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A Fourier transform method for powder diffraction based on the Debye scattering equation.

Acta crystallographica. Section A, Foundations of crystallography·2011

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A new approach to calculating powder diffraction patterns based on the Debye scattering equation.

Noel William Thomas¹

¹Fachhochschule Koblenz, Fachbereich Ingenieurwesen, Fachrichtung Werkstofftechnik Glas und Keramik, Rheinstrasse 56, 56203 Höhr-Grenzhausen, Germany. thomas@fh-koblenz.de

Acta Crystallographica. Section A, Foundations of Crystallography

|December 24, 2009

Summary

A novel method enhances the Debye scattering equation (DSE) for calculating X-ray and neutron powder diffraction patterns, enabling analysis of crystallite sizes up to 200 nm.

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Area of Science:

Materials Science
Crystallography
Computational Chemistry

Background:

The Debye scattering equation (DSE) is a fundamental tool for analyzing diffraction patterns.
Accurate modeling of powder diffraction patterns requires consideration of crystallite size and atomic interactions.

Purpose of the Study:

To develop a new computational method for calculating X-ray and neutron powder diffraction patterns.
To extend the applicability of the DSE to larger crystallite sizes and incorporate structural disorder.

Main Methods:

The DSE was adapted by splitting pairwise atomic interactions into lattice-pair and cell-pair vectors.
The method utilizes unit-cell parameters, atomic coordinates, and displacement factors as input.
The approach was validated using sodium chloride (NaCl), alpha-quartz, monoclinic lead zirconate titanate (PZT), and kaolinite.

Main Results:

The new method successfully calculates full diffraction patterns, including backgrounds and reflection profiles, for crystallites up to approximately 200 nm.
The influence of crystallite size on diffraction patterns was demonstrated for NaCl, quartz, and kaolinite.
A method for modeling static structural disorder in kaolinite was successfully defined.

Conclusions:

The developed method provides a robust framework for calculating powder diffraction patterns from the DSE, extending its utility to larger crystallites.
This approach facilitates the analysis of materials with varying crystallite sizes and structural disorder.
Future work aims to optimize computational efficiency by directly calculating patterns from crystal structures.