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Pair distribution function


Disordered materials

Pair distribution function analysis is an analytical technique that can provide structural information from disordered materials by using the complete powder XRD pattern. Both the Bragg scattering and the underlying diffuse scattering are determined. The PDF technique is also known as total scattering analysis. From the Bragg peaks in an X-ray diffractogram the long range order of the atoms can be deduced. The short range order, i.e. the local atomic structure, is present in the broad, less well- defined features in the diffractogram. This local structure is described quantitatively by the atomic pair distribution function.

Applications of PDF analysis

Pair distribution function analysis is applied to the structural characterization of materials that are intrinsically disordered. Such materials can be amorphous, poorly crystalline, nano-crystalline or nano-structured. Typically, such samples are:

  • Nanopowders
  • Glasses
  • Polymers
  • Pharmaceutical ingredients
  • Liquids

The PDF function itself is also used by the pharmaceutical industry as a fingerprint for amorphous materials. Other attractive areas of solid state chemistry research for PDF analysis include the study of energy related materials: materials for solid oxide fuel cells (SOFC), magnetic materials, MOF’s, zeolites and Li-battery materials.

PDF determination and analysis

From the measured X-ray diffractogram the so-called structure function is determined following initial basic data reduction steps. The radial atomic pair distribution function is then calculated by a Fourier transformation. The PDF describes the probability of finding two atoms separated by a certain distance in the material under investigation. Software is then used to find the structural model that best fits the determined PDF function.

Requirements for PDF measurements

To obtain the desired spatial resolution for the local atomic structure, data acquisition for PDF analysis must be performed:

  • Up to diffraction angles as high as possible (large Q-range)
  • Using X-rays of short wavelength (high-energy radiation)
  • With very good counting statistics
  • With optimal background suppression.

Due to these demanding requirements, the technique until recently almost exclusively relied on the high-quality X-ray beams that are available at synchrotron radiation sources. In practice it is often difficult and time-consuming to get access to such large-scale facilities. It is therefore highly desirable and sometimes even required to perform pre-screening on candidate samples in the research laboratory ahead of time.

PANalytical solutions for PDF analysis in the lab

The Empyrean and X'Pert³ Powder multi-purpose X-ray diffraction platforms can be configured for total scattering experiments for PDF analysis.

The configuration uses:

  • Silver or molybdenum X-ray tube
  • Incident beam focusing mirrors or a slit collimation system
  • Capillary spinner
  • Hybrid pixel detector (GaliPIX3D), line detector (X’Celerator)
  • Anti-scatter kit for background suppression.

Much attention has been paid to achieve a clean and featureless background, which is essential for obtaining meaningful results on highly disordered or fully amorphous materials.

Experimental data obtained with PANalytical systems allow for comparison with synchrotron results. The measured raw data can be processed and further analyzed with PDF analysis software packages that are available as freeware.

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