We cannot discuss powder diffraction structure techniques without comparing them with single-crystal structure determination. Single-crystal crystal structure determination was done as far back as 1913, but crystal structures determined from powder diffraction were also reported later in that same decade. Structure determination from single crystals prospered greatly in the subsequent half-century, as instruments improved and structure solution techniques were developed. As computational model-fitting was adopted, structures could be described with quantitatively determined coordinates, and of perhaps equal importance, statistical uncertainties on those values. Even so, due to detector improvements and even greater computer advances, I think that single-crystal work has seen as much advancement in the past few decades as it did in the first half-century. Powder diffraction crystallography, on the other hand, was largely left behind in that first half-century, until Hugo Rietveld and some of his coworkers at the Netherlands’ Petten High Flux Nuclear Reactor pursued the problem in the 1960’s and developed a method where crystal structures were determined by fitting to the observed powder diffraction data.
To understand Rietveld’s motivation, in that period, neutron single-crystal measurements required crystals the size of a finger-tip (which are quite rare) and weeks, if not months, of continuous data collection. So, there was a plethora of samples where only powder diffraction could be measured. It was true then, and is still true now, that when single-crystal data are available for a material, the single-crystal measurement will provide much more structural detail than powder diffraction. However, the single-crystal data needs to be from a material with the desired composition and where the measurements are under the conditions of interest. There are many materials where single-crystals cannot be formed with the desired chemical or physical properties. Or, measurements are not possible under the desired conditions: in some cases one wants to learn about processes that occur under conditions that degrade single-crystals to a polycrystalline material. Thus, while I consider powder diffraction as a second-choice technique, it is often the only choice. With powder diffraction, it becomes relatively easy to make a combined fit using multiple types of data, such as x-ray and neutron, or with data collected near x-ray absorption edges (known as resonant scattering or anomalous dispersion measurements). In fact, x-ray single-crystal measurements results can often be enhanced, when combined with powder diffraction measurements with neutrons or other x-ray wavelengths.
Further, in the subsequent decades since Hugo’s work, we have found many other applications for this type of fitting. It provides information not only about atomic arrangements (sub-nanoscale structure), but also about microstructure – information on larger scales than atomistic information, such as crystallite size, microstrain and texture. When materials are mixtures of phases, powder diffraction can provide quantification of the components of the mixture, as well as crystallographic information on the component phases. Multiphase materials are common, either by intent, as mixtures can improve materials properties, or because it not known how to create the pure phase.
Powder diffraction measurements can be made under in situ or operando conditions. Due to the speed and simplicity of the measurement, it is now common to perform parametric experiments where even thousands of complete datasets are collected on a sample as conditions are changed. It is no surprise that when a neutron or synchrotron center builds a powder diffractometer, while not the most sexy cutting-edge of techniques at the institution, these instruments go on to become some of the most in-demand and most productive instruments at the facility. Also, powder diffraction measurements can be quick. In fact, as far as I am aware the world’s record has been a complete measurement made 100 picoseconds.
Sometimes the term “full-pattern fitting” is used to describe this type of work, rather than Rietveld analysis. I prefer to honor Hugo Rietveld. He was not the only person to work on ideas for fitting powder diffraction patterns, but was the first to put the technique into practice. In developing such a code, he had to overcome a number of technical difficulties with, by modern standards, tiny and slow computers. After showing that the technique was possible and of value, he rewrote his code in a more accessible computer language and freely distributed his code to anyone who wanted a copy. A few decades after Hugo’s work was completed, there were a number of Rietveld programs in use, but almost all contained some code that Hugo had written. I have written a short history of Rietveld analysis as chapter 4.7 in the International Tables for Crystallography, Volume H, for those who might want to learn more and this provides citations to the original literature.