Bragg's law

Bragg's law is written nλ = 2d sin θ. Here λ is the wavelength of the incident radiation, d is the distance between parallel lattice planes in a crystal, θ is the angle between the incident beam and those planes, and n is a positive integer describing the diffraction order. Under the idealized plane-reflection picture, rays scattered from neighboring planes travel different distances; when the path difference equals an integer number of wavelengths, their waves reinforce one another. This is the condition for a diffraction maximum.

The relation does not describe literal reflection from flat crystal surfaces. It is a geometric way to express constructive interference from a periodic arrangement of scattering centers. In full treatments, diffraction is analyzed using the crystal's reciprocal lattice and scattering amplitudes; Bragg's law provides an intuitive and widely used condition for the observed angles.

In an X-ray diffraction experiment, the wavelength is often known and the detector records the angles at which intensity peaks occur. Bragg's law then relates those angles to spacings between families of crystal planes. A crystal has many such plane spacings, so the set of measured reflections can be compared with structural models or reference patterns to identify and characterize crystalline materials. Conversely, known plane spacing can be used to select or analyze particular wavelengths in diffraction instruments.

The formula also shows why only certain orientations produce strong diffracted beams for a fixed wavelength and lattice spacing: the sine condition must be met. Since sin θ cannot exceed one, a specified wavelength and spacing allow only a finite range of diffraction orders.

William Henry Bragg and his son William Lawrence Bragg developed the law in the early twentieth century to interpret X-ray diffraction by crystals. Their work connected diffraction geometry with the analysis of crystal structure. In 1915, the Nobel Prize in Physics was awarded jointly to the two Braggs for their work in analyzing crystal structure by means of X-rays.