Transcript Chapter 7
VII. Bragg’s law
7-1. Bragg’s law
When the total path difference 2d sin
equals to n , diffraction occurs.
n: order of
Bragg’s Law: 2d sin n
reflection
The Bragg’s equation can be rewritten as
d
2 sin
n
1 2 3
Therefore,
d
2 sin 2d hkl sin
n
7-2. Ewald sphere construction
k : the wave number of the incident beam
k ' : the wave number of the outgoing beam
' 2
kk k
'
k
' k
Define S
; S
2
2
' *
S S Ghkl
Proof:
'
(i) S S 2 S sin
'
k
2
sin
S S 2
sin 2
sin 2
2
2
2d hkl sin
2
sin
1
d hkl
'
*
sin
1
S S 2
Ghkl
d hkl
'
(ii) S S is parallel to (h, k, l) plane normal
' *
S S // Ghkl
Therefore,
' *
S S Ghkl
'
*
k k 2Ghkl
7-3. Ewald Sphere
1
The reciprocal lattice is derived from the
crystal structure
Diffraction occurs at
' *
S S Ghkl
'
*
k k 2Ghkl
Ewald Sphere
''
S
2 B2
S
2 B1
'
S
S
''
S
S
Diffraction condition
'
S
S
1/
'
'' 1
S S S
*
S Ghkl