A crystal's periodic arrangement of atoms produces coherent interference when illuminated by waves whose wavelength is comparable to the lattice spacing. Bragg diffraction expresses the constructive-interference condition for reflection from parallel crystal planes separated by distance $d$.

For incident and scattered rays making angle $\theta$ with the planes, the path difference between waves reflected from adjacent planes is $$2d\sin\theta.$$ Constructive interference occurs when this equals an integer number of wavelengths: $$2d\sin\theta=n\lambda,\qquad n=1,2,\ldots$$ This is Bragg's law.

For example, if x-rays of wavelength $\lambda=0.154,\mathrm{nm}$ produce a first-order peak at $\theta=30^\circ$, then $$d=\frac{\lambda}{2\sin30^\circ}=0.154,\mathrm{nm}.$$ The measured angle therefore reveals a real-space lattice spacing.

In reciprocal-space language, diffraction occurs when the scattering-vector change satisfies $$\Delta\mathbf k=\mathbf G,$$ for a reciprocal-lattice vector $\mathbf G$. This form generalizes naturally to three-dimensional diffraction patterns.

Peak positions reveal lattice geometry and spacings; intensities also depend on the arrangement and scattering strength of atoms within the unit cell through the structure factor. Diffraction therefore turns wave interference into a measurement of microscopic crystal structure and is used with x-rays, electrons and neutrons.