Use of X-ray diffraction to find atomic arrangements

Once it had been shown that crystals diffract X rays, the relationship between the observed effect and the experimental conditions was put on a sound mathematical basis by Max von Laue, Paul P. Ewald and many others.X-ray diffraction by crystals represents the interference between X rays scattered by the electrons in the various atoms at various locations within the unit cell. It must, however, be stressed again that any molecule or ion can diffract X rays or neutrons. It is only when this diffraction is reinforced by the repetition of the unit cell in the crystal that diffraction by atoms is a conveniently observable effect, for example as spots of differing intensity on photographic film. Of particular interest to chemists and biochemists is the work by W. L. Bragg,who demonstrated that measurement of the diffraction patterns gives information on the distribution of electron density in the unit cell, (i.e., the arrangement of atoms within this unit cell). 

The question at this stage is How does one derive the atomic arrangement in a crystal, such as that of sodium chloride or potassium chloride, from the intensities in their respective diffraction patterns The answer is that the diffracted X-ray beams, which have amplitudes represented by the square roots of their measured intensities, must be recombined in a manner similar to that achieved by a lens in an optical microscope. This recombination is done by a mathematical calculation called a Fourier synthesis. The recombination cannot be done directly because the phase relations among the different diffracted X-ray beams usually cannot be measured. If the phases, however, can be estimated by one of the methods described in Chapter 8, an approximate image of the arrangement of atoms in the crystal can be obtained. 

1 19th century chemical studies of molecular structure 

A historical account of some of the early structures studied by X-ray diffraction techniques will illustrate how the structural principles, laboriously derived by organic and inorganic chemists in the nineteenth century, were verified in the twentieth century. 

The problem of determining the shape of a molecule has been the subject of research for a long time. This was addressed at the beginning of the nineteenth century by John Dalton. He proposed that the combining proportions of atoms in the molecules that make up compounds could be explained by assuming that each element had a different weight (its atomic weight). By chemical analysis of simple compounds he could determine their formulae and propose the connectivities of the component atoms. Attempts to describe the shapes of molecules continued to interest 

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