Noyan, I. Cevdet | Search NASA

DOE OSTI2017

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Correlating Sampling and Intensity Statistics in Nanoparticle Diffraction Experiments

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.

77 NANOSCIENCE AND NANOTECHNOLOGY↗