The Bragg-Wulff condition, determines the directions in which maxima of intensity can arise when X-radiation is elastically scattered by a crystal in the diffraction of X-rays. It was established in 1913 independently of each other by the English physicist W. L. Bragg and the Russian scientist G. V. Wulff.
If a crystal is regarded as a set of parallel atomic planes spaced a distance d apart (Fig.), the diffraction of the radiation can be pictured as its reflection from such a system of planes. Maxima of intensity (diffraction maxima) then arise only in those directions in which all the waves reflected by the atomic planes are in one phase, that is, at those angles 2ν to the direction of the primary beam for which the Bragg-Wulff condition holds: the path difference between two rays reflected from neighbouring planes, equal to 2d sin ν, must be a whole number of wavelengths λ: 2d sin ν = mλ (m — a positive integer, called the order of reflection). The Bragg-Wulff condition can be obtained from the more general conditions for the diffraction of radiation by a three-dimensional lattice.
The Bragg-Wulff condition makes it possible to determine the interplanar spacings d in a crystal, since λ is usually known and the angle ν (called the Bragg angle) can be measured experimentally. It is used in X-ray structure analysis, in the X-ray examination of materials and in X-ray topography. The Bragg-Wulff condition remains valid for the diffraction of γ-radiation, of electrons and of neutrons (see Diffraction of microparticles), for the diffraction of electromagnetic radiation of the radio and optical ranges by periodic structures, and for that of sound.