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10.6 X-Ray Crystallography

Each crystal is contained within a well defined set of surfaces. These surfaces are called lattice planes. Each set of these planes consists of a large number of planes parallel to each other and separated by a fixed distance. This distance between the two planes of similar type and parallel to each other is called interplanar distance (d). These distances are of the atomic dimensions. The wavelengths of X-rays are also of the atomic dimensions. This led Max von laue to suggest that a crystal should act as a three-dimensional diffraction gratings for X-rays.
x-ray crystallography

X-ray diffraction by a crystal

This means, that when X-rays are made to fall on a crystal, the X-rays give diffraction pattern characteristic of the crystal. Determination of the internal structure of crystals by using X-rays is called X-ray crystallography.

For diffraction maxima to occur, the path difference must be equal to an integral multiple of wavelength. Thus

<crystallography

The equation is called Bragg's equation.

where d is the interplanar distance, i.e., distance between the two planes of the constituent particles.

l is the wavelength of the X-rays.

q is the angle at which X-rays strike the planes which gives diffraction. 2q is the angle between the diffracted beams of X-ray with the direction of the incident beams.

n is the integer (1, 2, 3...). n represents the order of the diffracted beam.

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