Advanced Certificate in Powder Diffraction on the Web Chapter 16 School of Crystallography, Birkbeck College, University of London

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Aims & Objectives

This is first of the chapters on the subject of structure refinement from powder diffraction data. Although powder diffraction dates back to the early 20th century, it was only with the advent of the Rietveld method, as published in 1969, that structure refinements from powder samples became a serious proposition. The aim of this section is to introduce you to the basic concepts involved in the Rietveld method; you will be shown some practical tips on how to get started with the Rietveld method in a later chapter.

Specific objectives are listed below:

• You will start with an introduction to the subject of structure refinement, with an explanation of the need for the method as proposed by Rietveld.
• You will then learn about the concepts involved in the Rietveld method as originally published, both in theory and then in practice.
• In order to appreciate the least-squares refinement procedure as used by Rietveld computer programs, some knowledge of least-squares is required: it is strongly emphasised that concepts are important here, and not the mathematics! In particular, you will learn why both matrix and iterative methods are used for non-linear least-squares problems.
• You will then learn about the agreement indices, known as R-factors, that are used to monitor the goodness-of-fit during the refinement process. These are not the only factors that are used to measure the quality of a fit: of equal importance are the estimated standard deviations (standard uncertainties) that are calculated from the least-squares matrix.
• Finally, a case study is provided to demonstrate to you on a step-by-step basis how the structure of lead sulphate is refined from a round-robin data powder neutron diffraction data set by the Rietveld method.

This subject will be continued in further chapters so many points not discussed here should be covered in the subsequent sections.

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