[Physics Class Notes] on Bragg's Law Pdf for Exam

Physics, Bragg’s law or we can say the Wulff–Bragg’s condition, it’s a special case of diffraction of Laue, this whole thing gives the angles for coherent and incoherent scattering from a lattice crystal. When the X-rays are incident on an atom and they make the cloud of electronic movement. As any electromagnetic wave does. 

These movement charges which reradiate waves with the frequency which is same and even slightly due to an effect of variety. This whole phenomenon is known as Rayleigh scattering or even we can see elastic scattering. The scattered waves can be scattered but this scattering which is secondary is assumed to be negligible.

A process which is similar occurs upon scattering neutron waves which are from the nuclei or we can say by a coherent spin interaction with an electron which are unpaired. The wave which is the resulting interference pattern is the basis of diffraction analysis. This analysis is also known as Bragg diffraction.

History 

In 1913 Bragg diffraction which is also called as the Bragg formulation of X-ray diffraction was first proposed by Lawrence Bragg and his father William Henry Bragg in response to discovery of crystalline solids. Finally, they found that these crystals which are present at wavelengths of certain specific and incident angles that produce a reflected effect type of  radiation which is intense.

Sir Lawrence Bragg explained in his thesis this result by modeling the crystal as a set of parallel discrete planes which are separated by a constant parameter which is denoted as d. It was proposed that the ray of incident that is X-ray radiation would be producing a Bragg peak if their reflections of planes interfere every time. Interference is constructive in nature when there is a shifting phase which is a multiple of 2π that is this condition which can be expressed by law of Bragg’s. This confirmed the existence of particles which are real although it is very simple at the atomic scale, as well as it provides a powerful tool for study of crystals in the form of X-ray and diffraction of neutrons.

Sir Lawrence Bragg along with his father who was named William Henry Bragg in 1915 were awarded with the Nobel Prize in physics for their work in determining crystal structures which are beginning with  ZnS, NaCl.

Conditions 

The conditions for Bragg diffraction occur when radiation along with a wavelength is comparable to atomic spacings, that is scattered in a fashion which is specular by the atoms of a crystalline system. And at times it also undergoes constructive interference. For a solid which is crystalline the waves are scattered from lattice planes which are later separated by the interplanar distance which is denoted as d. Wave gets scattered at that time the interference constructively remains in phase since the difference between the path and length which are of the two waves is equal to an integer multiple of the wavelength. And we should also note that this differs from the convention in Snell’s law where θ is measured from the normal of the surface. The constructive effect of destructive interference is because of the effect of reflection in successive crystallographic planes that is h, k, l of the crystalline lattice as described by sir Miller notation earlier.

Applications 

In X-ray diffraction which is also called as the XRD is the interplanar which is spacing d-spacing of a crystal is used for characterization and  identification purposes. Incident ray wavelength that is the X-ray is known and measurement is made of the incident angle denoted as: Θ at which constructive interference occurs at a point. An unknown given crystal is expected to have many plates which are rational of atoms in its structure and therefore, the collection of the “reflections” of all the planes can be used uniquely to identify an crystal which is unknown. Crystals in general with high symmetry that is isometric systems which tend to have relatively few atomic planes, on the other hand crystals with low symmetry that is in the monoclinic system and triclinic systems tend to have a very large number of possible atomic planes in their structures.

In wavelength case the dispersive spectrometry that is WDS or X-ray fluorescence spectroscopy denoted by XRF, crystals of known d-spaces are used for analyzing crystals in the spectrometer. The position of the sample which is mentioned and the detector which is fixed in these applications has the position of angle which is of the reflecting crystal is with Bragg’s law so that a particular wavelength of interest can be directed as a detector for quantitative analysis. Every element which is present in the Periodic Table has an energy which is a discrete difference which is between the orbital “shells” that is . K, L, M, in such a manner that every element will produce X-rays of a fixed wavelength.