Bragg's law

Bragg's law states that when X-rays hit an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re-radiates waves with the same frequency (blurred slightly due to a variety of effects); this phenomenon is known as Rayleigh scattering (or elastic scattering). The scattered waves can themselves be scattered but this secondary scattering is assumed to be negligible. A similar process occurs upon scattering neutron waves from the nuclei or by a coherent spin interaction with an unpaired electron. These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add together to produce stronger peaks or subtract from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. Both neutron and X-ray wavelengths are comparable with inter-atomic distances (~150 pm) and thus are an excellent probe for this length scale.

The interference is constructive when the phase shift is a multiple of 2p; this condition can be expressed by Bragg's law,

n λ= 2d sinθ 

where n is an integer determined by the order given, λ is the wavelength of the X-rays (and moving electrons, protons and neutrons), d is the spacing between the planes in the atomic lattice, and

θ is the angle between the incident ray and the scattering planes.Note that moving particles, including electrons, protons and neutrons, have an associated De Broglie wavelength.

A colloidal crystal is a highly ordered array of particles which can be formed over a very long range (from a few millimeters to one centimeter) in length, and which appear analogous to their atomic or molecular counterparts. The periodic arrays of spherical particles make similar arrays of interstitial voids, which act as a natural diffraction grating for visible light waves, especially when the interstitial spacing is of the same order of magnitude as the incident lightwave.

Thus, it has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations with interparticle separation distances often being considerably greater than the individual particle diameter. In all of these cases in nature, the same brilliant iridescence (or play of colors) can be attributed to the diffraction and constructive interference of visible lightwaves which satisfy Bragg's law, in a matter analogous to the scattering of X-rays in crystalline solids.