X-ray diffraction by crystalline powders is one of the most powerful and most widely used methods for analyzing matter. It was discovered just 100 years ago, independently, by Paul Scherrer and Peter Debye in Göttingen, Germany; and by Albert Hull at the General Electric Laboratories, Schenectady, USA.
Figure 1. Right: Peter Debye in 1912. Image Credit: Public Domain via Wikimedia Commons. Left: Paul Scherrer. Image Credit: Courtesy of Paul Scherrer Institut, Vilingen, Switzerland. Used with permission.
Debye, born in Maastricht, the Netherlands, was at first assistant to A. Sommerfed in Munich, then successively Professor at the Universities of Zürich, Utrecht, and Gronigen. In 1912, he published a paper on specific heat and lattice dynamics which made Sommerfeld fear Max von Laue’s planned experiment might fail, which it didn’t, as we know. In a series of papers published in 1913, Debye calculated the influence of lattice vibrations on the diffracted intensity (the Debye factor), and, in February 1915, he expressed the intensity diffracted by a random distribution of molecules. This prompted him to incite his student Paul Scherrer to try and observe the diffraction of X-rays by a crystalline powder.
Figure 2. Powder diffraction diagrams: Left: aluminium filings. ©1917 by the American Physical Society, used with permission. Right: graphite filings by Debye and Scherrer, 1917. Used with permission.
Scherrer, who was preparing his thesis under Debye, first tried charcoal as a sample, with no result. He then constructed a cylindrical diffraction camera, of 57 mm diameter, with a centering head for the sample, a very fine crystalline powder of lithium fluoride (LiF). They were happily surprised by the sharpness of the lines of the first diagram, which they correctly interpreted as that of a face-centered cubic crystal. The work was presented to the Göttingen Science Society on 4 December 1915 and submitted to Physikalische Zeitschrift on 28 May 1916. A second work, also published in 1916, was devoted to diffraction by liquids, in particular benzene, and a third one, published in 1917, on the structure of graphite (Fig. 2, right). In 1918, Scherrer published a seminal paper on the relation between grain size and line broadening (the Scherrer formula). This formula, modified by N. Seljakov in 1925 and generalized, first by Max von Laue in in 1926, then by A. L. Patterson in 1928, plays a major role in the applications of powder diffraction. The same year, Debye and Scherrer deduced from the analysis of the intensity of the diffraction lines that, in LiF, one valence electron is shifted from the lithium ion to the fluorine ion, a first step towards the study of electron density with X-ray diffraction.
Albert Hull was at first a professor at the Worcester Polytechnic Institute, MA before joining General Electric Laboratories in 1914. At the occasion of a visit by Sir W. H. Bragg, Hull had asked the “big man” whether the structure of iron was known. Upon the answer that it wasn’t yet, Hull saw there a challenge and he decided to try to find the structure of crystalline iron. Since he didn’t have a single crystal of iron available, he used iron filings instead. He rapidly obtained good diffraction patterns and found a 3% Si iron crystal, showing that its diffraction pattern was that of a body-centered cubic crystal. He then went back to the powder diffraction pattern and correctly interpreted it. These results were presented on 27 October 1916 at a meeting of the American Physical Society and published at the beginning of 1917. At that time, in the middle of the First World War, the echo of the researchers in Germany had not come to him. Observing the decrease in intensity with increasing Bragg angle, Hull concluded that the X-rays were diffracted by the electron cloud around the nucleus, and not by point diffraction centers. Diffraction by powders thus led both Debye and Scherrer and Hull to make observations of a fundamental nature. Hull then undertook an impressive series of 26 structure determinations of elements including Al (Fig. 2, left), Ni, Li, Na, and graphite. Debye and Scherrer had concluded that graphite was trigonal, but Hull showed that it is hexagonal.
Powder diffraction spread rapidly and easily since it didn’t require specimens of a good crystalline quality. Its fields of applications are very wide in mineralogy, petrology, metallurgy, and materials science. One of the difficulties of the method lies in the indexation of the diffraction lines for non-cubic samples, particularly if there are no crystallographic data available. A systematic mathematical analysis scheme was proposed by C. Runge as early as 1917, but it is cumbersome, and it was only applied when computer programs were developed. Another scheme was proposed by Hull himself and his co-worker W. P. Davey in 1921. It makes use of d-spacing plots of all possible diffracting planes, and is particularly suitable for crystals belonging to the trigonal, tetragonal, or hexagonal systems.
The first of the applications of powder diffraction is the determination of crystal structures and lattice parameters. The method was improved by W. H. Bragg in 1921 by using a flat powder sample and an ionization chamber to measure intensities. H. Seeman, in 1919, and H. Bohlin, in 1920, used a curved sample and focalizing spectrometer, a set-up further ameliorated by J. C. M. Brentano in 1924. A great many structures of alloys were determined in the 1920s, both in Europe and in the United States. Accurate phase diagrams could now be established and phase transformations such as order-disorder transformations were observed. The determination of more complex structures was, however, difficult and had to wait for the development of new refinement techniques by Hugo Rietveld in 1966. This led to a complete renewal of the powder diffraction method, with applications to the study of different classes of new materials in chemistry, materials science, and biology.
The diffraction lines in a powder diagram are also very sensitive to the degree of perfection of the crystal. A general analysis, taking distortions within the grains into account, was given by A. R. Stokes and A. J. C. Wilson (1942, 1944). The profile of the lines depends both on the size of grains, as mentioned above, and on the distribution of defects. B. E. Warren and his school studied in the 1950s the influence on line shape of micro-twins and stacking faults such as those introduced during cold-work of metals and alloys. During annealing of these materials, the grains recrystallize along preferred orientations, their size increases, and the diffraction lines become discontinuous.
Another major application of powder diffraction is the identification of crystalline phases and unknown substances. It was introduced as early as 1919 by Hull as a new method of “X-ray chemical analysis”. The powder diagram of a given substance is indeed unique and specific of that substance, like a fingerprint. It is therefore possible to identify a material by comparison of its diagram to those of known substances sorted in databases. J. D. Hanawalt and H. M. Rinn of the Dow Chemical Company proposed in 1936 a search scheme. In 1937, the “Powder Diffraction File” was established by a committee set up by the American Society for Testing and Materials. This file is maintained since 1969 by the Joint Committee on Powder Diffraction standards, which became in 1978 the International Centre for Diffraction Data. There are now more than 700,000 substances included in the file.
Feature image credit: X-ray diffraction pattern of crystallized 3Clpro, a SARS protease. (2.1 Angstrom resolution) by Jeff Dahl. CC BY-SA 3.0 via Wikimedia Commons.