How do you obtain the diffraction pattern for a crystalline substance ?

Explanation

Diffraction of electromagnetic radiation takes place when a beam of light is scattered by an object containing regularly spaced lines (or ) points . This scattering phenomenon can happen only if the spacing between the lines (or) points is comparable to the wave length of the radiation .
`to ` From the following figure diffraction is due to interface between two waves passing through the same region of space at the same time .
`to` If the waves are in phase , peak to peak and trough to trough , the interference is constructive and the combined wave is increased intensity .
`to` If the waves are out of phase , the interference to destructive interference and the wave is cancelled .
`to` Constructive interference gives rise to intense spots observed on Laue's photographic plate , while destructive interference causes the surrounding high areas .

Derivation of Bragg's equation : When X- rays are incident on the crystal or plane , they are diffracted from the lattice points (lattice points may be atoms or ions or molecules) . In the crystal or plane , they are diffracted from the lattice points (lattice points may be atoms or ions or molecules) . In crystal the lattice points are arranged in regular pattern . When the waves are diffracted from these points , the waves may be constructive or destructive interference .
The `1^(st)` and `2^(nd)` waves reach the crystal surface .
They undergo constructive interference . Then from the figure `1^(st)` and `2^(nd)` rays are parallel ways . So , they travel the same distance till the wave front AD . The second ray travels more than the first by an extra distance (DB + BC) after crossing the grating for it to interfere with the first ray in a constructive manner . Then only they can be in the same phase with one another . If the two waves are to be in phase , the path difference between the two ways must be equal to the wavelength `(lambda)` or integral multiple of it `(n lambda` , where n = 1 , 2 , 3 ....)
(i.e.,) `n lambda = (DB + BC) " "` [where n = order of diffraction ]

`theta `= angle of incident beam ,
d = distance between the planes
`DB = BC = d sin theta`
`(DB + BC) = 2 d sin theta`
`n lambda = 2 d sin theta ` This relation is known as Bragg's equation .