Lipson’s strips and Beevers’ balls | Opinion – Chemistry World

A photograph showing Cecil Arnold Beevers

Every year I find myself having to lead a set of tutorials about x-ray crystallography, a topic that, I confess, I’ve never felt very comfortable with. One of the questions requires students to calculate the structure factors of a set of reflections. The summation of sines and cosines takes a little care and patience; not surprisingly the question produces a certain grumpiness among the students. While trying to restore morale, I sometimes find myself having to avoid sounding like the four Yorkshiremen sketch. ‘We’d have been glad of the price of a cup o’ tea then…’

Since a modern diffractometer collects and processes a complete dataset largely automatically in a couple of hours, it is hard to appreciate just how brutally hard and repetitive crystallography was before the advent of computers. Data collection using the Braggs’ ionisation spectrometer (Chemistry World, December 2013, p37) was exquisitely slow. The intensity of hundreds of spots on x-ray photographs would then be estimated by eye using a small magnifier and transcribed to a notebook. As to processing, that was a different ball-game altogether.

An image showing Lipson's strips and Beever's balls

Unlocking the unit cell

Initially Lawrence Bragg considered crystals as containing point atoms that scattered x-rays in proportion to their atomic number; in-phase scattering gave intensity at particular angles. This was done without a precise knowledge of x-ray wavelengths; it was only by combining scattering data with the density of high symmetry substances like zinc blende that both structures and wavelengths were established.

As the complexity

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