CHEM01200604009 Sreejith Kaniyankandy - Homi Bhabha ...

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of crystal planes appear at different angles, this forms the basis for identification of different
phases. The angle of diffraction is clearly indicative of distances between the planes. The
relationship between lattice plane spacing and angle of diffraction is given by Bragg’s law.
n
2dsin
(2.4)
In equation 2.4 n is the order of diffraction; is diffraction angle; d is the lattice spacing.
Another important factor which helps in indexing an XRD pattern is the intensity of
diffraction. The intensity is also a function of atomic scattering factors and miller indices of
the planes. The atomic scattering factors influences intensity as the scattering centers in
atoms are electrons. Therefore higher the number of electrons, greater is scattering from that
particular atom. Phase characterization can be done just by comparing the diffraction pattern
obtained for samples with that of previously reported patterns as given by database from by
Joint Committee on Powder Diffraction Standards (JCPDS), International Centre for
Diffraction Data (ICDD).
Apart from phase characterization one can obtain information on particle size assuming the
particles are spherical. For a bulk crystallite or a large crystal, scattering signal is sharp,
however in nanocrystallites the peaks are broadened due to coherence lengths of X-ray.
Therefore the broadening is related to size of the diffracting domain therefore of crystallite
size.
k
D
2cos
(2.5)
In the equation above, k is the shape factor and is generally close to 1; D is the crystallite
size. The broadening of an x-ray peak is actually a combination of instrumental broadenings
arising from incident x-ray peak breadth and detectors etc. Instrumental factors are