by Andrew Brown
The crucial series of experiments was carried out by two junior assistants in Laue’s department, who constructed a lead box to hold the crystal and a photographic plate. One side of the box had a 3 mm diameter hole drilled through it to admit a narrow beam from an X-ray tube; the X-ray beam was further narrowed to about a 1 mm pencil by passing through a series of apertures. The first crystal studied was copper sulphate, which was irradiated for about twenty hours, with interruptions every so often to let the X-ray tube cool down. The photographic plate on the far side of the crystal showed a large central dark blob with a pattern of smaller spots surrounding it. The copper sulphate crystal was then ground into a powder and the experiment repeated. This resulted in just a central circular spot from the primary beam with no peripheral spots, suggesting that indeed the first pattern was due to diffraction of the X-ray beam by the intact crystal. Convincing evidence came when they next used a crystal of zinc sulphide, which has a more symmetrical form than copper sulphate. This time the cubic crystal was carefully mounted so that the X-ray beam intersected one face of the crystal at ninety degrees. Now the dark spot on the plate due to the primary beam passing straight through the crystal was enclosed by a regular pattern of smaller elliptical spots. The most prominent feature was a diamond shaped ring of these subsidiary spots, showing four-fold symmetry as one would expect from a cube.
Word of these revolutionary findings quickly reached England and were discussed by William Bragg with his son, Willie,† during his summer vacation from Cambridge. At the time, the younger Bragg was ‘an ardent supporter’ of his father’s view that X-rays consisted of a stream of high velocity particles, and made some unsuccessful experiments to see if he ‘could get evidence of “X-ray corpuscles” shooting down the avenues between the rows of atoms in the crystal’.7 When he returned to Cambridge after the summer vacation, Lawrence Bragg continued to ponder Laue’s results and became convinced that the observed effect was due to the X-rays having a wave nature and being diffracted by the crystal’s atomic lattice. Bragg realized though that Laue’s analysis of the process was incorrect. Laue had interpreted the pattern of spots seen on the exposed photographic plate as being due to X-rays of a few discrete wavelengths produced by resonating atoms in the crystal lattice, but struggle as he might, he was not able to account for all the spots in the diffraction pattern. Lawrence Bragg, a 22-year-old research student in J.J. Thomson’s Cavendish Laboratory, considered the problem from several aspects before proposing a simpler and more complete explanation that required one supreme flash of intuition. Bragg’s crucial insight was that successive planes in the crystal lattice effectively acted like mirrors, and reflected a fraction of the incident X-rays so that each spot on the photographic plate represented a parallel set of these atomic planes.
Visible light is reflected from the facet of a crystal in a continuous way so that the surface still looks shiny as the crystal is turned in the light. X-rays are oblivious to the crystal facets, but can be scattered by the array of atoms within. The atoms scatter the X-rays into wavelets that retain the ability to interact with one another to produce interference patterns. At some angles, the wavelets are in phase and reinforce each other so that diffraction occurs. At other angles, the wavelets are out of phase and cancel each other out so that nothing is detected on a photographic film. The spotted pattern that results on the film gives the clue to the internal structure of the crystal and is the key to X-ray diffraction as an investigative technique.
Bragg found that he could account for all the spots in Laue’s zinc sulphide pattern if he assumed that the atoms were arranged in a face-centred cube (with atoms not only at the corner of adjoining cubes, but at the centre of each face). The pair of figures below shows a face-centred cubic lattice on the left and its corresponding X-ray diffraction pattern on the right. The diagrams are for common salt, another face-centred cubic lattice, with the sodium atoms shown as light spheres and the chlorine atoms dark. The spots or reflections found in the diffraction pattern show four-fold symmetry: the pattern is identical when rotated through ninety degrees. The crystal and its diffraction pattern share the same symmetry, but there is not a direct correlation between the position of the molecules in the crystal lattice and the reflections on the X-ray photograph (note, too, that the intensity of the reflections varies).
