Question

Briefly describe the diffraction of x rays( or electrons) from crystal planes. Derive Bragg law based on constructive and extinctif interference. Indicate the difference in diffraction between XRD and TEM.

Answer 1

DESCRIPTION OF X-RAY DIFFRACTION IN CRYSTAL :

When an intense beam of x-ray strikes the crystal, depending on the structure and the orientations of different crystal planes, each crystal plane (which are composed periodic arrangement of crystal atoms ) reflects the beam differently. These reflections are shown in the figure below:

From the above figure it is observed that incident ray R2 (which is reflected from the middle crystal plane) has to travel deeper (say difference is 'a' ) than the incident ray R1 (which is reflected from the top crystal plane). Then this difference 'a' would deternine whether there be a constructive interference between two rays R1 and R2 or not.

Then final diffraction pattern would consist of reflections of different intensity ,which can be used to determine the full structure of the crystal.

DERIVATION OF BRAGG'S LAW :

XRD and TEM :

1. XRD is used to generally determine whether a substance has crystalline or amorphous i.e it is used for phase identification, but this cannot be used to analyse the various defects that are present in the crystal

But with TEM we can both characterize the defects and phases of the material

2. TEM be used for determination of site occupancy preferences of the atoms in the crystal structures.

But XRD cannot such analyis

3. Main disadvantage of using TEM lies in the sample preparation procedure , as it requires thickness of the material to be less than 200 nm in order to pass the electron beam through.

No such small order of sample thickness required for XRD