Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

Öztürk, Hande; Noyan, I. Cevdet

doi:10.1107/S1600576717010494

Title: Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

Journal Article · Thu Aug 24 00:00:00 EDT 2017 · Journal of Applied Crystallography (Online)

DOI:https://doi.org/10.1107/S1600576717010494· OSTI ID:1392243

^[1]; Noyan, I. Cevdet ^[2]

Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II
Columbia Univ., New York, NY (United States). Applied Physics and Applied Mathematics

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystalline powder samples.

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Research Organization:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012704; AC02-98CH10886

OSTI ID:: 1392243

Report Number(s):: BNL-114264-2017-JA; JACGAR

Journal Information:: Journal of Applied Crystallography (Online), Vol. 50, Issue 5; ISSN 1600-5767

Publisher:: International Union of CrystallographyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 4 works

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References (20)

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Structure and magnetic properties of mechanically alloyed nanocrystalline Fe-46 at.% Co-34 at.% Ni-20 at.% alloy powder from cryogenic to elevated temperatures Thotakura, Ganesh Varma; Rathi, Anuj; Jayaraman, Tanjore V. Applied Physics A, Vol. 125, Issue 4 https://doi.org/10.1007/s00339-019-2535-7	journal	March 2019

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sampling and intensity statistics
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Title: Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

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