As a professional, employed at neutron and synchrotron sources for most of my career, as well as through Rietveld software support, I have interacted with many people who are attempting to get started with Rietveld analysis. These are typically very bright and well-educated young scientists and engineers; nearly all are a pleasure to work with. However, it is more frequent than I would prefer that I encounter someone who does not understand key aspects of the what the measurements reflect and what the software is doing. It makes it hard for them to know how to do things correctly and if the results they have obtained are meaningful. I strongly believe that working with Rietveld refinement requires a good understanding of diffraction, symmetry and powder diffraction. I think modern scientists who want to perform analysis of powder diffraction are at a severe disadvantage without mastery of these concepts.
I may be prejudiced, since my introduction to crystallography was through single crystal diffraction – and sufficiently long ago so that the methods were then certainly far from “black box” techniques – but I believe having this background allowed me to come to powder diffraction with a good understanding of many basic crystallographic concepts. While I do not want to write yet another textbook on basic crystallographic concepts, there already are plenty of good ones, I think a valuable place to start is to review foundational concepts and I will try to show how they are interrelated. For this reason, I will start this book with three chapters labeled as “prerequisites.” My hope is that this material will largely be a review to you, though I do also hope that on occasion I may present some of this in a new way. Should any of this material be unclear to you as you read these prerequisite chapters, I suggest you make an immediate detour and read about the topic(s) in a basic crystallography text. The subsequent chapters will then be much easier to understand and you will be much better prepared to perform Rietveld analysis and judge the quality of your results.