The crystal structure and the crystallite size of the synthesized nanoparticles can be determined using the X-ray diffraction technique. The basic principle behind the X-ray diffraction technique is the diffraction of the x rays from the periodic lattice of the crystal.
The main condition for the diffraction to occur is that the wavelength of the wave must be comparable to the size of the diffracting object and here in the case of interplanar distance in the crystal, it is of the same order of the wavelength of the x rays. In the case of crystals there scattering from many atoms and the intensity from all these scatterings add up either constructively or destructively based on their phase difference between the scattered beams. The basic equation used is the Braggs law which relates the interplanar distance, the wavelength and the order of the diffracted beam.
An x-ray diffractometer consists of three components mainly and they are the x-ray source, the specimen and the detector. All of these three lie in the circumference of a circle called the focusing circle. The Bragg angle () is the angle between the detector and the projection of the x-ray source and is half the value of the angle between the detector and the projection of the x-ray source. In this particular setup called (theta 2theta), the detector moves with a certain range of the angle while the x-ray source is fixed. The value of the intensity of the diffracted beam for various values of the angle(2theta) is plotted against the 2 theta value. For each plane with specific Miller indices, the will be a peak for a particular angle for a given sample.
The x-ray diffraction spectra also give an idea about the average crystallite size of the particles in the sample and can be calculated from the width of the intensity peaks using the Debye Scherrer formula. (diameter(d) =.9lambda /beta costheta)