Idealized crystal lattice structure of common salt (left) with the sodium atoms shown as light and the chlorine atoms dark. The corresponding X-ray diffraction pattern (right) showing the same four-fold symmetry. © Jeremy Karl Cockcroft
Once Bragg had made the momentous assumption that the primary mechanism was like reflection from successive atomic planes, it was easy for him to formulate Bragg’s Law:
nλ = 2d sin θ
where n is an integer, λ is the wavelength of the X-ray, θ is the glancing angle at which the radiation falls on the atomic plane, and d is the distance at which the diffracting planes are spaced. The most exciting implication of this to Lawrence Bragg was that ‘X-ray diffraction could be used to get information about the nature of the crystal pattern’,8 and before the First World War interrupted his research, he had analysed the structures of rock salt (NaCl), fluorspar (CaF2), pyrites (FeS2), calcite (CaCO3) and simple potassium salts in addition to zincblende (ZnS). Bragg was thereby able to confirm the long-held belief that the internal atomic structure of crystals displays a periodicity or repeating pattern – what the nineteenth-century French crystallographers had called ‘la molécule intégrante’.
W.H. Bragg soon reconciled himself to the fact that X-rays could not be regarded solely as particles, but in some circumstances appeared to behave as waves. This duality, which would be at the heart of quantum theory in the 1920s, he internalized by thinking of X-rays as waves on Mondays, Wednesdays and Fridays, as particles on Tuesdays, Thursdays and Saturdays, and nothing at all on Sundays! While his son concentrated on analysing diffraction patterns to establish the atomic structures of various crystals, Bragg senior was more interested at first in the other side of his son’s equation – the wavelengths of X-rays.
Bragg senior invented an instrument called the X-ray spectrometer that was as important to the development of crystallography and to the exploration of the X-ray spectra of different elements, as the telescope was to astronomy or the microscope to biology. Having carried out no original work until well after his fortieth birthday, W.H. Bragg made a series of spectacular contributions over the next decade. During the enforced hiatus of the Great War he turned his hand to acoustic methods for submarine detection, but could not wait to return to X-ray crystallography research. Eschewing the highly symmetrical inorganic crystals that his son had begun to analyse so brilliantly, he decided to attack the much less symmetrical, soft, organic molecules, whose main atomic constituents are carbon, oxygen and hydrogen. His first results for naphthalene and anthracene were published in 1921, and that same year he gave his Presidential Address to the Physical Society on ‘The structure of organic crystals’.9 While recognizing the daunting complexity of studying such large molecules, Bragg predicted that if methods could be developed, it seemed likely that ‘they would quickly be fruitful’. As a start, he presented diffraction data to show that the benzene ring of six carbon atoms and the double naphthalene ring were real entities and have ‘a definite size and form, preserved with little or perhaps no alteration from crystal to crystal’.10 The multifarious duties that came with the chiefship of the Royal Institution, not to mention the other distractions that accrete to the great and the good, inevitably limited Bragg’s opportunities to work in his own laboratory. Instead he would prove himself as an inspirational and open-minded mentor of a young research group, without ever seeming intent on directing them.
When Sage arrived at the Royal Institution in October 1923, he joined a group of about a dozen research workers. Most were in their twenties like him, and new arrivals were put under the general supervision of Alexander Müller, a Swiss physicist in his mid-thirties. Müller h
ad been Bragg’s research assistant for a year before moving to the RI, and together with George Shearer had carried pioneering work on the structure of long-chain organic compounds, such as the fatty acids and paraffins. Both men were talented instrument makers, and when confronted by the clumsy, talkative, new recruit, who had a habit of breaking equipment, Müller tended to become ‘extremely abusive’.11 Closer to Bernal in age and perhaps in their general view of the world were Bill Astbury and Kathleen Yardley (one of three young women in the group). Both were from poor backgrounds – Astbury’s father was a potter’s turner in the Potteries of Staffordshire, and Yardley was the last of ten children, in a family where four of her brothers died in infancy. Both had succeeded through winning scholarships, as they mounted each rung of the educational ladder.
