Diffraction of X-Rays by Crystals

X-rays are diffracted by crystals in a manner dependent on the wavelength of the rays and the space lattice of the crystal. Thus X-ray diffraction provides a means for study of the structure of crystalline substances, or of substances which have crystalline phases. The method adopted depends on the form in which the substance is available. With large crystals Laue diagrams can provide useful characterization, but more frequently the crystal is rotated when mounted at the center of a cylindrical film, thus bringing successive sets of crystalline planes into position. The Debye-Scherrer ring or powder method is used when the specimen consists of a number of small crystals. Because of the number of crystals, randomly distributed, some are usually available in each plane to the diffract the X-ray beam.

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        X-rays is a type of electromagnetic radiation of much shorter wavelength, about m. In order to observe the effects of diffraction, the grating spacing must be of the order of the wavelength of the radiation used. The regular array of the atoms in a crystal forms a natural diffraction grating with spacing that is typically m. The scattering of X-rays from the atoms in a crystalline lattice gives rise to diffraction effects very similar to those observed with visible light incident on ordinary grating.

       The study of atomic structure of crystals by X-rays was initiated in 1914 by W. H. Bragg and W. L. Bragg with remarkable achievements. They found that a monochromatic beam of X-rays was reflected from a crystal plane as if it acted like mirror. To understand this effect, a series of atomic planes of constant inter planer spacing d parallel to a crystal face are shown by lines PP', P1P1', P2P2' and so on, in the figure given below:

   Fig    Diffraction of X-rays from the lattice plane of crystal

      Suppose an X-rays beam is incident at an angle θ on one of the planes. The beam can be reflected from both the upper and the lower planes of atoms. The beam reflected from lower plane travels some extra distance as compared to the beam reflected from the upper plane. The effective  path difference between the two reflected beams is 2dsinθ. Therefore, for reinforcement, the path difference should be an integral multiple of the wavelength. Thus

2dsinθ =nλ

      
       The value of n is referred to as the order of reflection. The above equation is known as the Bragg equation. It can be used to determine inter planar spacing between similar parallel planes of a crystal if X-rays of known wavelength are allowed to diffract from the crystal.

    X-ray diffraction has been very useful in determining the structure of biologically important molecules such as hemoglobin, which is an important constituent of blood, and double helix structure of DNA.