X-rays have wavelengths on the order of angstroms, which is comparable to the spacing between atoms in crystalline solids. This makes x-rays useful for diffraction from crystal lattices. In 1912, Max Von Laue discovered that crystals could act as diffraction gratings for x-rays due to their regular atomic spacing. Bragg and Bragg later developed Bragg's law in 1914 to explain the diffraction of x-rays by crystal planes, showing that constructive interference occurs when the path difference of scattered rays equals an integer multiple of the wavelength.

2.  X-Rays are electromagnetic radiations with
wave lengths of the order of 0.1nm.
 X-rays are produced when electrons from a
heated filament strike the metal target.
 In 1912 physicist Max Von Laue discovered
that a crystalline solid , consisting as it does of
regular array of atoms ,might form a natural
three - dimensional diffraction grating for x-
rays.

3.  Question:
So if all electromagnetic radiation can diffract,
why are X-rays used in crystallography?
Ans….
 X-rays have wavelengths on the order of a few
angstroms (1 Angstrom = 0.1nm). This is the
typical inter-atomic distance in crystalline
solids, making X-rays the correct order of
magnitude for diffraction of atoms of
crystalline materials.

4.  A grating with d= wavelength is desirable for x-
ray diffraction.
 diffraction occurs when a wave encounters a
series of regularly spaced obstacles that are;
 Capable of scattering the wave.
 Have spacing that are comparable in magnitude
to the wavelength

5.  If a collimated beam of x-rays, is allowed to
fall on a crystal ,intense beams appear in certain
sharply defined directions.
 if these beams fall on a photographic film, they
form an assembly of Laue spots.
 fundamentally, the x-rays are diffracted by
electrons ,diffraction by nuclei being negligible
in most cases.

6.  thus the diffracting characteristics of a unit cell
depend on how the electron are distributed
throughout the volume of the unit cell.
 by studying the directions of diffracted x-ray
beams, we can learn the basic symmetry of the
crystal.
 and by studying intensities we can learn how
the electron are distributed in a unit cell.

7.  In 1914 W.H Bragg and W.L Bragg study the
atomic structure of crystal by using X-rays
 Consider the two parallel planes of atoms A-A´
And B-B‛ which are separated by interplanar
spacing d.
 Now assume that a parallel , monochromatic
beam of x-rays of wavelength ⋏ is incident on
these two planes at an angle ⏀.
 two rays in this beam , labeled 1 and 2 are
scattered by atoms P and Q.

8.  ray 2 covered some extra path as compared to
ray 1
 this extra path is called path difference .
 Constructive interference of scattered rays 1‘
and 2‘ at an angle ⏀ to the plane, if the path
difference between 1- P-1’ and 2-Q-2‘ ,is equal to
whole number , n , of wavelength;
 so

9.  n⋏=SQ+QT
 n⋏=d sin⏀+ d sin⏀
 n⋏=2d sin⏀
 this is known as Bragg’s law.