There is more in a diffractogram than just the Bragg peaks. The past decade has shown an increased interest in the study of nanocrystalline materials due to their specific properties. Structural information about these materials is present as broad, not very well-defined features in a diffractogram. Analysis of nanomaterials, therefore, needs a total scattering approach. One of the most promising analysis methods used is the atomic pair-distribution (PDF) technique. Originally, this method was used to study amorphous and highly disordered materials. Nowadays, it is also frequently used for the analysis of nanostructured materials.

What is PDF

In the pair-distribution function analysis, the atomic structures of nanoparticles and nanostructured materials are being investigated. This atomic structure is not accessible by conventional methods used on crystalline materials because, by their very nature, nanostructured materials are not periodically long-range ordered. This is an important unsolved problem in nanoscience.

Pair distribution function analysis is a method of extracting structure-related information from powder diffraction data. Since the technique takes both Bragg and diffuse scattering into account, it provides useful information not only about the long-range (>1 nm) atomic ordering but also about the short-range ordering of the atoms in the materials. The method is performed in the following steps:

  1. the diffraction pattern is corrected for background (using a separate diffraction measurement of an empty glass capillary), Compton scattering, detector dead-time, absorption, diffraction geometry, and polarization;
  2. the corrected X-ray diffraction (XRD) data is scaled into electron units and the structure-function is calculated;
  3. the structure-function is Fourier transformed to obtain the atomic pair distribution function: G(r) = 4πr ( ρ(r) – ρ0 ).

In PDF analysis, Fourier analysis is being used for analyzing the occurrence of periodicity in the sample, in other words: it reveals the presence of certain interatomic distances. Even a liquid like water does show some features, these correspond to the O-O distances between the individual water molecules. Nanomaterials are typically an intermediate between a crystalline and an amorphous material.

PDF analysis is most useful in cases where the materials have a certain degree of disorder or when they are nanocrystalline, amorphous or liquids. In crystalline materials, the PDF method can reveal local deviations from the average crystal structure that can be determined using other methods, like the Rietveld method.

For years, the PDF technique was often done at synchrotron and neutron facilities as it requires high-energetic X-ray or neutron beams, in some cases up to 100 keV. However, one would need to apply for beam time – a lengthy process with unsure outcome – and need to screen their samples in their own laboratories, using a conventional diffractometer.

PDF in the home lab

At present, thankfully, it is also possible to study nanomaterials on a home laboratory instrument by a carefully optimized optical path with a featureless background. Meaningful PDF results can be obtained from laboratory instruments with simple means:

  • A hard X-ray radiation source (tube with Mo or Ag anode), beta filter and beam shielding.
  • Focusing mirrors are well suited for small amounts of sample material.

With the right configuration, it is possible to collect data suitable for PDF analysis in a relatively short time frame. With Mo, a maximum Q range of 17 Å-1 can be reached and with Ag even 21 Å-1. Although this takes more time than a synchrotron measurement, it is typically available within one day and does not require the long waiting time needed for getting beam line access. And although it might not give us the performance of a synchrotron, it delivers good quality PDFs.

Become a PDF-pro

In order to achieve reliable PDF results, you would need to completely control the sample preparation process and the configuration. Also, you’d want to optimize the measurement strategy. If you would like to hear about best practices: all this and other experimental aspects will be covered in the next session in our ‘Ask an Expert!‘ webinar series on the 4th of May.