690 Chapter 12. Radiation Spectroscopy
reflected from these planes. The reflected rays can interfere constructively as well
as destructively. The condition for constructive interference of two parallel x-rays,
according to Bragg’s law, is given by
2 dsinθ=nλ, (12.1.14)whereλis the wavelength of x-rays,dis the distance between the two atomic planes,
θis the angle of incidence of x-rays with respect to atomic planes, andnis an integer.
θ θθ θddAtomsAtomic Planes2θθFigure 12.1.17: Reflection of parallel x-rays from atomic planes of a crys-
talline lattice.Bragg’s relation implies that if we scan the intensity of diffracted x-rays of known
wavelength at all angles, we can determine the spacing of atomic planes. Since a
typical lattice has planes with different spacings therefore the distribution of scat-
tering angles can give information about the shape of the lattice as well. This is the
principle of x-ray diffraction spectroscopy.
Let us now move on to the practical aspects of XDS. What we need is an x-ray
source and a detector that can measure the diffracted x-ray intensities at different
angles. The choice of x-ray source depends on the type of sample, desired accuracy,
and cost. Although synchrotron radiation is the best choice in most instances but
its use is tagged with fairly high beam time cost. If cost is a limiting factor, one
can resort to conventional x-ray beams capable of delivering x-rays in the required
energy range. The other apparatus we need for the XDS setup is a photon detector
to detect diffracted x-rays. Certainly the best choice would be to use a position
sensitive detector covering the full range of the angles of diffraction. However this
may not be possible due to cost and complexity. A more practical approach is to
use a single channel detector mounted on an assembly such that it could be moved
around the sample. Such a setup is shown in Fig.12.1.18. Generally the mounting
assembly is designed such that it has the capability to rotate the sample as well.
This enables one to study the diffraction patterns with respect to different lattice
planes.