An Improved Regularization Technique for Analysis of Anomalous X-ray Scattering Data; Platinum Uridine Blue Sulfate as an Example

A new iterative way to apply the Tikhonov regularization method for solving partial structure factors from anomalous X-ray scattering data is presented. It is used to obtain the regularized Pt-Pt partial structure factor in a complex amorphous material, platinum uridine blue, containing many atomic species, utilizing experimental anomalous wide-angle X-ray scattering data. Since only platinum has a suitable absorption edge for the measurement, the problem is very much ill-posed, and without regularization only unreliable solutions are obtained. The average Pt-Pt distances, determined from the Pt-Pt partial distribution function, are 3.0 and 5.7 Å and the coordination number at 3.0 Å is about 1. Accordingly, the dominating Pt-structures of Pt-uridine blue are dinuclear. The success of this method indicates that we may use anomalous scattering to obtain important, detailed information about the structure of very complex amorphous materials.