Physics with Neutrons WS 2012/2013 - E21 - Technische Universität ...

Physics with Neutrons
WS 2012/2013
Peter Böni
Physik-Department E21
Technische Universität München
D-85748 Garching
E-mail:Peter.boeni@frm2.tum.de
Web: www.e21.ph.tum.de
https://campus.tum.de/tumonline/lv.detailclvnr=950011566
03/12/2012
VL7, Physics with Neutrons I, Nov. 26, 2012

Equivalence: Ewald‘s Construction – Bragg‘s Law
2
Q = G k
2k
i
sinq
B
G
hkl
2q B

Miller-Indices: Example (121)
3
(m n p) = (1 2 1) (1 ½ 1) (h k l) = (2 1 2)
inversion
make it integer again

Structure Faktor of the Body Centered Cubic Lattice
4
F hkl = 2b, if h + k + l = even
F hkl = 0,
if h + k + l = odd
bcc: plane with l = 0
interferes to 0
allowed

Neutron Diffraction from Cr (bcc)
5
rocking
scan
q/2q
scan
interferes to 0
allowed
magnetic peak
l = 0 plane
higher
order
d = 2p/a

Diffraction Patterns of Important Materials
6
fcc:
intensity for (h k l)
either all even or all
odd
hcp: graphite
excellent
monochromator
(Clinton Pile: see
next viewgraphs)
diamond:
(222) not visible
excellent monochromator
E. O. Wollan and C. G. Shull, Phys. Rev. 73, 830 (1948)

Clinton Pile (Nov. 4 1943, ORNL)
7

8
Diffraction at the Clinton Pile
collimation
pile shield
paraffin
lead
NaCl
(200)
powder
sample
2d
hkl
sinq
B
n
E i = 70 meV
monochromator
E. O. Wollan and C. G. Shull, Phys. Rev. 73, 830 (1948)

9
k i
k f
Bragg-Brentano Method: Principle
surface of
sphere with
|Q| = |G k |
Setup of diffractometer:
defines Q

Bragg-Brentano Method: Information
10
information on lattice constant
(chemical homogeneity, stressstrain)
information on distribution
of mono crystalline grains
(“rocking curve”, w-scan)

Single Crystal Diffractometer TriCS @ PSI
11
Ge monochromator
rocking curve: EuS
Euler cradle at sample position
http://trics.web.psi.ch/
at FRM II: RESI (thermal), HEIDI (hot)

12
Laue-Method
k f
k f
2dhkl
sinq B
reciprocal lattice
points within shaded
area are visible
image
plate
single
crystal
2q B
k i
white neutron
beam
Applications:
• small samples
• rapid chemical
crystallography
• very efficient

Laue Diffraction from a Quasi Crystal
13
10 9
1
8
2
7
3
6
4 5

Laue Diffraction from Lysozym
14
http://en.wikipedia.org/wiki/Lysozyme