Averaging the intensity of many‐layered structures for accurate stacking‐fault analysis using Rietveld refinement. Issue 5 (29th September 2016)

• Record Type: Journal Article
• Authors: Coelho, Alan A.; Evans, John S. O.; Lewis, James W.
• Is Part Of: Journal of applied crystallography. Volume 49:Issue 5(2016)
• Page Start: 1740
• Page End: 1749
• Publication Date: 2016-09-29
• Subjects: stacking faults -- Rietveld refinement -- crystallography -- TOPAS software; Crystallography -- Periodicals; 548.05
• DOI: 10.1107/S1600576716013066
• Languages: English
• ISSNs: 0021-8898

Abstract

Abstract : Fast algorithms for calculating diffraction patterns from stacking‐faulted materials have resulted in real speed gains of the order of 10 000 and more, allowing rapid structural and microstructural analysis of complex systems. These processes have been implemented in the computer program TOPAS Version 6. Abstract : Many technologically important synthetic and natural materials display stacking faults which lead to complex peak broadenings, asymmetries and shifts in their powder diffraction patterns. The patterns can be described using an enlarged unit cell (called a supercell) containing an explicit description of the layers. Since the supercell can contain hundreds of thousands of atoms with hundreds of thousands of hkl reflections, a Rietveld approach has been too computationally demanding for all but the simplest systems. This article describes the implementation of the speed‐ups necessary to allow Rietveld refinement in the computer program TOPAS Version 6 (Bruker AXS, Karlsruhe, Germany). Techniques implemented include: a peaks buffer that allows hundreds of thousands of hkl ‐dependent peak shapes to be automatically approximated by a few hundred peaks; an averaging process for hundreds of large supercells with minimum impact on computational time; a smoothing technique that allows for the use of small supercells which approximate supercells ten to 20 times larger; and efficient algorithms for stacking sequence generation. The result is Rietveld refinement of supercells operating at speeds several thousand times faster than traditional Rietveld refinements. This allows quantitative and simultaneous analysis of structure and microstructure in complex stacking‐faulted samples.