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

^{[1]}
;
^{[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
 Publication Date:
 Report Number(s):
 BNL1142642017JA
Journal ID: ISSN 16005767; JACGAR
 Grant/Contract Number:
 SC0012704; AC0298CH10886
 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 16005767
 Publisher:
 International Union of Crystallography
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Xray diffraction; nanocrystals; powder diffraction; sampling and intensity statistics; Lorentz factor
 OSTI Identifier:
 1392243
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.,
Web. doi:10.1107/S1600576717010494.
Öztürk, Hande, & Noyan, I. Cevdet. Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment. United States. doi:10.1107/S1600576717010494.
Öztürk, Hande, and Noyan, I. Cevdet. 2017.
"Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment". United States.
doi:10.1107/S1600576717010494. https://www.osti.gov/servlets/purl/1392243.
@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 = {2017},
month = {8}
}