Laue equations and reciprocal lattice

1
Laue equations and reciprocal lattice
2
Laue camera
SiGe
forward reflexion photo (spots on ellipses)
Unfiltered X-radiation through collimator
back reflexion photo (spots on hyperbolas)
3
Rotating crystal
axis of rotationcrystal axis
unwrapped film
r
g2
monochromatic X-ray
beam trap
film held against inside wall of cylinder
4
Powder method
r
unwrapped film
Lack of orientation make crystal structure
determination difficult
5
Powder method
gradient(l/2a)2
Slide paper until matched
6
Powder method
3
0
1
2
5
4
6
7
9
14
15
8
12
13
16
11
10





simple cubic
BCC
hkleven
110
200
211
220
222
321
310
FCC
all even or all odd
311
200
111
220
222
400
all odd even when hkl4n
diamond
111
220
311
400
7,15,23,28,31. m2(8n-1) can not be expressed as
h2 k2 l2 useful gaps in sequence
7
Electron and Neutron diffraction
Electron diffraction
Neutron diffraction

• Weak interaction with
• charged particles, but strong
• interaction with magnetic nuclei
• and electronic magnetisation
• Wavelength of the neutron l(Å)
• 0.28/ÖEe(eV), l1Å for Ee0.08eV
• (lh/p, Eep2/2M)

• Suitable for study only thin films
• and crystals, surfaces because
• of strong interaction of the electrons
• with atoms and electrons in
• solids
• LEED Low Energy Elastic Diffraction
• probes structure of 2D surface of solids.
• Surface should be free of absorbed atoms
• Wavelength of the electron l(Å)
• 12/ÖEe(eV), l1Å for Ee150eV
• (lh/p, Eep2/2m)

Fe
70o
30o
50o