The Rietveld Refinement Method: Half of a Century Anniversary

Abstract

RecommendationsT he first powder diffraction pattern was reported over a century ago. 1 In a typical powder diffraction measurement, the sample consists of microcrystalline powder with a large number of randomly oriented crystallites.All these crystallites simultaneously diffract the incoming beam in all directions, resulting in diffraction cones.The intensity and distribution of the cones are then measured on the 2θ axis of the powder pattern.The collapse of three-dimensional reciprocal space onto one-dimensional data sets leads to a severe reduction of information, caused by an accidental and systematic peak overlap.This is known as the grave "powder problem".For the first 50 years, the application of powder diffraction in structural analysis of materials was severely limited.In 1969, Hugo Rietveld published the seminal article 2 on what has become known as the Rietveld refinement method.As a result, in the last 50 years, we have witnessed a true revolution in the application of powder diffraction in crystallographic research.We honor this half of a century anniversary with a collection of articles in a virtual special issue that showcase the applications of the Rietveld method in modern chemistry, materials, and structural sciences.This method offers an elegant way to sidestep the problem of peak overlap.The underlying idea relies on modeling a calculated powder neutron diffraction pattern, described by a set of parameters.These parameters include various contributions to the pattern, such as the background, crystal lattice and symmetry, crystal structure, microstructure, instrumental factors, and others.In fact, with modern software, users can include or omit, fix, or refine any parameter, making the method modular.All of these parameters can be simultaneously refined by the least-squares method, until the calculated pattern matches the experimentally collected data.Once a satisfactory match is achieved, the crystal structure is considered refined.Hugo M. Rietveld studied physics at the University of Western Australia in Perth.In 1960, he and Ted Maslen undertook the first single-crystal neutron diffraction study in Australia, on the organic compound p-diphenyl benzene. 3In the early days of his research career, automation in data collection was not common, Fourier maps were hand-plotted, and data analysis was tedious.During this time, he became familiar with the IBM 1620 computer, which used Fortran II, with punched cards for input and output.This led him to explore the possibilities of automation made available by the introduction of computers.Four years later, in 1964, Rietveld

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