kb/data/en.wikipedia.org/wiki/Diffraction-4.md

title	chunk	source	category	tags	date_saved	instance
Diffraction	5/5	https://en.wikipedia.org/wiki/Diffraction	reference	science, encyclopedia	2026-05-05T10:54:57.453682+00:00	kb-cron

== Bragg diffraction ==

Diffraction from a large three-dimensional periodic structure such as many thousands of atoms in a crystal is called Bragg diffraction. It is similar to what occurs when waves are scattered from a diffraction grating. Bragg diffraction is a consequence of interference between waves reflecting from many different crystal planes. The condition of constructive interference is given by Bragg's law:

    m
    λ
    =
    2
    d
    sin
    ⁡
    θ
    ,
  

{\displaystyle m\lambda =2d\sin \theta ,}

where

    λ
  

{\displaystyle \lambda }

is the wavelength,

    d
  

{\displaystyle d}

is the distance between crystal planes,

    θ
  

{\displaystyle \theta }

is the angle of the diffracted wave, and

    m
  

{\displaystyle m}

is an integer known as the order of the diffracted beam. Bragg diffraction may be carried out using either electromagnetic radiation of very short wavelength like X-rays or matter waves like neutrons whose wavelength is on the order of (or much smaller than) the atomic spacing. The pattern produced gives information of the separations of crystallographic planes

    d
  

{\displaystyle d}

, allowing one to deduce the crystal structure. For completeness, Bragg diffraction is a limit for a large number of atoms with X-rays or neutrons, and is rarely valid for electron diffraction or with solid particles in the size range of less than 50 nanometers.

== Importance of coherence ==

The description of diffraction relies on the interference of waves emanating from the same source taking different paths to the same point on a screen. In this description, the difference in phase between waves that took different paths is only dependent on the effective path length. This does not take into account the fact that waves that arrive at the screen at the same time were emitted by the source at different times. The initial phase with which the source emits waves can change over time in an unpredictable way. This means that waves emitted by the source at times that are too far apart can no longer form a constant interference pattern since the relation between their phases is no longer time independent. The length over which the phase in a beam of light is correlated is called the coherence length. In order for interference to occur, the path length difference must be smaller than the coherence length. This is sometimes referred to as spectral coherence, as it is related to the presence of different frequency components in the wave. In the case of light emitted by an atomic transition, the coherence length is related to the lifetime of the excited state from which the atom made its transition. If waves are emitted from an extended source, this can lead to incoherence in the transversal direction. When looking at a cross section of a beam of light, the length over which the phase is correlated is called the transverse coherence length. In the case of Young's double-slit experiment, this would mean that if the transverse coherence length is smaller than the spacing between the two slits, the resulting pattern on a screen would look like two single-slit diffraction patterns. In the case of particles like electrons, neutrons, and atoms, the coherence length is related to the spatial extent of the wave function that describes the particle.

== Main articles involving diffraction == Dynamical theory of diffraction – Multiple diffraction of waves Electron diffraction – Bending of electron beams due to electrostatic interactions with matter Fraunhofer diffraction – Far-field diffraction Fresnel diffraction – Near-field diffraction Gas electron diffraction – Method of observing gaseous atomic structure Grazing incidence diffraction – Diffraction using small incidence angles Helium atom scattering – Diffraction of He from surfaces Kinematical diffraction – Single scattering diffractionPages displaying short descriptions of redirect targets Low energy electron diffraction – Technique for determining surface structuresPages displaying short descriptions of redirect targets Neutron diffraction – Technique to investigate atomic structures using neutron scattering Powder diffraction – Experimental method in X-ray diffraction Reflection high-energy electron diffraction – Electron diffraction by reflection from surfaces X-ray diffraction – Elastic interaction of x-rays with electrons

== See also ==

== References ==

== External links ==

The Feynman Lectures on Physics Vol. I Ch. 30: Diffraction "Scattering and diffraction". Crystallography. International Union of Crystallography. Using a cd as a diffraction grating at YouTube