The History of X-Ray Crystallography
The discovery of X-rays
This discovery was made in 1895, when a German named W. C. Röntgen was conducting a number of experiments on cathode rays, emanations of electrons from the cathode end of a vacuum-pumped glass tube. Röntgen’s tube had thin aluminium windows, to allow the cathode rays out, and tinfoil-coated cardboard covering, which served the dual purpose of protecting the aluminium from the strong electrostatic field and preventing visible light to penetrate out from the tube. High energy electric discharge entered the tube through an anode (a positively charged electrode), and exited through the negatively charged cathode. These cathode rays are invisible, but Röntgen observed their existence from the fluorescent effect they produced when a screen coated with barium platino-cyanide was placed close to the window (cathode rays were known to only penetrate a few centimetres of air). He then repeated the experiment, but without aluminium windows, and discovered that this time the screen fluoresced, even when it was several metres away. Clearly this was not the result of cathode rays, but of a new form of radiation. Röntgen named his discovery X-rays, and found that the relative transparency of objects was dependant on their density (his experiment had already shown that cardboard was entirely transparent; he soon discovered, to the benefit of medicine, that the rays passed easily through flesh, but not through bone).
Röntgen’s ‘X-ray tube’ was soon improved upon; later experimenters placed a platinum plate, or ‘anticathode’, in the path of the cathode rays. They made the cathode concave, in order to focus the electron beam on the anticathode, which was the new source of the X-rays.
The nature of X-rays
We now know that X-rays are a form of electromagnetic radiation, but in the decades following their discovery, a debate raged over whether they were waves or particles. Röntgen himself had found them comparable to light, as they appeared to travel in straight lines and shadows were cast over opaque objects in their path. By that time the electromagnetic wave theory of light was, according to Lawrence Bragg, ‘one of the more firmly established scientific postulates’, following Young’s pin-hole experiments on interference and Maxwell’s mathematical interpretation of Faraday’s laws of electromagnetic induction. An important quality of electro-magnetic waves is that the electric and magnetic fields are perpendicular to the direction in which the waves are travelling. Thus the waves can be ‘polarized’ (some or all of the vibrations restricted to a particular direction) by using a device which allows through the electric vector in one direction, whilst blocking the vector which is perpendicular. This polarization property can be shown by a ‘scattering’ experiment, and in 1905 C. G. Barkla used such a technique to quite convincingly suggest that X-rays could be polarized, just like light waves. However, from 1907, W.H. Bragg (father of Lawrence), was convinced that the rays had particle properties, after comparing them with γ-rays from radioactive bodies.
This is the technique of shooting X-rays through crystals to produce a diffraction pattern, and it can be viewed as a far more complicated version of diffraction through a grating. In optics, a grating is an arrangement of parallel wires in a plane (or alternatively a polished surface ruled with very close fine parallel lines). When a beam of light is directed through this a spectra of colours is produced (the diffraction of the light); this occurs because the spaces between the lines are similar to the wavelength of the light. The wavelengths of X-rays are much smaller; in fact they are almost equal to the distances between atoms in a crystal.
(By Astbury’s time, the most commonly used for X-ray crystallography were produced from an X-ray tube of copper anticathode, and were known as Cu Kα rays. These have a wavelength of 1.54 Ångstrom units).
In 1912, following a discussion with P. P. Ewald, this useful quality led Max von Laue, a Privat-Dozent in Arnold Sommerfield’s Institute of Theoretical Physics in Munich, to consider whether crystals could be used as 3-dimensional optical gratings. Believing X-rays to be waves, he supposed (correctly) that such waves would have sufficiently small wavelengths to be diffracted through a crystal.
Two colleagues, Friedrich and Knipping, carried out the experiment (despite Sommerfield not being keen), and it was published in theProceedings of the Royal Bavarian Academy of Science. A beam from an X-ray tube was directed into a lead box, where it was reduced to the width of about 1mm before it made contact with the crystal; any diffracted rays were caught by photographic plates. The patterns of spots obtained on these plates behaved exactly as theories of wave diffractions dictated they should, displaying an interference pattern. Laue, correctly, attributed them to the diffraction of X-ray waves. However Laue was unable to correctly determine the causes of repetition within these patterns, believing it was due to secondary X-rays, and where he faltered the Braggs took over.
William Bragg’s son, Lawrence, considered Stokes’ theory of X-rays as pulses of electro-magnetic radiation, caused by electrons in the X-ray tube hitting the anticathode. He was also influenced by C.T.R. Wilson’s lectures on the diffraction of light. Wilson taught that there were two ways to view white light: as a combination of light of all wavelengths, where each different wavelength is diffracted at its appropriate angle by a grating; or as formless pulses, which the grating converts into a series of waves.
A 3-dimensional crystal is a multitude of sets of layers, the sets running in all different directions, with the layers in any one set spaced apart at a constant distance; each layer is (for practical purposes) effectively a 2-dimensional pattern of atoms. Where Laue had viewed the crystal as a 3-dimensional extension of a diffraction grating (requiring 6 angles, 3 lattice spacings and 3 integers to calculate the directions of the diffracted beams), Lawrence simplified this by viewing each layer as a ‘reflective’ plane, and thus a crystal as simply a family of such planes. This simplified matters as on a plane the incident angle is equal to the angle of reflection. Drawing analogies with Wilson’s theories on diffraction gratings, he believed that each layer could convert formless pulses into a regular series of waves.
Following this, he was able to construct the fundamental law of X-ray diffraction, a simple equation known as Bragg’s Law:
Here, n is an integer (the ‘order’ of reflection), λ is the wavelength of the X-ray, d is the distance between each plane in the set (the spacing), and θ is the angle between the plane and the X-ray falling upon it (the glancing angle).
Bragg’s first paper on the interpretation of Laue’s results was entitled The Diffraction of Short Electromagnetic Waves by a Crystal and was read to the Cambridge Philosophical Society in November 1912. He did not refer to these waves as X-rays, hoping that his father’s corpuscular theory could still hold true and that the electromagnetic waves he had been studying simply accompanied X-rays.
The X-ray spectrometer
The ‘X-ray Spectrometer’, a technology that would become invaluable in the science of X-ray crystallography, was designed by William H. Bragg and constructed at Leeds University in 1913 by Jenkinson, his instrument maker. Lawrence Bragg believed that the freedom and resources his father was given (in contrast to Lawrence’s experience at the Cavendish laboratory) were crucial in his own development of X-ray analysis. He describes the first, most primitive, X-ray spectrometer:
“The apparatus . . . resembled an optical spectrometer. A slit at O in front of the X-ray tube acted as collimator, the crystal which was mounted on a table that could turn around an axis at Prepresented the grating, and the ionization chamber which received the reflected rays through a slit at Q, and which was on an arm turning around P, represented the telescope. The settings of crystal and chamber were read on a circular scale around P. The amount of radiation entering Q was measured by applying a potential of about 100 volts to the outer wall of the chamber, and driving the ions to a central insulated wire along its axis. The wire was connected to a Wilson gold-leaf electroscope, which measured the charge it received. In order to increase the effect, the chamber was filled with a heavy gas such as sulphur dioxide or methyl iodide. The X-ray tube was enclosed in a lead box to reduce stray radiation.”
In X-ray crystallography, the X-ray beams are diffracted by a crystal according to Bragg’s law, and success in X-ray analysis can be achieved by measuring and interpreting the intensities of these beams. For each diffracted pencil, the ratio of the total diffracted energy to the total incident energy needs to be calculated. This is difficult when faced merely with a photograph of blurry dots: the intensity of each individual spot has to be measured in a time-consuming procedure. However, the spectrometer measured the total amount of ionization, allowing for greater accuracy and quantitative results. While the elder Bragg used this new technology to study the nature of X-rays (and, in particular, determine whether they were indeed the causes of Laue’s results), it was left to Lawrence to investigate its use in determining crystal structures.
The structure of NaCl had been deduced solely from the diffraction photographs taken by Laue, but, according to Bragg, ‘the first results with the X-ray spectrometer showed at once how far more powerful it was as an analytical tool’.
