Bragg's law

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1. BRAGG’S LAW M FACTS
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2. BRAGG’S LAW M FACTS
INTRODUCTION
Bragg’s Law was introduced by Sir W. H. Bragg and his son Sir W. L. Bragg.
In physics, it is a special case of Laue Diffraction and gives the angle of coherent
and incoherent scattering from a crystal lattice.
The law correlates the X –ray wavelength λ, interplanerspacing d , and
reflection angle θ.
According to the law, when the x-ray is incident on to a crystal surface, its angle
of incidence will reflect back with a same angle of scattering.

3. BRAGG’S LAW
Bragg’s Law means that diffraction can occur only when the following
equation is satisfied:
where
n is a positive integer,
λis the wavelength of the X-ray ,
d is the distance between the lattice planes ,
θis the incident angle.
ais lattice parameter.
M FACTS
nλ= 2d sinθ2 2 2
Cubic crystal
hkl
a
d
h k l



4. BRAGG’S LAW M FACTS
ThemostsignificantpointoftheBragg’sLawcanbeexplainedbythe
constructiveinterference,whichoccurswhenthepathdifferenceoftravelling
wavesmatcheswiththeintegralmultiplicationofthewavelength.
BRAGG’SCONDITION:
TheBragg’sLawdoesnotonlymeantheconstructiveinterferenceofBragg’s
equation,butithasmuchmorestrictmeaning.
Diffractionwillneveroccur,ifBragg’sequationisnotsatisfied,incaseof
infinitelylargenumberoflatticeplanes.
Inotherwords,diffractionmaybeobserved,evenifthesituationisslightly
deviatedfromthecondition,incaseoffinitenumberoflatticeplanes.

5. BRAGG’S LAW M FACTS
sin θ= x/ d
hkl
=> x = d
hklsinθ
Path difference ∆ = 2x => phase shift
Constructive interference if ∆ = nλ
This gives the criterion for constructive
interference =>
∆ = 2d
hklsinθ= nλ
Bragg’s Law tells at which angle θ
Bto expect maximum diffracted intensity for a
particular family of crystal planes .For large crystals, all other angles give zero
intensity.
DERIVATION OF BRAGG’S LAW

6. BRAGG’S LAW
Three geometrical facts are worth remembering:
1)The incident beam, the normal to the diffraction plane, and the diffracted beam are
always coplanar.
2) The angle between the diffracted beam and the transmitted beam is always 2θ.This
is known as the diffraction angle.
3) θ is angle of incidence known as Bragg’s angle.
Bragg’s equation is a negative law
If Bragg’s eq. is NOT satisfied NO reflection can occur
If Bragg’s eq. is satisfied reflection MAY occur
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