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
kk 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  2Ghkl
7-3. Ewald Sphere
1

The reciprocal lattice is derived from the
crystal structure
Diffraction occurs at
'   *
S  S  Ghkl
' 
*
k  k  2Ghkl
Ewald Sphere
 ''
S
2 B2

S
2 B1
'
S

S
 ''
S

S

Diffraction condition
'
S

S
1/
 '
 '' 1
S S S 
 *
S  Ghkl