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For nanocrystalline organic compounds, crystal structure determination is often challenging. If the X-ray powder diffractogram (XRPD) contains less than about 20-30 sharp peaks, indexing frequently fails, and the lattice parameters remain unknown. Consequently, all classical methods for structure determination from powder data cannot be applied.

If indexing fails, only few methods remain:
1) Recrystallisation attempts trying to obtain better powder data
2) A search for an isostructural compound with a known crystal structure
3) Crystal structure prediction by global lattice-energy minimisations
4) Structure solution by a global fit to the powder pattern without prior knowledge of lattice
parameters and space group ("FIDEL Global Fit")
5) Structure determination by a fit to the pair-distribution function ("Global PDF fit")
6) Electron diffraction

This presentation focusses on the FIDEL Global fit and on the Global PDF fit.

The FIDEL Global Fit [1] starts from a large number (106-108) of random structures, having random lattice parameters, molecular position and orientation in different space groups. All structures are fitted to the experimental X-ray powder pattern with the program FIDEL ("Fit with deviating lattice parameters"), which uses cross-correlation functions for comparing simulated and experimental powder patterns as long as the lattice parameters do not match. The best resulting structures are subjected to a Rietveld refinement using TOPAS [2]. The presentation explains the method, gives examples and shows the limitations of the method.

The Global PDF fit [3] functions in a similar fashion as the FIDEL Global Fit, but the fit is performed to the PDF instead of the powder pattern itself. Again, the cross-correlation function is used for comparing simulated and experimental PDFs [4,5]. Finally, a PDF fit with TOPAS is performed. The presentation explains the method, gives examples and shows the limitations of the method.Amorphous organic compounds: If the powder pattern contain no peaks at all, the PDF can still be used to investigate, whether an amorphous powder is fully amorphous (i.e. consists of a random arrangement of molecules), or if it exhibits a preferred local structure (i.e. a preferred arrangement of neighbouring molecules), and if this local structure is similar to the structure of a crystalline form.

References:

1. S. Habermehl, C. Schlesinger, M. U. Schmidt: "Structure determination from unindexed powder data from
   scratch by a global optimization approach using pattern comparison based on cross-correlation functions".
   Acta Cryst. 2022, B78, 195–213. doi.org/10.1107/S2052520622001500 .
2. TOPAS Academic, see A.A Coelho: "TOPAS and TOPAS-Academic: an optimization program integrating
   computer algebra and crystallographic objects written in C++" . J. Appl. Cryst. 2018, 51, 210–218.doi.org/10.1107/S1600576718000183 .
3. C. Schlesinger, S. Habermehl, D. Prill: "Structure determination of organic compounds by a fit to the pair
   distribution function from scratch without prior indexing". J. Appl. Cryst. 2021, 54, 776–786.
   doi.org/10.1107/S1600576721002569 .
4. S. Habermehl, C. Schlesinger, D. Prill: "Comparison and evaluation of pair distribution functions, using a
   similarity measure based on cross-correlation functions". J. Appl. Cryst. 2021, 54, 612–623.
   doi.org/10.1107/S1600576721001722
5. S. Habermehl, C. Schlesinger, M.U. Schmidt, D. Prill: "Vergleich von Atompaar-Verteilungsfunktionen
   mittels Kreuzkorrelationsfunktionen (Comparison of atomic pair distribution functions using cross-
   correlation functions)". German Patent Application 2022, DE 10 2020 004 292 A1.
   depatisnet.dpma.de/DepatisNet/depatisnet?action=pdf&docid=DE102020004292A1&xxxfull=1 .