This is the famous BRAGGS’ EQUATION nƛ = 2d sine ø
This explains why the cleavage faces of crystals appear to reflect x-ray beams at certain angles of incidence(theta) the variable d is the distance between atomic layers in a crystal and the variable lambda () the wave length of the incident x-ray beam. The rays of the incident beam are always in phase and parallel up to the at which the top beam strikes the top layer at atom “z”. The second beam continues to the next layer where it is scattered by atom “B”. The second beam must travel an extra distance of AB+BC if the two beams are to continue travelling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (ƛ) for the phases of the two beams to be the same.
n=AB+BC
recognizing “d” as the hypotenuse of the right-angled triangle ABZ we can use trigonometry to relate “d” and to the distance AB is opposite to theta
As sin theta is opposite side by hypotenuse
The equation can be written as
Sine theta = AB/d
AB = d sine theta
Because AB=BC the equation n= AB+BC becomes
n= 2AB. Substituting in the equation AB = d sine theta
n= 2d sine theta
substituting ƛ in the equation above we get the famous BRAGGS’ EQUATION
nƛ = 2d sine ø
K.A.BALASUBRAMANIAN
Ph.D.(IARI NEW DELHI) Ph.D.(LONDON) D.I.C.(LONDON)
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