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

Abstract

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.

Authors:
ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II
  2. Columbia Univ., New York, NY (United States). Applied Physics and Applied Mathematics
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1392243
Report Number(s):
BNL-114264-2017-JA
Journal ID: ISSN 1600-5767; JACGAR
Grant/Contract Number:  
SC0012704; AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Crystallography (Online)
Additional Journal Information:
Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 50; Journal Issue: 5; Journal ID: ISSN 1600-5767
Publisher:
International Union of Crystallography
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; X-ray diffraction; nanocrystals; powder diffraction; sampling and intensity statistics; Lorentz factor

Citation Formats

Öztürk, Hande, and Noyan, I. Cevdet. Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment. United States: N. p., 2017. Web. doi:10.1107/S1600576717010494.
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Öztürk, Hande, & Noyan, I. Cevdet. Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment. United States. https://doi.org/10.1107/S1600576717010494
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Öztürk, Hande, and Noyan, I. Cevdet. Thu . "Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment". United States. https://doi.org/10.1107/S1600576717010494. https://www.osti.gov/servlets/purl/1392243.
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@article{osti_1392243,
title = {Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment},
author = {Öztürk, Hande and Noyan, I. Cevdet},
abstractNote = {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.},
doi = {10.1107/S1600576717010494},
journal = {Journal of Applied Crystallography (Online)},
number = 5,
volume = 50,
place = {United States},
year = {Thu Aug 24 00:00:00 EDT 2017},
month = {Thu Aug 24 00:00:00 EDT 2017}
}
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https://doi.org/10.1107/S1600576717010494
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    Works referencing / citing this record:

    Structure and magnetic properties of mechanically alloyed nanocrystalline Fe-46 at.% Co-34 at.% Ni-20 at.% alloy powder from cryogenic to elevated temperatures
    journal, March 2019

    • Thotakura, Ganesh Varma; Rathi, Anuj; Jayaraman, Tanjore V.
    • Applied Physics A, Vol. 125, Issue 4
    • DOI: 10.1007/s00339-019-2535-7
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