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

Abstract

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 A and the coordination number at 3.0 A 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.

Structure of nickel nanoparticles in a microcrystalline cellulose matrix studied using anomalous small-angle X-ray scattering

“…Instead of using an analytical formula of this PSF we solved the whole equation to reveal the possible mirror effects in the PSFs (Munro, 1982). Extraction of the PSFs was attempted by directly solving equation (2), by using the simple Tikhonov regularization technique (Neumaier, 1998;Serimaa et al, 1996) to solve the equation, and by the derivative technique (Fuoss et al, 1981), in which the S bb ðqÞ and S ab ðqÞ PSFs can be obtained by a linear fit to dIðq; EÞ=df b ðEÞ. These methods were first tested with simulated scattering data, in which statistical errors comparable to the estimated experimental statistical errors had been introduced.…”

Structural analysis of calcium reactive hydride composite for solid state hydrogen storage

“…For a two-phase system, the resonant scattering intensity can be extracted from equation (2) by measuring the small-angle scattering (SAXS) intensity at a minimum of three different energies adjacent to an absorption edge of the resonant element i. For more detail the reader is referred to Simon & Lyon (1994), Serimaa et al (1996) and Goerigk et al (2004). The chemical state of the additive and its local environment can be characterized using XAS.…”

Deconvolution of X-ray diffraction profiles by using series expansion

“…This fact leads to strong oscillatory components in the`pure' pro®le, especially in the tails. On the other hand, iterative techniques, such as the methods presented by Ergun (1969) and Mencik (1974), and the very powerful regularization techniques (Groetsch, 1984;Tikhonov et al, 1995;Engl et al, 1996) have been successfully used in deconvoluting the X-ray diffraction pro®les Trubin & Szasz, 1991;Serimaa et al, 1996). The regularization procedures are especially interesting to overcome the ill-posed nature of equation 1, minimizing the oscillations in the f function.…”