Correlating Sampling and Intensity Statistics in Nanoparticle Diffraction Experiments

Journal Article · Sat Aug 01 04:00:00 EDT 2015 · Journal of Applied Crystallography

DOI:https://doi.org/10.1107/S1600576715011747· OSTI ID:1228977

Ozturk, Hande ^[1]; Yan, Hanfei ^[2]; Hill, John P. ^[2]; Noyan, I. Cevdet ^[1]

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1. Columbia Univ., New York, NY (United States)
2. Brookhaven National Lab. (BNL), Upton, NY (United States)

In this article, [Öztürk, Yan, Hill & Noyan (2014). J. Appl. Cryst. 47, 1016-1025] it was shown that the sampling statistics of diffracting particle populations within a polycrystalline ensemble depended on the size of the constituent crystallites: broad X-ray peak breadths enabled some nano-sized particles to contribute more than one diffraction spot to Debye-Scherrer rings. Here it is shown that the equations proposed by Alexander, Klug & Kummer [J. Appl. Phys. (1948), 19, 742-753] (AKK) to link diffracting particle and diffracted intensity statistics are not applicable if the constituent crystallites of the powder are below 10 nm. In this size range, (i) the one-to-one correspondence between diffracting particles and Laue spots assumed in the AKK analysis is not satisfied, and (ii) the crystallographic correlation between Laue spots originating from the same grain invalidates the assumption that all diffracting plane normals are randomly oriented and uncorrelated. Such correlation produces unexpected results in the selection of diffracting grains. Three or more Laue spots from a given grain for a particular reflection can only be observed at certain wavelengths. In addition, correcting the diffracted intensity values by the traditional Lorentz term, 1/cos [theta], to compensate for the variation of particles sampled within a reflection band does not maintain fidelity to the number of poles contributing to the diffracted signal. A new term, cos [theta]B/cos [theta], corrects this problem.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• OSTI ID: 1228977
• Report Number(s): BNL--111052-2015-JA
• Journal Information: Journal of Applied Crystallography, Journal Name: Journal of Applied Crystallography Journal Issue: 4 Vol. 48; ISSN 0021-8898
• Publisher: International Union of Crystallography
• Country of Publication: United States
• Language: English

Related Subjects

77 NANOSCIENCE AND NANOTECHNOLOGY
lorentz factor
nanoparticles
sampling statistics
x-ray diffraction