naa a22 4500 510769837 CHVBK 20180411083209.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s11837-012-0451-9 doi (NATIONALLICENCE)springer-10.1007/s11837-012-0451-9 Goerigk Günter F-I2 Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, 14109, Berlin, Germany aut The Impact of the Turing Number on Quantitative ASAXS Measurements of Ternary Alloys [Elektronische Daten] [Günter Goerigk] During the last ten years, anomalous small-angle x-ray scattering (ASAXS) became a precise quantitative method resolving scattering contributions two or three orders of magnitude smaller compared with the overall small-angle scattering, which are related to the so-called pure-resonant scattering contribution. The technique gives access to the analysis of weak concentration fluctuations in systems undergoing spinodal decomposition, which cannot be resolved by transmission electron microscopy (TEM) images because these systems are to a large degree homogeneous. In addition to the structural information, precise quantitative information about the different chemical concentrations localized in the nanosized structures of ternary alloys 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 two ternary alloys, one in the state of spinodal decomposition. The example deals with the quantitative analysis of the resonant invariant (RI-analysis). From the integrals of the pure-resonant scattering contribution, the chemical concentrations in the nanoscaled phases are determined. Moreover the Turing numbers of the vector equation stated by the ASAXS measurement are calculated giving a decisive quantitative measure thereby indicating whether the quantitative parameters obtained from the matrix inversion are significant. TMS, 2012 JOM Springer US; http://www.springer-ny.com 65/1(2013-01-01), 44-53 1047-4838 65:1<44 2013 65 11837 https://doi.org/10.1007/s11837-012-0451-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11837-012-0451-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Goerigk Günter F-I2 Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, 14109, Berlin, Germany aut NATIONALLICENCE 773 0- JOM Springer US; http://www.springer-ny.com 65/1(2013-01-01), 44-53 1047-4838 65:1<44 2013 65 11837 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer