Texture Analysis of EXAFS-Samples using the Rietveld Method

Texture Analysis of EXAFS-Samples using the Rietveld Method

C. Hennig1, G. Nolze2
1Forschungszentrum Rossendorf e.V., ESRF- ROBL/CRG, B.P. 220, F-38043 Grenoble
2Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen 87, D-12205 Berlin

Until now a lot of EXAFS measurements have been carried out on polycrystalline samples. It is known that powdered samples are characterized by a more or less strong texture, caused by an axial pressure during sample preparation. Owing to the polarized synchrotron radiation, this leads to an incorrect determination of the coordination number Nj, in particular for compounds with an anisotropic coordination center. Exemplarily, a strong polarization dependence can be detected in EXAFS spectra for oriented single crystals containing a uranyl coordination center [1]. The influence of preferred orientation on EXAFS measurements will be shown here for polycrystalline uranyl phosphate hydrate samples. The amplitude function of the EXAFS formula describes this polarization dependency with the term
Njeff = 1/2 Nj (1 + 3cos2*j), (1)
where *j is the angle between the polarization vector of the synchrotron radiation and the interatomic vector between the absorber and backscatterer. The exact calculation of the coordination number Nj is especially difficult because of its strong correlation to the Debye-Waller factor *j. A way to determine the preferred orientation is the use of X-ray diffraction measurements. The powder diffraction technique allows to determine the effective multiplicity of each Bragg reflection. One of the commonly used descriptions of a simple preferred orientation is this given by March and Dollase [2]. There, the preferred orientation is characterized by a single vector and the degree of preferred orientation:
Icorr = Istr (G2cos2 *k + G-1 sin2 *k )-2/3 (2)
For a given reflection hkl, this formula describes the relation between the corrected intensity Icorr and the integral intensity Istr resulting from well-known crystal structure data. Istr will be corrected by the preferred orientation in dependence of the orientation parameter G and the angles *k between the scattering vectors of all symmetry-equivalent lattice planes and the preferred orientation vector , assumed as lattice vector. In contrast, the orientation parameter G is valid for all reflection and must be fitted in a special refinement procedure. Most of Rietveld programs allows the use of the March-Dollase function. Both, the preferred orientation vector and the orientation parameter G should be introduced as additional amplitude correction terms for the calculation of polarization dependent EXAFS measurements on powder samples.

[1] C. Hennig, et al., Z. Krist. Suppl. 15, (1998) 156
[2] Dollase W.A., J. Appl. Cryst. 19 (1986) 267-272