Pair distribution function (PDF)

  ZnO PDF Copyright: © Mirijam Zobel

The pair distribution function (PDF) corresponds to a histogram of interatomic distances. Any atom of the sample serves as an arbitrary centre, from which all interatomic distances to all other atoms are measured. All interatomic distances are summed up and projected over the radius r.

The figure shows the ab-plane of the wurtzitic crystal structure of zinc oxide (ZnO) with blue Zn and red O atoms. The summation of the interatomic distances is exemplarily shown for a blue Zn atom serving as centre atom. Consequently as in a histogram, each peak corresponds to a distance, where neighbouring atoms are most likely found in the sample.

The PDF is gained from X-ray or neutron scattering data, occasionally from electron diffraction. We have a lab PDF diffractometer in our workgroup. Additionally, high-quality PDF data is collected at large scale research facilities, most frequently using high-energy X-rays (50 – 70 keV) in order to measure the scattering data to very large diffraction angles.

Laboratory diffractometer for PDF measurements

We have developed a laboratory diffractometer in transmission geometry beyond previous state-of-the art with respect to instrumental resolution and low background.

Key facts: STOE STADI P MYTHEN2 4K with

  • Capillary transmission mode with an Ag anode
  • Mythen2 4K detector module (Dectris)
  • Transmission capillary geometry with capillary spinner
  • Q range of 0.3 - 21 inverse Angstroem (144 °)
  • High speed XRD over a 2theta range of 72 ° (Q = 13 A-1) or high-quality PDF over a 2theta range of 144 ° (Q = 21 A-1).
  • Measurement time for nanoparticle powders: ca. 6 hours
  • Heating chamber up to 950 °C

Publication on the instrument:

S. J .L. Thomä, N. Prinz, Th. Hartmann, M. Teck, S. Correll, M. Zobel, Pushing data quality for laboratory pair distribution function experiments, Rev. Sci. Instrum. 90, 043905 (2019),

Further publications from the STOE STADI P MYTHEN2 4K:

S. Weiß, M. Ertl, S. D. Varhade, A.V. Radha, W. Schuhmann, J. Breu, C. Andronescu, Trivalent iron rich CoFe layered oxyhydroxides for electrochemical water oxidation, Electrochimica Acta (2020), 350, 136256,

Schlem, Roman; Banik, Ananya; Eckardt, Mirco; Zobel, Mirijam; Zeier, Wolfgang G.*, Na3-xEr1-xZrxCl6 - A halide-based fast sodium-ion conductor with vacancy-driven ionic transport, ACS Appl. Energy Mater. (2020) 3, 10, 10164–10173,

Prinz, Nils; Schwensow, Leif; Wendholt, Sven; Jentys, Andreas; Bauer, Matthias*; Kleist, Wolfgang*; Zobel, Mirijam* Hard X-ray-based techniques for structural investigations of CO2 methanation catalysts prepared by MOF decomposition, Nanoscale (2020), 12, 15800 - 15813,

R. Schlem, et al., Mechanochemical Synthesis: A Tool to Tune Cation Site Disorder and Ionic Transport Properties of Li3MCl6 (M = Y, Er) Superionic Conductors, Adv. Energy Mater. 2019, 1903719,

A. Gautam, et al., Rapid crystallization and kinetic freezing of site-disorder in the lithium superionic argyrodite Li₆PS₅Br, Chem. Mater. (2019),

P. Lyu, et al., Structure Determination of the Oxygen Evolution Catalyst Mössbauerite J. Phys. Chem. C (2019) 123, 41, 25157-25165,