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   X – Ray Diffraction Method, Chemistry tutorial

Introduction

X - Rays are electromagnetic radiation by fairly elevated penetration power or energy. The rays have the normal properties of waves most particularly, they can be diffracted.

Diffraction procedure generally happens whenever a wave meets a barrier through one or more openings of about the similar size as the equivalent wavelength. Frequently, the atoms or ions in crystals are arranged in these a way that they are divided from one another through a particular distance. These distances are in the right range to source x - rays to be diffracted. Therefore, the layers of atoms in a crystal act as a diffraction grating for x-rays.

Definition

X-ray diffraction is an occurrence in that waves of x-rays spread and bend as they pass through small openings or around barriers.

As we know that: Diffraction is more pronounced whenever the opening, or aperture, or the barrier is alike in size to or smaller than the wavelength of the incoming wave.

Basic Concept of X-ray Diffraction

X-rays are electromagnetic waves in that the wavelengths are comparable in size to the spacing between the atoms in crystals. When these waves pass through crystals, they diffract (for example spread out or bend) and form interference patterns. Such patterns can be analysed to expand information about geometric structure and properties of the crystals. The major cause why atoms are capable to generate diffraction patterns is due to the number of electrons they hold. The electric field of x-rays interacts by the electron cloud around the atom. Therefore, the consequence of many of such interactions generates the diffraction pattern. Huge atoms have many electrons. As a consequence, they produce the strongest patterns. Small atoms, these as hydrogen, have little consequence on x-ray since of the few number of electrons.

Types of X-ray Diffraction Experiments

The 1st x-ray diffraction experiments were executed via bombarding Zinc Sulphide through elevated energy electrons. Then the X-rays were passed through a single crystal as revealed below:

1026_A simplified diagram of scattering of x-ray by a crystal.jpg

Fig: A simplified diagram of scattering of x-ray by a crystal  

The 2nd experiment engages utilize of a powdered substance that is recognized as Powder technique. In this experiment, crystals of example to be analysed are ground to a fine powder and then situated in a tube made of glass that has little consequence on x-rays. The example is surrounded via a cylindrical sheet of photographic paper. The x-rays are permitted to penetrate throughout a small hole in the cylinder and passed into the model, where the diffraction takes place. A piece of lead that absorbs any x-rays that pass through the example is situated opposite the entrance hole.

329_Diffraction by powdered crystals.jpg

Fig: Diffraction by powdered crystals  

As can be seen, the powdered crystals are at the centre. The reflections of the x-rays create curved lines on the photographic paper. As we know: the above diagram symbolizes only one set of plane in a crystal. The division between the planes is exposed as an angle to the incoming x-rays. The angle is symbolized as θ. Diffractions from crystals by their sets of planes at angle θ will be arranged in form of a cone. This is since the photographic film is in the shape of a cylinder; the reflections from the crystals generate a set of curved models on the film.

The Effect of X-ray Diffraction on the Arrangement of Atoms

Generally, the extent of diffraction based on the nature and arrangement of the individual atoms inside a crystal. Therefore, the greater the number of electrons in an atom, the stronger the diffraction or reflection. If the intensities of the individual spots on X-ray snap can be compared precisely, then it is possible to relate them by the nature of the electron cloud around the atoms. For correct dimension of the intensities, an instrument termed diffract meter is utilized. Therefore, the intensities of the diverse reflections are computed straight via electronic means rather than through photographs. When the consequences are computerized, electron density maps can be created.

Bragg's equation

Bragg's proposed that the formation of diffraction patterns could be explained by assuming that the X-rays were reflected from the various planes of atoms in a crystal. According to Braggs's explanation, it is possible to consider that both diffraction and reflection are equivalent to one another. Therefore, when 2 rays are diffracted in 2 different planes, the difference in the distance travelled through these rays is 2d sinθ. So, for constructive interference, we have:

   nλ = 2d sinθ

Where nλ is referring to the path difference in crystals, n is a whole number, λ is a wavelength. If n = 1, reflection is assumed to be 1st order. If n = 2 it is a 2nd order reflection and so on.

Instance: When X-rays of wavelength 1.54x 10-8 cm passed through Sodium Chloride, an intense cone is shaped at θ = 15.870. If this is taken as 1st order reflection then    

1.54 x 10-8 cm = 2 d sin (15.870)

  That is   d= 1.54*10-8/2 sin 15.87 = 2.82 * 10-8 cm

Note: d is referring to the spacing between the planes.

Applications

X-ray diffraction can be utilized to find out the structures of crystals. The diffraction examples of X-ray can as well be utilized to find out the arrangement of electrons around the atoms. This gives good evidence about the forms of molecules. X-ray diffraction has led to the detection of the double helical structure of DNA.

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