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

e21.ph.tum.de

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

11/12/2012

VL9, Physics with Neutrons I, Dec. 10, 2012


Bragg Cut-Offs in Fe (bcc) and Al (fcc)

2

1/v - law

black symbols: tabulated

gray symbols: measured

N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, and J. Banhart, Nucl. Instr. Methods A 605, 13 (2009).


3

primary extinction

Extinction

after: A. Furrer, J. Mesot and T. Strässle

secondary extinction powder

Attenuation:

I

d

I 0

e

d

• Bragg scattering reduces intensity

• Primary extinction: strong in perfect crystals:

neutrons mostly from surface region

• Secondary extinction: non-perfect crystals, scattering from grains

• Extinction usually unimportant in polycrystals [Be!]


Beryllium Filter: Cold Neutrons

4

l (Å)

Total cross section of

polycrystalline Be:

cut-off near E = 5.2 meV

l < 4 Å

l < 4 Å

l > 4 Å

T = 77 K

typically: l = 150 mm

l < 4 Å

l < 4 Å

b = 0.779 + 2.3110 -7 i 10 -12 cm


Graphite Filter (HOPG)

5

E = 13.9 meV

l = 2.43 Å

k i

T (barn)

HOPG (002)

l/2

1 10 100 E (meV)

Hexagonal crystal structure:

• lattice constants:

a = 2.4612 Å

c = 6.7079 Å

• Bragg peaks along c-direction:

(002), (004), (006), ...

• 1 st Bragg cut-off:

E = 1.818 meV

B.O. Loopstra, Nucl. Instr. and Meth. 44, 181 (1966).

b = 0.6648 + 1.3910 -7 i 10 -12 cm


Velocity Selector

6

ASTRIUM: Neutron velocity selector (3000 – 28‘300 rpm)


Debye-Waller Factor: P(T)-Function

7

T

P


T

1


2

/ T


0

xdx

1

x

e

T T

P 4


D

After: G. Busch and H. Schade, “Vorlesungen über Festkörperphysik”, p. 89, Birkhäuser Verlag Basel 1973.


Thermal Diffuse Scattering: Pyrolytic Graphite

8

Pyrolytic graphite: T-dependence of TDS

T = 77 K

T = 293 K

1 10 100

E (meV)

1 10 100

E (meV)

J. Bergsma and C. Van Dijk, Nucl. Instrum. Methods 51, 121 (1967).


Debye-Waller Factor: Aluminum/Lithium

Intensity

9

G. Pankow, Helv. Phys. Acta 9, 87 (1936)

lithium

90 K

293 K

aluminum

(fcc)

D = 428 K

periodic

T > 0 K

Bragg reflection:

zero phonon line

thermal diffuse scattering

Bragg angle


Emission of a Phonon

10

Q

k f

k i

Q

k i

k f

normal and

umklapp processes

scattering triangle

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