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  • X-ray diffraction is a non-destructive analytical technique. It is mainly used in identification

  • of crystalline materials. In an X-ray diffraction experiment, a sample is place at the center

  • of the instrument and a beam of X-rays is passed through the sample. The sample absorbs

  • these x-rays and re-emits them in the form of new x-rays. The re-emitted radiation is

  • recorded by the detector in the form of a graph. The peak observed in the xrd spectrum

  • tells about the atomic structure of the sample. Each crystalline material has a different

  • atomic structure therefore gives different XRD spectrum. In crystalline material, crystals

  • are composed of regular arrangement of atoms and each atom is composed of a nucleus surrounded

  • by its electrons. When x-rays hit an atom its energy is absorbed

  • by the electrons. Since this is not enough energy to be released in form of heat or other

  • form. Electrons re-emit the energy in the form of a new x-ray but the same energy as

  • the original. This process is called elastic scattering. The phenomena by which X-rays

  • are reflected from the atoms in a crystalline solid is called diffraction. The intensity

  • of scattered rays depends on the scattering power of the individual atoms, which intern

  • depends on the number of electrons in the atom.

  • X-rays are high energy light with a repeating period called wavelength. The wavelength of

  • an X-ray is similar to the distance between atoms in a crystal, therefore when x-rays

  • interact with each other special interference effect occurs. If the waves are in same phase,

  • the waves combine together to increase the light intensity. This is called constructive

  • interference. If the waves are out of sync the signal is destroyed. This is called destructive

  • interference. In order for constructive interference to

  • be occur the scattered waves must be in same phase.

  • Now constructive interference can only occur if the incident and scattered wave travel

  • equal distance. Since, we know that in a crystal the repeating arrangement of atoms form distinct

  • planes and these planes are separated from each other by a well-defined distance, known

  • as d spacing. When x-ray fall on atomic planes, x-rays are scattered by the regularly spaced

  • atoms. When x-ray fall on top layer then both incident and scattered ray travel same distance.

  • But when x-ray fall on internal layer, both incident and scattered ray travel some extra

  • distance. Similarly if x-ray fall on third layer, both the rays have to travel some more

  • extra distance. This extra distance traveled by x-rays is known as path difference. Because

  • of this path difference it is not necessary that scattered rays will interfere constructively.

  • So the only possibility when scattered rays can interfere constructively is that when

  • incident and scattered rays must travel a whole number. Suppose if the path difference

  • is equal to 1 wavelength so in that case both the rays will be in same phase because ½

  • of the distance is traveled by the incident radiation and half of the distance is traveled

  • by the scattered ray. Similarly if the path difference is equal to 2 wavelengths so in

  • that case also both the rays will be in same phase as 1 wavelength distance will be traveled

  • by the incident ray and 1 wavelength distance will be traveled by the scattered ray. So

  • for constructive interference path difference is equal towhere n=0,1,2,3 etc.

  • The incident rays interact with the atom at an angle θ and reflect at a certain angle.

  • In case of reflection both incident and scattered or reflected angles are same. Therefore angle

  • between ACB will be θ and so for the triangle ADB.

  • So in triangle ACB, Sin θ = CB/AB and we know that AB = d, so CB= d sin θ

  • Similarly in triangle ADB Sin θ = DB/AB and AB = d, so DB= d sin θ

  • Now replace CB and DB by d Sin θ in path difference equation

  • Finally we get a new equation that is 2d sin θ =nλ. This equation is known as Bragg's

  • Equation. So Bragg's law states that diffraction will

  • occur only if angle of incidence is equal to angle of scattering. And the waves constructively

  • interfere with path difference of a whole no of wavelength. So with the help of Bragg's

  • equation we can directly measure wavelength of x-ray, d spacing of crystals and diffraction

  • angle.

X-ray diffraction is a non-destructive analytical technique. It is mainly used in identification

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X-ray Diffraction and Bragg's Law

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    lovegastar に公開 2022 年 08 月 12 日
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