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

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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

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