Astbury12 took first-class honours in both parts of the Natural Sciences Tripos at Cambridge, and had been recommended to Bragg by Arthur Hutchinson, two years before he set Bernal on his way. Kathleen Yardley13 was a diminutive young woman, whose fiercely independent mother moved her surviving children from the poverty of rural Ireland to a slightly better life just beyond the East End of London. She was rewarded by seeing her youngest daughter, Kathleen, gain admission to Bedford College for Women in London, where she graduated in 1922 at the top of the London University list in physics, with the highest marks recorded for ten years. W.H. Bragg, who was one of her examiners, needed no outside referral in her case and sent for her immediately to offer her a research studentship and a government grant of £180 a year. Almost certainly, Sage would have regarded Astbury and Yardley not as examples of how the British system could identify and promote men and woman of exceptional ability, but as shining reminders of the untold thousands, kept in poverty, who would never be able to express their talents.
Astbury and Yardley were both skilled users of the Bragg X-ray spectrometer, but Bernal gave up after a few days of instruction from Kathleen Yardley, recognizing that he did not have the level of patience required to master the exacting technique. Instead he was attracted to a new method of photographic analysis, which gave far less accurate estimates of the intensities of diffracted X-rays but could measure many more reflected spots. Bragg’s longstanding laboratory steward, who had built the first X-ray spectrometer, gave Sage ‘a few pieces of brass… some miner’s lamp glasses, a little aluminium foil for the window, plenty of sealing wax to stick everything together… some glass tubing and a little mercury to make a diffusion pump, some copper and iron wires for a transformer and as an essential ingredient an aluminium hot-water-bottle and a small piece of platinum to make the interrupter’.14 Even with assistance of Müller and Shearer, Sage could not get things to work, and after three months of endlessly burning himself and breaking things, there was not even ‘the trace of an X-ray out of the apparatus’.15 At this point he approached Sir William and pleaded to be allowed to return to the theory of crystallography. Although Bragg had seen the young man with his thick shock of fair hair almost daily at teatime in the library, this was the first time that they had spoken since Bernal was taken on. When Sir William seemed nonplussed by his request, Sage reminded him of the space group dissertation. Bragg, raising his tufted eyebrows a little, retorted ‘You don’t think I read your paper’, which perversely cheered Sage up.
Now the ice was broken between the Director of the Royal Institution and his most loquacious research student, their relationship flourished, and over time Sage came to regard W.H. Bragg as a sort of scientific father.16 With Bragg’s unobtrusive support, Bernal persisted in the laboratory and made some significant experimental discoveries. At the same time, he invented new techniques for interpreting the complex data that were emerging and was always seeking a theoretical framework to tie things together. The first scientific problem that Bragg passed on to Bernal was the unresolved structure of graphite. In 1913, Bragg had been the first to demonstrate the arrangement of carbon atoms in diamond (each atom being surrounded by four others in a regular tetrahedron), but to date there had been no satisfactory model for the humbler isomer of carbon, graphite. There had been previous X-ray diffraction studies on graphite, but they were not in accord. Single crystals of graphite are difficult to obtain, and in fact the two published reports employed a new technique of diffraction by powder, in which X-rays are diffracted by thousands of microscopic crystals orientated at random in all directions. The powder method was invented independently during World War I by Debye and Scherrer in Germany and by an American, Albert Hull, working in the General Electric Research Laboratory. Both of those groups soon applied the technique to graphite powder. Bernal read their papers and also the older mineralogical literature, and decided that there was still no satisfactory solution to the structure of graphite, although it did appear to have hexagonal symmetry. The most compelling evidence for this was provided by Ewald, who had taken a Laue photograph of a single graphite crystal in 1914.
