2. BRAGGโS LAW
๏ Bragg's law gives the angles for coherent
and incoherent scattering from a crystal
lattice. When X-rays are incident on
an atom, they make the electronic
cloudmove as does any electromagnetic
wave. The movement of these charges re-
radiates waves with the same frequency this
phenomenon is known as Rayleigh
scattering (or elastic scattering).
3.
4. ๏ A similar process occurs
upon scattering neutron waves from
the nuclei. These re-emitted wave
fields interfere with each other either
constructively or destructively producing a
diffraction pattern on a detector or film. The
resulting wave interference pattern is the
basis of diffraction analysis. This analysis is
called Bragg diffraction.
5.
6. Bragg diffraction (also referred to as the Bragg
formulation of X-ray diffraction) was first
proposed by William Lawrence Bragg and William
Henry Braggin 1913 in response to their discovery
that crystalline solids produced surprising patterns
of reflected X-rays.The concept of Bragg
diffraction applies equally to neutron
diffraction and electron diffraction processes.
7.
8. ๏ W. L. Bragg explained this result by
modeling the crystal as a set of discrete
parallel planes separated by a constant
parameter d. It was proposed that the
incident X-ray radiation would produce a
Bragg peak if their reflections off the various
planes interfered constructively. The
interference is constructive when the phase
shift is a multiple of 2ฯ;
9. ๏ So Braggโs law given as
๏ Where n is an integer,
๏ Lambda is a wavelength of incident wave,
๏ d is the space between the plane in atomic lattice,
is the angle between incident ray and the scattering
plane.
10. ๏ Bragg's Law was derived by physicist Sir William
Lawrence Bragg in 1912 and first presented on 11
November 1912 to theCambridge Philosophical Society.
Although simple, Bragg's law confirmed the existence
of real particles at the atomic scale, as well as
providing a powerful new tool for studying crystals in
the form of X-ray and neutron diffraction.
11. ๏ William Lawrence Bragg and his father, Sir
William Henry Bragg, were awarded
the Nobel Prize in physics in 1915 for their
work in determining crystal structures
beginning with NaCl, ZnS, and diamond.
12. ๏ Bragg diffraction occurs when electromagnetic radiation or
subatomic particle waves with wavelength comparable to atomic
spacings are incident upon a crystalline sample, are scattered in a
specular fashion by the atoms in the system, and undergo
constructive interference in accordance to Bragg's law. For a
crystalline solid, the waves are scattered from lattice planes
separated by the interplanar distance d. Where the scattered
waves interfere constructively, they remain in phase since the
path length of each wave is equal to an integer multiple of the
wavelength. The path difference between two waves undergoing
constructive interference is given by 2dsinฮธ, where ฮธ is the
scattering angle. This leads to Bragg's law, which describes the
condition for constructive interference from
successive crystallographic planes.
