Page "X-ray crystallography" Paragraph 121

In principle, an atomic structure could be determined from applying X-ray scattering to non-crystalline samples, even to a single molecule.

However, crystals offer a much stronger signal due to their periodicity.

A crystalline sample is by definition periodic ; a crystal is composed of many unit cells repeated indefinitely in three independent directions.

Such periodic systems have a Fourier transform that is concentrated at periodically repeating points in reciprocal space known as Bragg peaks ; the Bragg peaks correspond to the reflection spots observed in the diffraction image.

Since the amplitude at these reflections grows linearly with the number N of scatterers, the observed intensity of these spots should grow quadratically, like N < sup > 2 </ sup >.

In other words, using a crystal concentrates the weak scattering of the individual unit cells into a much more powerful, coherent reflection that can be observed above the noise.

This is an example of constructive interference.