The European Physical Journal Special Topics

, Volume 208, Issue 1, pp 259–274 | Cite as

Quantitative anomalous small-angle X-ray scattering — The determination of chemical concentrations in nano-scaled phases

  • G. Goerigk
  • K. Huber
  • N. Mattern
  • D. L. Williamson
Open Access


In the last years Anomalous Small-Angle X-ray Scattering became a precise quantitative method resolving scattering contributions two or three orders of magnitude smaller compared to the overall small-angle scattering, which are related to the so-called pure-resonant scattering contribution. Additionally to the structural information precise quantitative information about the different constituents of multi-component systems like the fraction of a chemical component implemented into the materials nanostructures are obtained from these scattering contributions. The application of the Gauss elimination algorithm to the vector equation established by ASAXS measurements at three X-ray energies is demonstrated for three examples from chemistry and solid state physics. All examples deal with the quantitative analysis of the Resonant Invariant (RI-analysis). From the integrals of the pure-resonant scattering contribution the chemical concentrations in nano-scaled phases are determined. In one example the correlated analysis of the Resonant Invariant and the Non-resonant Invariant (NI-analysis) is employed.


Metallic Glass European Physical Journal Special Topic Spinodal Decomposition Yttrium Atom SAXS Curve 
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Copyright information

© EDP Sciences, Springer-Verlag 2012

Authors and Affiliations

  • G. Goerigk
    • 1
  • K. Huber
    • 2
  • N. Mattern
    • 3
  • D. L. Williamson
    • 4
  1. 1.Institute of Soft Matter and Functional MaterialsHelmholtz-ZentrumBerlinGermany
  2. 2.Fakultät für Naturwissenschaften, Department ChemieUniversität PaderbornPaderbornGermany
  3. 3.Institute for Complex MaterialsLeibniz-Institute IFWDresdenGermany
  4. 4.Colorado School of MinesColoradoUSA

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