Principle. THE Bragg’s method for study of the internal structure of crystals is based upon. Bragg’s equation (put forward by W.L. Brag in 1919) which mats be derived as follows.

A crystal mat be considered to be made up of a number of parallel equidistant atomic planes, as represented by the lines XX’, YY’, ZZ’ etc. in suppose a beam of X-rays is incident on tarsal at angle . A part of the beam, e.g., the ray AB is reflected at the point Belong the path BC. On the other hand some rays like DE, GH, etc. penetrate into the crystal and are reflected by the atoms present in the atomic plans  YY’, ZZ’, etc as shown in below :


Evidently ,a compared to the ray AB, a ray like DE has travel a longer Bk are perpendiculars drawn on the lines DE and EF respectively. The reflected bents like BC, EF, etc., then undergo interference with each other, If these reflected rays are in phase (i.e. n the reflected rays, crests fall over the crests and troughs over the troughs), they reinforce into each other and the intercity of the reflected rats is maximum. On the other hand, if the reflected rats of the reflected rats is maximum. On the other had, if the reflected rats are out of phase (i.e. crests fall over the through), the intensity of the reflected beam is very sow. If photographic plate is placed to receive the reflected rays, diffraction pattern is obtained.

It s obvious that in order that the reflected rays BC and EF may be in phase, the extra distance JEK traversed by the ray DE should be an integral multiple of the wavelength  of the X – rays, i.e.,

Distance

Where n is an integer, i.e. 1,2,3,4, etc. If d is the distance between the successive atomic planes, it is obvious form fig that
So that
                             
Putting this value in equation , we get
                            
This equation is called Bragg’s equation.