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| Left: X-ray diffraction from single-crystal diamond. Right: Bragg's calculation of where the spots would be if diamond had what we now know is the correct structure. |
Thursday, February 09, 2023
Tour de force work: Bragg, diffraction, and diamond
There are some examples of scientific progress that just seem so far above and beyond the norm, it's almost jaw dropping in terms of the mental leap needed for the insight. One example that I always liked to point out to first-year undergrads learning about gravity is Johannes Kepler in 1601-1609 analyzing Tycho Brahe's data by hand (obviously) and deducing that planets move in elliptical orbits and the associated laws of planetary motion. Imagine staring at page after page of hand-written numerical tables and somehow seeing that.
Another example from condensed matter physics is the 1912 discovery by William Lawrence Bragg, then 25 years old, that he could deduce the crystal structure of solids from the positions of the spots revealed on photographic film as the solid diffracted a beam of x-rays. The very fact of diffraction of x-rays by crystals had only been found earlier the same year by von Laue and collaborators. Bragg had the insight that interference effects due to the x-rays bouncing off different planes of atoms would determine the pattern of spots, as constructive interference only takes place for certain combinations of directions for a given wavelength of x-rays. The image here is based on Figs. 11 and 12 from this paper, "The Structure of Diamond", by Bragg and his father (who built the diffractometer!). That was published back-to-back with the more general (and single-author!) paper, "The Structure of some Crystals as Indicated by Their Diffraction of X-rays", where Bragg wrote what is now known as Bragg's Law and the prescription for finding the distance between adjacent planes of atoms. Imagine looking at the smudgy spots on the photographic plates, having the "aha!" insight about the origin of the pattern, and having the raw computational prowess to just go ahead and calculate it. Unreal.
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In a lecture a few years ago, the crystallographer Chris Hammond told a story of Bragg (the son) walking along a river pondering on the nature of the bright spots in one of their diffraction patterns. The eureka moment came when he realized that they were reflections because of the *shape* of the spots. The same phenomenon of a compressed/squeezed image was see when he glanced at reflections of objects on the opposite side of the river. He realized that the major axes of all the elliptical (reflected) beams were orthogonal to their scattering vector and thus corresponded to sets of planes at different angles inside the crystal.
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