11.20 : X-ray Crystallography

In 1913, the father and son scientists William Henry Bragg and William Lawrence Bragg noticed that when X-rays strike a crystalline solid at a certain angle, the X-rays diffract and produce a pattern of regularly spaced spots.

This led to the development of X-ray crystallography, which uses this phenomenon to determine the structures of crystalline solids ranging from simple ionic compounds to complex macromolecules like nucleic acids and proteins.

Recall that diffracted electromagnetic waves undergo constructive and destructive interference. This produces interference patterns, or diffraction patterns, showing the varying intensity of the diffracted waves at different points in space.

X-rays are diffracted by the electrons of atoms if the atoms are regularly spaced and the X-ray wavelength is similar to the interatomic distance.

When X-rays diffract from atoms in different planes, the diffracted waves may or may not be in phase. This depends on the interplanar spacing, d, and the angle at which the X-rays struck the atoms, or the incidence angle, theta.

This is because the paths that the X-rays take from the source to the detector have different lengths. If the path difference is an integer multiple of the wavelength of the X-rays, then the X-rays constructively interfere.

This results in the pattern of regularly spaced spots of diffracted waves observed by the Braggs, where each spot represents a diffraction angle resulting in constructive interference.

The relationship between the angle of diffraction, the interplanar spacing, and the X-ray wavelength is expressed with Bragg’s equation. This relationship provides information about the underlying highly ordered arrangement of the atoms in the crystal.

Ultimately, the lattice parameters can be derived from this information via a series of calculations. Modern instruments collect diffraction patterns from many different orientations and use the patterns and spot intensities to identify the crystal structure that is most likely to produce the observed combination of results.