3D Transition Metal Ordering and Rietveld Stacking Fault Quantification in the New Oxychalcogenides La₂O₂Cu_2–4xCd_2xSe₂

Abstract

. (2016) '3D transition metal ordering and Rietveld stacking fault quantication in the new oxychalcogenides La2O2Cu24xCd2xSe2.', Chemistry of materials., 28 (9). pp. 3184-3195. Further information on publisher's website:http://dx.doi.org/10.1021/acs.chemmater.6b00924 Publisher's copyright statement: This document is the Accepted Manuscript version of a Published Work that appeared in nal form in Chemistry of Materials, copyright c American Chemical Society after peer review and technical editing by the publisher. To access the nal edited and published work see http://dx.doi.org/10.1021/acs.chemmater.6b00924].Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 1+ and Cd 2+ ions segregate into distinct fully occupied and half occupied checkerboard-like layers respectively, leading to complex long-range superstructures in the 3rd (stacking) dimension. To understand the structure and microstructure of these new materials we have developed and implemented a new methodology for studying low and high probability stacking faults using a Rietveldcompatible supercell approach capable of analyzing systems with thousands of layers. We believe this method will be widely applicable.

Averaging the intensity of many-layered structures for accurate stacking-fault analysis using Rietveld refinement

“…Stacking sequences are generated from a stacking probability matrix of the type used in the DIFFaX package [Treacy et al (1991); see for example Fig. 9 of Ainsworth et al (2016)]. In an initial step the probability matrix is used to generate N avg N str N v layers, and from this prediction run the number of Coelho, Evans and Lewis Stacking-fault analysis using Rietveld refinement 1741 electronic reprint each layer i to j transition is determined and placed in a summation matrix S, which is then divided by N avg to give S pred .…”

“…Using I avg,hkl reduces ripples caused by poor faulting statistics, but does not eliminate the ripples caused by small N v . Ainsworth et al (2016) therefore used a large supercell, N v = 5000, to minimize both effects and generate a smooth pattern. Being able to reduce N v whilst (i) reducing ripples and (ii) describing smearing due to the use of a single c lattice parameter without degrading the faulted pattern would be hugely beneficial; the number of reflections would be greatly reduced, resulting in much less computer memory allocation and far greater computational speed.…”

“…We can consider the computational effort using a traditional approach [e.g. TOPAS Version 4 (Bruker, 2009)] for averaging N str = 100 structures each with N v = 960 layers using the La 2 O 2 Cu 0.667 Cd 0.667 Se 2 example investigated by Ainsworth et al (2016). Each structure has N hkl = 54 881 hkl reflections and six layer types N L = 6, with four layers having seven atoms per layer and two layers having eight atoms per layer.…”

“…In that work many stacking sequences relating to the structure of NiCl(OH) were trialled, with each run taking days of computing time. The present work addresses the time-consuming computational aspects of the supercell approach and is an extension of the work by Ainsworth et al (2016). Bottlenecks associated with unit cells comprising thousands of atoms resulting in hundreds of thousands of reflections are tackled.…”

“…Bottlenecks associated with unit cells comprising thousands of atoms resulting in hundreds of thousands of reflections are tackled. In particular the 3 h 1000 repeat Rietveld refinements performed by Ainsworth et al (2016) for averaging of supercells can now be performed in under 1 min.…”