Diffraction gives you coordinates

Start in about 1910, when chemistry knew a great deal about structure and had never once looked at any of it. Every arrangement of atoms in every formula had been argued out from reactions. Not observed — reasoned to, from what a substance would and would not do. Benzene. Kekulé put the six carbons in a ring in 1865 because disubstituted benzene comes in exactly three isomers, and no other arrangement of six carbons and six hydrogens gives three. The tetrahedral carbon. Van ’t Hoff and Le Bel, independently in 1874, put four bonds on carbon in a tetrahedron rather than a square, because a flat carbon predicts isomers nobody could find and a tetrahedral one predicts optical activity that everybody could see. Coordination compounds. Werner spent from 1893 to 1911 establishing that cobalt sits at the centre of an octahedron of six ligands, entirely by counting how many isomers of each formula could be isolated. This is inference of a very high order, and almost all of it was right. It is also completely indirect, and there was no prospect whatsoever of checking it. Everyone involved knew that. Werner’s octahedron was confirmed by looking, in 1921. He had been dead for two years.

Two arguments were running in 1912, in two different subjects, and neither was close to settled. What are X-rays? Röntgen had produced them in 1895 and could not say what they were. By 1912 the field was split. Charles Barkla argued they were electromagnetic waves of very short wavelength, on the evidence of polarisation. William Henry Bragg argued they were neutral particles, on the evidence of how they knocked electrons out of matter — and his case was strong enough that a serious physicist could hold it without embarrassment. Nobody had diffracted them, and diffraction is what settles that question. Are crystals periodic lattices? René-Just Haüy had inferred it in 1784 from the fact that calcite cleaves into identical smaller rhombs however far you go, as though the solid were built of stacked bricks. Auguste Bravais had worked out, by 1848, every lattice such a stacking could produce — fourteen of them, and no more. It was an elegant idea supported by cleavage angles and by nothing else at all. Two open questions. It is not obvious that they have anything to do with each other.

The man who turned that photograph into a technique was 22, and his father was on the losing side of the argument it had just settled. William Lawrence Bragg was a research student at Trinity College, Cambridge. William Henry Bragg, his father, was Cavendish Professor at Leeds and had spent years arguing that X-rays were neutral particles. The son read Laue’s paper over the autumn of 1912 and made two changes to it, both of which Laue had got wrong. Treat the spots as reflections from planes of atoms. A crystal can be sliced into parallel sheets of atoms in a great many ways, and each set of sheets has its own spacing. A spot is what one of those sets does to the beam. Assume the beam holds a continuous range of wavelengths. Laue had assumed a few discrete ones, characteristic of the crystal’s own atoms. Bragg assumed white radiation, from which each set of planes simply selects whatever wavelength suits its spacing. He presented the result to the Cambridge Philosophical Society on 11 November 1912. It is one equation, and it is the reason this lesson exists. The collaboration that followed is worth describing accurately, because "the Braggs" is often left to do the work of a sentence. The father built the instrument — the ionisation spectrometer, which measured the strength of a reflected beam at each angle rather than photographing it, and which is the direct ancestor of every diffractometer since. The son did the interpretation, and the structures are his. They shared the 1915 Nobel Prize in Physics, and the elder Bragg was always clear about which of them had had the idea.

Then father and son turned the spectrometer on diamond, and got a number organic chemistry had been waiting thirty-nine years for. Every carbon has four neighbours, at 1.54 Å, arranged in a regular tetrahedron. Two interpenetrating face-centred lattices, offset by a quarter of the body diagonal, and no molecules — a diamond is one covalent object. Van ’t Hoff had deduced that tetrahedron in 1874 from counting isomers, and had been attacked in print for it: Hermann Kolbe, one of the most eminent chemists in Europe, wrote that van ’t Hoff had mounted Pegasus, evidently borrowed from the veterinary school, and flown to the chemical Parnassus. He was 22 when he published it and Kolbe’s attack came four years later. Here it was, in 1914, with a length attached to it. And it arrived by a route that owes nothing whatever to counting isomers — which is exactly what makes it a confirmation rather than a restatement.

The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.

1. 1784Haüy infers from the cleavage of calcite that a crystal is built of identical stacked units.
2. 1848Bravais enumerates the fourteen lattices such a stacking can produce. Nobody has seen one.
3. 1874Van ’t Hoff and Le Bel propose the tetrahedral carbon, from isomer counts alone.
4. 1895Röntgen produces X-rays and cannot say what they are.
5. 1912Friedrich and Knipping, on Laue’s suggestion, photograph the diffraction of X-rays by a crystal. Both questions fall at once.
6. 1912In November, W. L. Bragg reads his reinterpretation to the Cambridge Philosophical Society: nλ = 2d sin θ.
7. 1913The structure of rock salt. There is no NaCl molecule in it.
8. 1914The structure of diamond: four neighbours, 1.54 Å, tetrahedral. Laue takes the Nobel Prize.
9. 1915The Braggs share the Nobel Prize. W. L. Bragg is 25, and is in France working on sound ranging.
10. 1921Werner’s octahedral cobalt complexes are confirmed by diffraction, two years after his death.