Lessons and Lectures on Diffraction or ti si m t c h con o rs le ( m d fr fi ref m e o g n s s fro b ction fr spacin ctio red a plane er y ction ma refle d be conside om (200) or d’ refle es of efle ng der h -t r ci der lan 2nd or n er spa f ord a first-or nk nl) p an n fr o f Meaning h o le planes c reflectio -t nes xamp n n pla as (nh

1. Lecture on Diffraction

2. In 1812, von Laue postulated that if
crystals were composed of regularly
spaced atoms which might act as
scattering centers for x-rays
(considered to be EM radiation of
wavelength roughly the same as the
interatomic spacing between crystal
planes), then it should be possible to
diffract x-rays using crystals

3. X-rays diffracted by the crystal (copper
sulfate) to form a pattern of spots on a
photographic plate
W.H. Bragg and W.L. Bragg successfully
analyzed the results of the Laue
experiment and came up with the
mathematical equation for the condition
for diffraction

4. Consider a beam of x-rays
Assume it is plane-polarized such that
the electric field vector E is always in
one plane
Consider that the beam has two ray
components which are in phase, each
having half the amplitude of the beam

5. Wave front – surface perpendicular to
the direction of wave propagation
A path difference between the
components will introduce a possible
phase difference
Phase difference produces a change in
amplitude of the resultant wave

6. Two rays are completely in phase
whenever their path lengths differ
either by zero or by a whole number of
wavelengths
A diffracted beam is composed of a
large number of scattered rays mutually
reinforcing one another

7. Diffraction is essentially a scattering
phenomenon
Condition for diffraction given by Bragg
law first formulated by W.L. Bragg
n λ = 2 d’ sin θ

8. n = order of reflection
n is also the number of wavelengths in
the path difference between rays
scattered by adjacent planes

9. Diffracted beam is rather strong
compared to the sum of all rays
scattered in the same direction but
extremely weak compared to the
incident beam
Atoms in a crystal scatter only a small
fraction of the energy incident on them

10. Scattering Modes
1. By atoms arranged randomly in space, as in
a monatomic gas occurs in all directions
and weak
2. By atoms arranged periodically in space as
in a perfect crystal
a) In a very few directions (diffraction)
Amplitudes add
b) In most directions (not satisfying Bragg
law), scattered rays cancel one another

11. Fundamental differences between
diffraction and reflection
1. Diffracted beam from a crystal is made up of
rays scattered by all the atoms of the crystal
which lie in the path of the incident beam
reflection takes place in a thin surface layer
only
2. Diffraction of monochromatic x-rays takes
place only at angles of incidence satisfying
Bragg’s Law reflection of visible light takes
place at any angle of incidence

12. Fundamental differences between
diffraction and reflection
3. reflection of visible light by a good
mirror is almost a hundred percent
efficient diffraction is very inefficient
process

13. λ = 2 (d’/n) sin θ
Let d = d’/n
λ = 2 d sin θ

14. Meaning of n-th order reflection
An n-th order reflection from (hkl)
planes of spacing d’ may be considered
as a first-order reflection from the
(nh nk nl) planes of spacing d = d’/n
Example 2nd order reflection from (100)
planes can be considered as first order
reflection from (200) planes