Nano Research

, Volume 12, Issue 11, pp 2849–2857 | Cite as

Dimensional characterization of cadmium selenide nanocrystals via indirect Fourier transform evaluation of small-angle X-ray scattering data

  • Julian Cedric Porsiel
  • Bilal Temel
  • Alfred Schirmacher
  • Egbert Buhr
  • Georg GarnweitnerEmail author
Research Article


The correlation of single-particle imaging and absorption spectroscopy made the development of sizing curves possible and enabled rapid size determination of semiconductor nanocrystals based solely on optical properties. The increasing demand and production of such materials has resulted in a question of comparability between existing models and adequate volume-weighted size-determining measurement techniques. Small-angle X-ray scattering (SAXS) is a well-established method for obtaining nanostructural information from particle systems while operating sample quantities up to a commercial scale with a large amount of statistically based data. This work utilizes laboratory SAXS to characterize cadmium selenide nanocrystals with band edge energies between 1.97 and 3.08 eV. The evaluation of the scattering patterns is based on an indirect Fourier transformation (IFT), while dimensional parameters are derived from the model-free pair distance distribution functions (Dmode and Dg), as well as the modeled volume (v) and number (n)-weighted size-density distributions. We find that comparable data from n agree well with existing X-ray diffraction (XRD) and with transmission electron microscopy (TEM) results described in literature; this qualifies SAXS as an equivalent integral characterization method. Although based on an estimate, the radius of gyration yields equivalent accurate results. Additionally, corresponding volume-weighted data are shown that can be useful when transferring information to other techniques. Dmode parametrization represents the largest estimated size of the sample and implies that particles interact and deviate from the spherical morphology, whereas v demonstrates results not considering such effects. A full set of the parameters discussed quantifies the quality of a sample.


quantum dots small angle scattering indirect Fourier transform transmission electron microscopy optical absorption spectroscopy particle size distribution 


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The authors thank the Laboratory for Nano and Quantum Engineering (LNQE), Leibniz University Hannover, for the access to the TEM instrument and Dr. Brian Pauw from the Bundesanstalt für Materialforschung und-prüfung (BAM) in Berlin for the scientific discussion about SAXS and the provision of the Ag-reference. We also acknowledge the work of David Niedbalka and Marcel Pastuschek who contributed to this research during their time as students. This research was partially funded by Niedersächsisches Ministerium für Wissenschaft und Kultur through the “Quantumand Nano-Metrology (QUANOMET)” initiative (ZN3245) within the scope of the NP-1 project. Furthermore, we acknowledge financial travel support by the DFG Research Training Group GrK1952 “Metrology for Complex Nanosystems (NanoMet)”.

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Dimensional characterization of cadmium selenide nanocrystals via indirect Fourier transform evaluation of small-angle X-ray scattering data


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Copyright information

© Tsinghua University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Julian Cedric Porsiel
    • 1
    • 2
  • Bilal Temel
    • 1
  • Alfred Schirmacher
    • 2
  • Egbert Buhr
    • 2
    • 3
  • Georg Garnweitner
    • 1
    • 3
    Email author
  1. 1.Institute for Particle Technology (iPAT)Technische Universität BraunschweigBraunschweigGermany
  2. 2.Physikalisch-Technische Bundesanstalt BraunschweigBraunschweigGermany
  3. 3.Laboratory for Emerging NanometrologyTechnische Universität BraunschweigBraunschweigGermany

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