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Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
11:54

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Published on: June 25, 2018

Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of

Christopher L Farrow1, Simon J L Billinge

  • 1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|April 8, 2009
PubMed
Summary

The atomic pair distribution function (PDF) method and small-angle scattering (SAS) share mathematical links. PDF

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Structural Studies of Macromolecules in Solution using Small Angle X-Ray Scattering
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Published on: November 5, 2018

Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Nanotechnology

Background:

  • The atomic pair distribution function (PDF) and small-angle scattering (SAS) are key methods for characterizing materials at the nanoscale.
  • A sloping baseline in PDF analysis of bulk materials is a known phenomenon, but its origin is not fully understood.
  • Understanding baseline artifacts is crucial for accurate structural analysis, especially in nanoparticle characterization.

Purpose of the Study:

  • To explicitly demonstrate the mathematical relationship between PDF and SAS analysis equations.
  • To identify the origin of the sloping baseline observed in PDF measurements of bulk materials.
  • To investigate the origin and implications of nonlinear baselines in PDF analysis of nanoparticles.

Main Methods:

  • Theoretical analysis connecting PDF and SAS formalism.
  • Examination of intensity contributions typically neglected in PDF measurements.
  • Analysis of baseline features in PDF data from bulk and nano-sized materials.

Main Results:

  • The sloping baseline (-4pirrho0) in bulk material PDFs originates from neglected SAS intensity.
  • Nonlinear baselines in nanoparticle PDFs share the same origin.
  • The nanoparticle baseline contains valuable information regarding particle shape and size.

Conclusions:

  • PDF and SAS methods are intrinsically linked through their underlying mathematical frameworks.
  • The baseline in PDF analysis is not an artifact but a source of information, particularly for nanoparticles.
  • This finding offers new avenues for extracting nanoscale structural information from PDF data.