Exact and fast calculation of the X-ray pair distribution function

Reinhard B. Neder; Thomas Proffen

doi:10.1107/S1600576720004616

Exact and fast calculation of the X-ray pair distribution function

Reinhard B. Neder, Thomas Proffen

Powder Diffraction

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

Original language	English
Pages (from-to)	710-721
Number of pages	12
Journal	Journal of Applied Crystallography
Volume	53
DOIs	https://doi.org/10.1107/S1600576720004616
State	Published - Jun 1 2020

Funding

This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract No. DE-AC02-06CH11357.

Funders	Funder number
US Department of Energy
U.S. Department of Energy
Office of Science
Argonne National Laboratory	DE-AC02-06CH11357

Keywords

PDF
pair distribution function
powder diffraction.

Access to Document

10.1107/S1600576720004616

Cite this

@article{7e0c851587a240cba9f6a1b5d3079fe2,

title = "Exact and fast calculation of the X-ray pair distribution function",

abstract = "A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.",

keywords = "PDF, pair distribution function, powder diffraction.",

author = "Neder, {Reinhard B.} and Thomas Proffen",

year = "2020",

month = jun,

day = "1",

doi = "10.1107/S1600576720004616",

language = "English",

volume = "53",

pages = "710--721",

journal = "Journal of Applied Crystallography",

issn = "0021-8898",

publisher = "International Union of Crystallography",

}

TY - JOUR

T1 - Exact and fast calculation of the X-ray pair distribution function

AU - Neder, Reinhard B.

AU - Proffen, Thomas

PY - 2020/6/1

Y1 - 2020/6/1

N2 - A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

AB - A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

KW - PDF

KW - pair distribution function

KW - powder diffraction.

UR - http://www.scopus.com/inward/record.url?scp=85096938261&partnerID=8YFLogxK

U2 - 10.1107/S1600576720004616

DO - 10.1107/S1600576720004616

M3 - Article

AN - SCOPUS:85096938261

SN - 0021-8898

VL - 53

SP - 710

EP - 721

JO - Journal of Applied Crystallography

JF - Journal of Applied Crystallography

ER -

Exact and fast calculation of the X-ray pair distribution function

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this