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X-ray Crystallography

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

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Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles

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Published on: June 25, 2018

A simple formula for determining nanoparticle size distribution by combining small-angle X-ray scattering and

Sérgio L Morelhão¹, Stefan W Kycia²

¹Institute of Physics, University of São Paulo, São Paulo, SP, Brazil.

Acta Crystallographica. Section A, Foundations and Advances

|September 1, 2022

Summary

X-ray scattering and diffraction show size differences in nanoparticle analysis. Understanding these discrepancies provides a simple formula for accurate nanoparticle size distribution determination.

Keywords:

Guinier approximation Scherrer equation X-ray scattering and diffraction nanocrystalline materials nanoparticle size distribution

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Last Updated: Aug 30, 2025

Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles

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Published on: June 25, 2018

Asymmetrical Flow Field-Flow Fractionation for Sizing of Gold Nanoparticles in Suspension

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Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model

Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model

Published on: August 22, 2015

Area of Science:

Nanoscience and materials characterization.

Background:

X-ray scattering and X-ray diffraction are essential analytical techniques in nanoscience.
Discrepancies in size measurements of crystalline nanoparticles are frequently observed between these two methods.

Purpose of the Study:

To investigate the reasons behind size discrepancies between X-ray scattering and diffraction in nanoparticle systems.
To develop a method for accurately determining nanoparticle size distribution by reconciling these differences.

Main Methods:

Analysis of how size distribution affects X-ray scattering and X-ray diffraction measurements.
Mathematical modeling to explain the contrasting shifts observed between the two techniques.

Main Results:

Identified that differing sensitivities to size distribution cause the observed discrepancies.
Established a direct relationship between the discrepancies and the nanoparticle size distribution.

Conclusions:

The observed size discrepancies are a direct consequence of how each technique probes nanoparticle size distribution.
A straightforward formula can be derived from understanding these phenomena to accurately calculate nanoparticle size distribution.