Bernal decided that the X-ray analysis of single crystals would be more informative than the powder method, even though such specimens were difficult to obtain. He was given a piece of Ceylon graphite ‘from which, by careful dissection and picking out, I obtained a few crystalline fragments which, though very far from perfect, were sufficiently so for my purpose’.17 As if the acquisition of a suitable crystal were not trying enough, Bernal had to contend with the unwanted zeal of the Royal Institution charwoman, Mrs Dyke, who ‘had an extreme and quite unnecessary interest in laboratory cleanliness’.18 Sage had selected some potential crystals by looking at them under a microscope and carefully placed them on a clean sheet of paper. He then went to eat his sandwich lunch and play ping-pong (a Royal Institution ritual); on his return to the laboratory, the crystals had vanished. After searching unsuccessfully, he asked Mrs Dyke whether she had seen them. She exclaimed: ‘Them smuts? I swep’ ’em up.’ Bernal admitted that he was ‘not entirely upset when very shortly after that she tried to clean the X-ray apparatus while it was going’. The terminals always collected an enormous amount of dust, and she received a jolting electric shock for her efforts!
The apparatus used for the graphite work had to be constructed from scratch and included a cylindrical camera made out of a piece of brass tubing about one inch in diameter. The film lining the brass cylinder was held in place with bicycle clips, and Sage used ‘an old alarm-clock and a nail to mount and turn the crystal’.19 Crude though it was, the setup worked and others in the laboratory helped Bernal to build more stable and refined equipment with which he was able to confirm the hexagonal symmetry of graphite and also to make the first accurate determination of the dimensions of its unit cell. The crystal was rotated about two axes at right angles to one another and this enabled him to draw a stereographic projection of the reflecting planes, thereby obtaining indices or spatial coordinates for every reflection. Astbury took Laue photographs of several crystals with their cleavage planes perpendicular to the X-ray beam, and Miss Yardley provided some spectrometry measurements enabling Bernal to establish the complete structure for the first time. He concluded that the carbon atoms in graphite ‘lie in planes in which they form nets of hexagons’20 and he provided details of the inter-planar and inter-atomic distances. Now Sage could explain that ‘the great difference between the mechanical properties of graphite and diamond (hardness, flexibility, etc.) is due to the fact that the atoms are linked closely in a two-dimensional net in the former and in a three-dimensional lattice in the latter’. In the plane of a hexagonal net, the carbon atoms in graphite are strongly bonded together, 2.45 Å (Ångström units) apart, but successive cleavage planes are 6.82 Å apart and can slip over one another, accounting for the material’s flaky property.
The experimental method employed by Bernal of a small crystal mounted on a rotating spindle, positioned inside a cylindrical camera, had been devised in Germany a year or so earlier, but Bernal was the first to develop the full mathematical analysis of the system. The crystal lies on the axis of the cylindrical film and the diffracted X-ray
s make a complex pattern of spots on the film. In addition to the Bragg’s Law equation relating the distance between atomic planes in the crystal to the wavelength and glancing angle of the X-ray beam, in this method it is also necessary to allow for the angle between the reflecting plane and the axis of rotation about which the crystal revolves. Even a geometer as talented as Sage found the necessary calculations ‘rather laborious’21 and he devised a much simpler graphical method by which the spots on the film could be projected onto a standard family of curves so that values for the important angles could be read off directly.
While this method was sufficient for a simple crystal like graphite, Bernal realized that it would not be able to handle the X-ray diffractions from the more complex and less symmetrical organic crystals that the Royal Institution workers were beginning to tackle. For these crystals he devised other ready-made tables based on the general concept of the reciprocal lattice. The reciprocal lattice is a mathematical abstraction – the looking-glass world of crystallography – and while its definition is abstruse, it affords the crystallographer a convenient way of analysing the diffracted beams from all sets of parallel planes in the crystalline lattice. While the concept of the reciprocal lattice was first published by Paul Ewald in 1921, the same idea had occurred to Bernal, while still an undergraduate: his diary for 23 April 1920 contains a brief mention of some ‘very interesting investigations on three-dimensional reciprocation’ in which he ‘brought in some new surfaces, also reciprocation w[ith] r[espect] t[o] a circle of complex radius, and on various mesh systems’.22
