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Algorithm for distance list extraction from pair distribution functions
Author(s) -
Gu Ran,
Banerjee Soham,
Du Qiang,
Billinge Simon J. L.
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319008647
Subject(s) - gaussian , key (lock) , algorithm , distribution (mathematics) , debye , computer science , regular polygon , spectrum (functional analysis) , mathematical optimization , mathematics , mathematical analysis , physics , geometry , quantum mechanics , computer security
An algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non‐convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.