Quantitative anomalous small-angle X-ray scattering — The determination of chemical concentrations in nano-scaled phases
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.
KeywordsMetallic Glass European Physical Journal Special Topic Spinodal Decomposition Yttrium Atom SAXS Curve
- 8.G. Goerigk ‘Electronic and Computer Upgrade at ASAXS Beamline JUSIFA’, HASYLAB Annual Report (2006), p. 77Google Scholar
- 14.J. Westlake, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations. (New York: J. Wiley and Sons, 1968)Google Scholar
- 19.D.T. Cromer, D. Liberman, Acta Cryst. A37, 267 (1981)Google Scholar
- 25.O. Glatter, O. Kratky, Small-Angle X-ray Scattering (Academic Press, London, 1982)Google Scholar
- 33.Y. Xu, B.P. Nelson, D.L. Williamson, L.M. Gedvilas, and R.C. Reedy, Mat. Res. Soc. Symp. Proc. 762, A 10.2 (2003)Google Scholar