Journal Article

PUBDB-2025-01288

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Linearization routines for the parameter space concept to determine crystal structures without Fourier inversion

Vallinayagam, M. ; Nentwich, M. (Corresponding author)Extern*DESY* ; Meyer, D. C.Extern* ; Zschornak, M.Extern*

2025
Munksgaard Copenhagen

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Please use a persistent id in citations: doi:10.1107/S1600576725001955

Abstract: We present the elaboration and first generally applicable linearization routines of the parameter space concept (PSC) for determining one-dimensionally projected structures of m independent scatterers. This crystal determination approach does not rely on Fourier inversion but rather considers all structure parameter combinations consistent with available diffraction data in a para- meter space of dimension m. The method utilizes m structure-factor amplitudes or intensities represented by piecewise analytic hyper-surfaces, to define the acceptable parameter regions. By employing the isosurfaces, the coordinates of the point scatterers are obtained through the intersection of multiple isosur- faces. This approach allows for the detection of all possible solutions for the given structure-factor amplitudes in a single derivation. Taking the resonant contrast into account, the spatial resolution achieved by the presented method may exceed that of traditional Fourier inversion, and the algorithms can be significantly optimized by exploiting the symmetry properties of the isosurfaces. The applied one-dimensional projection demonstrates the efficiency of the PSC linearization approach based on fewer reflections than Fourier sums. The Monte Carlo simulations, using the projections of various random two- and three-atom structure examples, are presented to illustrate the universal applicability of the proposed method. Furthermore, ongoing efforts aim to enhance the efficiency of data handling and to overcome current constraints, promising further advancements in the capabilities and accuracy of the PSC framework.

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Contributing Institute(s):

1. Informationstechnologie (IT)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)442646446 - Parameter Space Concept als Strukturlösungsmethodik für die Einkristalldiffraktometrie (442646446) (442646446)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DEAL Wiley ; Ebsco Academic Search ; Essential Science Indicators ; IF >= 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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