X-ray small angle scattering. A new deconvolution method for evaluating electron density distributions from small...

Area of Science:

• Materials Science
• Crystallography
• X-ray Scattering Physics

Background:

• Direct determination of electron density distributions in multilayered specimens is challenging.
• The Q-function method by Hosemann and Bagchi requires deconvolution of the generalized Patterson function (Q(o)-function).
• Existing deconvolution methods can be complex and computationally intensive.

Purpose of the Study:

• To present a new, direct deconvolution method for the Q(o)-function.
• To enable direct determination of electron density distributions from X-ray small-angle scattering data.
• To provide an efficient computational tool for analyzing multilayered specimens.

Main Methods:

• Development of a direct deconvolution method based on Fourier series.
• Application to one-dimensional centrosymmetrical or antisymmetrical density distributions.
• Implementation in a FORTRAN program for computational analysis.

Main Results:

• A novel and direct deconvolution method for the Q(o)-function was successfully developed.
• The method is suitable for analyzing one-dimensional centrosymmetrical/antisymmetrical density distributions.
• The FORTRAN program demonstrated efficient execution (approx. 20s on UNIVAC 1106) and was validated on test cases.

Conclusions:

• The presented Fourier series method offers a direct and efficient approach to deconvoluting the Q(o)-function.
• This facilitates the direct determination of electron density distributions in multilayered materials.
• The computational tool is effective for analyzing membrane-type electron density distributions.