Laue condition
/ LOW-uh kun-DISH-un /
Bragg's law tells the diffraction story with the friendly picture of waves reflecting off stacked planes. The Laue condition tells the very same story in a more powerful language — the language of reciprocal space. Instead of asking 'at what angle do reflected waves line up?', it asks 'how much must a wave's direction change for the scattered wavelets to all reinforce?' and answers in one crisp rule.
Precisely, the Laue condition says that diffraction happens exactly when the change in the wave's direction — its scattering vector — equals one of the reciprocal lattice vectors. In plain terms, the incoming and outgoing waves must differ by a step that exactly matches the crystal's hidden periodicity. When that match is hit, every atom in the crystal scatters in step and the wavelets pile up into a bright spot; otherwise they wash out. The set of allowed spots is therefore simply the reciprocal lattice itself.
This matters because the Laue condition is the rigorous, three-dimensional heart of diffraction, and it makes the deep link explicit: diffraction spots are a direct picture of the reciprocal lattice. It also reproduces Bragg's law exactly, just dressed in vectors. The common confusion is to think the Laue condition and Bragg's law are rival theories — they are two views of one truth, and the Laue form is the one that connects cleanly to the Ewald sphere and to band theory.
Max von Laue's 1912 experiment fired X-rays at a copper-sulfate crystal and caught a symmetric constellation of spots on film — the first crystal diffraction pattern ever seen. Each spot sat where the scattering vector had matched a reciprocal lattice vector, mapping the crystal's hidden periodicity in a single shot.
Von Laue's first diffraction photograph: each spot is a satisfied Laue condition.
The Laue condition fixes the directions in which spots can appear; it says nothing about brightness. Whether a Laue-allowed spot is actually bright still depends on the structure factor, which can null it out entirely.