X-ray Diffraction and Crystal Structure-
The fact that the wave length of X-rays and the interatomic distances in a crystal are of the same order (10-8 cm) led Laue to suggest that crystals diffract X-rays. Bragg applied this fact in determining structure of X-rays.
Bragg equation: According to Bragg, a crystal (composed of series of equally spaced atomic planes) could be employed not only as a transmission grating (as suggested by Laue) but also as a reflection grating. When X-rays are incident on a crystal face, these penetrate înto the crystal and strike the atoms in suceessive planes. From each of these planes the X-rays are reflected like the reflection of a beam of light from a bundle of glass plates of equal thickness. Based on this model, Bragg derived a simple relation between the wavelength (\(\lambda\)) of the X-rays used, the distance (d) between the successive atomic planes and the angle of incident X-rays or the angle of reflection (θ).
\(n\lambda = 2d \sin \theta\) (where n = 1, 2 ,3....)
The equation is known as Bragg's equation or Bragg's law. The reflection corresponding to n = 1 (for a given family of planes) is called first order reflection; the reflection corresponding to n = 2 is the second order reflection and so on.
Thus by measuring n (the order of reflection of the X-rays) and the incidence angle θ, we can know \(d/\lambda\)
\(\frac d{\lambda} = \frac n{2\sin \theta}\)
From this, d can be calculated if a is known and vice versa. In X-ray reflections, n is generally set as equal to 1. Thus Bragg's equation may alternatively be written as
\(\lambda = 2d\sin \theta = 2d_{hkl} \sin \theta\)
where dhkl denotes the perpendicular distance between adjacent planes with the indices hkl. For experimental measurements, the apparatus usually employed is Bragg's X-ray spectrometer and determination is done by two methods, namely (i) Bragg's rotating crystal method, and (ii) Debye and Hull's powder method.
