand side) was implemented within the original (lefthand side) iterative procedure. This was done by modifying the electron density map with a histogram-matching algorithm, and then using the Fourier coefficients obtained from this map to repartition the structure factor amplitudes within each group of overlapping reflections.
The algorithm has been tested on a variety of structures, both organic and inorganic, with varying degrees of overlap, diverse symmetries, and different degrees of complexity. The histogram matching step was found to be particularly important for the more difficult structures. Links to two movies showing the electron density development for a typical charge-flipping run are given below.
Click on the image above to see the development of the electron density map during a typical charge-flipping run for a zirconium phosphate phase (3.9 MB).
Click on the image above to see a shorter movie showing only every 13th frame of the electron density development (512 kB). Here the final structure is superimposed, and the start of histogram matching and repartitioning is indicated.
charge flipping works in both real and reciprocal space, so additional
information can be added in either realm. By using phase information
from high-resolution transmission electron microscopy images to
generate starting phase sets for Superflip, the structure of the
zeolite catalyst IM-5 (left) could finally be solved. With 24 Si atoms and 47
O atoms in the asymmetric unit (864 atoms in the unit cell), this
zeolite framework structure is as complex as that of TNU-9, the most
complex known to date.
Click on the image to get a larger picture.
Supported by the Swiss National Science Foundation.
Ch. Baerlocher, L.B. McCusker and L. Palatinus,
"Charge flipping combined with histogram matching to solve complex
crystal structures from powder diffraction data", Z. Kristallogr. (2007), 222, 47-53
Ch. Baerlocher, F. Gramm, L. Massüger, L.B. McCusker, Z. He, S. Hovmöller and X. Zou, "Structure of the polycrystalline zeolite catalyst IM-5 solved by enhanced charge flipping", Science (2007), 315, 1113-1116
Ch. Baerlocher, D. Xie, L.B. McCusker, S.-J. Hwang, I.Y. Chan, K. Ong, A.W. Burton and S.I. Zones, "Ordered silicon vacancies in the framework structure of the zeolite catalyst SSZ-74" Nature Mater. (2008), 7, 631-635
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