The results of this new analysis appeared in a paper jointly written by the Braggs, titled ‘The Reflection of X-rays by Crystals’, which was published in the 1913 Proceedings of the Royal Society of London.
The ionization measurements did indeed produce far more accurate results but at a cost: it would take hours of observation to determine the intensity of a single reflection. This was sufficient for simple structures in the mineral field, but not for the more complicated organic substances which were soon to be analysed. They required only relatively accurate measurements, but on a large number of reflections. In 1929, Astbury developed an ‘Integrating Photometer’ which measured the total X-ray intensity but still used photographic methods.
X-ray diffraction of fibrous substances
At this time it was believed that X-ray diffraction would only work with crystals. In the Munich experiment of 1912, Friedrich and Knipping had in fact ground the crystal into a powder, and shown that this eliminated the diffraction effect. Substances of biological importance, which were powdered or fibrous, were believed in 1912, to be almost entirely amorphous, with barely any crystals in their structure. However, in 1915, Debye and Scherrer discovered the powder diagram; and Scherrer, Herzog and Jancke found the fibre diagram in 1920. Where the single crystal diagram displayed a 3-dimensional lattice throughout the crystal, the fibre diagram showed numerous tiny 3-dimensional lattices (crystallites), all facing the same direction, with respect to one dimension, the fibre axis; the powder diagram displayed crystallites with random orientation in all dimensions. Thus, it was pictured that textile fibres are constructed of molecules regularly arranged in crystallites, which themselves are regularly arranged in the fibre.
William Astbury was first introduced to this new development at the Royal Society, when, in 1926, William Bragg asked for his help in getting photographs of fibres. In 1928, he took the post of Lecturer in Textile Physics at Leeds, which would become the major centre of fibre research, particularly wools.
One notable difference between the x-ray analysis of crystals and that of fibres is that the fibres do not need to be rotated. This is because the aim is to analyse one of numerous crystallites, rather than an entire crystal. As the crystallites are all more or less oriented parallel to the fibre axis, but rotated in all different directions around it, it is inevitable that at least one such crystallite (assuming there are enough, as there are in textile fibres) will be in the optimal position for Bragg’s Law. The crystallites are thus already arranged in a way which produces a rotation photograph, without need for actual rotation.
However, along with this advantage of fibres over crystals, there do arise some disadvantages, due to the fact that the crystallites are not strictly parallel. This produces additional reflections, reflected from planes at right angles to the fibre axis; furthermore, arcs, rather than spots, tend to be produced on the rotation photograph. The lengths of the arcs measure the deviation from strict parallelism (they are spread out into full circles on a powder photograph), and this could be used to determine the strength and elastic properties of a fibre.
The fibre photographs produced broad, fuzzy spots, in stark contrast to the clear pictures produced by crystals. This is due to the tiny size of the crystallite, particularly in comparison with its molecules. When a crystallite is so small that there are too few repeats of the molecular pattern (when the dimensions of the crystallite are less than a few hundred Ångstrom units) it is no longer capable of efficiently reflecting X-rays. However, this apparent flaw in the apparatus was used as an opportunity to measure the dimensions of the crystallite; a picture that was fuzzy beyond comprehension was not discarded as scientifically useless, but instead used as proof that the crystallite under analysis was smaller than one which would have produced a clear ‘useful’ picture.
The structure of textile fibre
“All textile fibres and most plastics are built from chain-molecules formed by the repeated condensation or polymerisation of simpler units. For example, cellulose consists of chains of hundreds of β-glucose residues, the proteins of polypeptide chains, and so on. In the most perfectly constructed fibres the chains lie either closely parallel to the fibre axis or along spiral paths about the fibre axis; but in some fibres they may deviate from parallelism quite considerably. In any case they tend to form long thin bundles – regular bundles that we identify as fibre crystallites. These chain-bundles or crystallites are also called ‘micelles’, and they have often been thought of in the past as discrete brick-like units. It is undoubtedly convenient to treat them like this sometimes, but we should always remember that they are in reality only the more crystalline regions of the structure: less perfect regions intervene, but chains pass from one micelle to the next and in this sense, at least, the structure is continuous.”
by Imogen Clarke