Bragg's Law And Its Application
Bragg's diffraction occur when radiation with wavelength comparable to atomic spacing is scattered in a specular fashion by the atoms of a crystalline system and undergoes constructive interference.
Summary
Bragg's diffraction occur when radiation with wavelength comparable to atomic spacing is scattered in a specular fashion by the atoms of a crystalline system and undergoes constructive interference.
Things to Remember
- 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.
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Bragg’s Law
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Bragg's Law And Its Application
Bragg's Equation
A crystal is considered to be composed of series of parallel and equidistance plane.X-rays are used to study the internal structure of crystal because
1)The interplanar distance of most of the crystal and wavelength of x-ray are of comparable range.
2)X-ray have greater penetration power as compared to any other rays.
Let us consider BB',CC' and DD' are some of the planes of a crystal.Let us consider a beam of monochromatic x-ray PQ is incident on a first plane BB' with an angle θ and reflected along QR.Similarly,the another beam XY is incident on a plane CC' with an angle and reflected along YZ.
Then from figure,the path difference between the reflected rays=MY+NY — i)
For ΔQMY,
$$sin θ=\frac{MY}{QY}$$
sin θ=\(\frac{MY}{d}\)
MY=dsinθ
Similarly,in ΔQNY,
sin θ=\(\frac{NY}{QY}\)
NY=dsinθ
Hence,path difference=dsinθ+dsinθ=2dsinθ — ii)
According to Bragg's law, the path difference between the reflected rays must be a integral multiple of wavelength of x-ray used.
i.e nλ=2dsinθ — iii)
where, n=1,2,3.......... represent the order of reflection.
Equation iii) is the required Bragg's equation.
Applications of Bragg's Law:
i)In x-ray diffraction,the interplanar spacing of a crystal is used for identification and characterization purposes.In this case,the wavelength of the incident x-ray is known and measurement is made up of the incident angle θ at which constructive interference occurs.Solving Bragg's equation gives the d-spacing between the crystal.Lattice planes of atoms that produce the constructive interference.A given unknown crystal is expected to have many rational plane of atoms in its structure;Therefore,the collection "reflections" of all the planes can be used to uniquely identify an unknown crystal.
- In the case ofwavelength dispersive spectrometry or X-ray fluorescence spectroscopy, crystals of known d-spacings are used as analyzing crystals in the spectrometer. Because the position of the sample and the detector is fixed in these applications, the angular position of the reflecting crystal is changed in accordance with Bragg's Law so that a particular wavelength of interest can be directed to a detector for quantitative analysis. Every element in the Periodic Table has a discrete energy difference between the orbital "shells" (e.g. K, L, M), such that every element will produceX-rays of a fixed wavelength. Therefore, by using a spectrometer crystal (with fixed d-spacing of the crystal) and positioning the crystal at a unique and fixed angle (Θ), it is possible to detect and quantify elements of interest based on the characteristic X-ray wavelengths produced by each element.
References
Prutton, S.H Maron & c. Principles of Physical Chemistry. Oxford & Pub. Co., 1992.
http://chemwiki.ucdavis.edu/Core/Analytical_Chemistry/Instrumental_Analysis/Diffraction/Bragg's_Law
Lesson
Solid State Chemistry
Subject
Chemistry
Grade
Bachelor of Science
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