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

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Lower uncertainty bounds of diffraction-based nanoparticle sizes.

İsmail Cevdet Noyan¹, Hande Öztürk²

¹Department of Applied Physics and Applied Mathematics, SEAS, Columbia University, 500 W 120th Street, New York, NY 10027, USA.

Journal of Applied Crystallography

|June 20, 2022

Summary

Traditional particle size determination methods for single-crystal nanoparticles have errors around 5%. Errors depend on particle shape, with specific techniques offering lower error bounds for accurate nanoparticle size analysis.

Keywords:

Fourier analysis Scherrer approach diffraction integral breadth particle size determination

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Area of Science:

Materials Science
Crystallography
Nanotechnology

Background:

Accurate determination of nanoparticle size is crucial for understanding material properties.
Traditional diffraction-based techniques are widely used but can be subject to errors.
The Patterson approach provides synthetic diffraction profiles for analyzing these techniques.

Purpose of the Study:

To perform a self-consistent analysis of traditional diffraction-based particle size determination techniques.
To evaluate the accuracy and error bounds of these methods when applied to synthetic diffraction data.
To identify factors influencing the reliability of size determination for various particle shapes.

Main Methods:

Generation of synthetic diffraction profiles using the Patterson approach.
Application of traditional techniques: peak fitting, Fourier analysis, integral breadth, and Fourier decomposition.
Analysis of error bounds and dependence on particle shape and diffraction profile characteristics.

Main Results:

Traditional techniques for single-crystal nanoparticles show best-case error bounds of approximately 5%.
Lower error magnitudes for arbitrarily shaped particles are achievable by analyzing thickness fringe zeroes.
Errors in integral-breadth and Fourier-decomposition methods are shape-dependent, with specific scattering profiles yielding lower errors.

Conclusions:

The accuracy of diffraction-based particle size determination is significantly influenced by particle shape and the chosen analysis method.
Non-uniform chord length distributions can introduce nonlinearities in Fourier decomposition analysis.
Routine analysis should involve applying multiple domain size determination techniques to all reflections and assessing result divergence for reliability.