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In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength ...
X-ray crystal truncation rod scattering is a powerful method in surface science, based on analysis of surface X-ray diffraction (SXRD) patterns from a crystalline surface. For an infinite crystal , the diffracted pattern is concentrated in Dirac delta function like Bragg peaks .
While the Bragg formulation assumes a unique choice of direct lattice planes and specular reflection of the incident X-rays, the Von Laue formula only assumes monochromatic light and that each scattering center acts as a source of secondary wavelets as described by the Huygens principle. Each scattered wave contributes to a new plane wave given by:
The Laue equations can be written as = = as the condition of elastic wave scattering by a crystal lattice, where is the scattering vector, , are incoming and outgoing wave vectors (to the crystal and from the crystal, by scattering), and is a crystal reciprocal lattice vector.
Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil.
In X-ray crystallography, wide-angle X-ray scattering (WAXS) or wide-angle X-ray diffraction (WAXD) is the analysis of Bragg peaks scattered to wide angles, which (by Bragg's law) are caused by sub-nanometer-sized structures. [1] It is an X-ray-diffraction [2] method and commonly used to determine a range of information about crystalline materials.
It also corrects for refraction at the Bragg condition and combined Bragg and specular reflection in grazing incidence geometries. A Bragg reflection is the splitting of the dispersion surface at the border of the Brillouin zone in reciprocal space. There is a gap between the dispersion surfaces in which no travelling waves are allowed.
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions , =, …,.Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction).