A method for correcting slowly varying small-angle scattering curves for collimation effects

Abstract

A technique has been developed for correcting slowly varying small-angle X-ray scattering curves for the distortions produced by the length of the collimating slits when, as is very often true, slit-width effects are negligible. The method, which is useful with measured scattering curves which decay so slowly with increasing scattering angle that the usual correction procedures do not converge, is based on approximating the measured curve by a polynominal in h 2, where h = 4rt2-1 sin 0; 20 is the scattering angle and 2 is the X-ray wavelength. The orderj of the polynomial is selected to give the best fit to the measured curve over the entire interval of angles for which data are available. The corrected curve is also a polynomial in h z of order j, and the coefficients of this polynomial can be easily evaluated. Tests of the method on a theoretical scattering curve and two experimental curves are described.

The structure of zinc polyphosphate glass studied by diffraction methods and 31P NMR

“…8 excellently agree in the regions where they overlap. To separate the scattering of the disordered network, which is not resolved by the small angle X-ray scattering experiment [36], the IðsÞ curve obtained with the Rigaku Denki goniometer was approximated in the interval 5 nm À1 6 s 6 6:8 nm À1 by a polynomial in s 2 [37]. After subtracting the approximated curve from the measured intensities the curve of the scattering heterogeneities of electron density remains.…”

The structure of phosphate glass evidenced by small angle X-ray scattering

“…In this case, the contributions I F (s), and possibly I IP (s), must be mathematically eliminated in a previous step. For this purpose, the scattering of the disordered network, I F (s), can be approximated by the polynomial [10] …”

Small-Angle X-ray Scattering of Inorganic Glasses. Data Treatment and Analysis

“…This result gives evidence for the fact that the chromophores form spherical particles with a narrow size distribution. The comparison of this scattering curve recorded at a synchrotron beamline with that obtained using the Rigaku Denki goniometer ( (1)], the measured scattering curve I(s) was approximated in the interval 3.4 nm -i < s < Smax by a polynomial in s 2 (Walter & Schmidt, 1981).…”