neutron reflectivity (2)

7/29/2019 Neutron Reflectivity (2)

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Neutron reflectivity

As in the case of electromagnetic waves, the wave vector of neutrons inside amaterial is , where is the wave vector in vacuum and is the index ofrefraction (see manuscript on X-ray reflectivity). Again in analogy to X-rays,

can be written as

nk k nn

2

21 1

bn

k

=

where is the number density of the nuclei and b is the average (coherent)

scattering length of the material. For natural nickel, consisting of

, and58 60 61 62 64Ni68% , 26% , 1% , 4% , 1%andNi Ni Ni Ni 28 39 10 m = 15

10.3 10b m= , so that . This is the same order ofmagnitude as for x-rays. The only qualitative difference is that for some isotopes

such as natural

5~3.7 10 5for

( )153.4 10Ti b m= or pure ( )62 158.7 10Ni b m= , thescattering length is negative, so that . This has important consequences forthe reflection of neutrons from interfaces:

1n >

1n< 1n >

vacuum

material

total external reflection

for 1cosC n

< =

no total externalreflection;total internal reflection for

1cosC n

< =

If ,1n

iik r

i e

JJK

K

ri k rr e

JJK

K

x

ztik r

t eJJK

K

1


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boundary conditions at interface ( )0z = :

&

ix rx tx

i r t

i triz i iz r tz t

iz txr

i iz tz

k k k

d ddk k k

dz dz dzk k

k k

= =

+ =

+ = =

=

+

c

d

e

d e

From here, the derivation proceeds precisely as in the case of the Fresnelreflectivity for x-rays, where we had found the following result:

1

2

r

i

R

=

22 2

4

16~

bR

Q

CQ 2 2 siniz iQ k k= =

An interesting and powerful tool available for research using neutron (but notx-ray) reflectivity is contrast matching by isotope substitution. For instance, it

is possible to change the ratio of hydrogen and deuterium in water such that theindex of refraction is precisely equal to 1 (null water):

http://physchem.ox.ac.uk/~rkt/techniques/nrmain.html

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http://physchem.ox.ac.uk/~rkt/techniques/nrmain.htmlhttp://physchem.ox.ac.uk/~rkt/techniques/nrmain.html


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This effect is very useful in research on biological materials. For instance, theneutron reflectivity of a lipid membrane on null water is entirely determined bythe lipid, with no contribution from the water. By adjusting the ratio of theorganic tail groups of the lipid molecules as well, one can selectively study theproperties of the headgroups.

/H D

Neutron reflectivity in biology:

http://cell.e22.physik.tu-muenchen.de/research/sackmann.htm

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http://cell.e22.physik.tu-muenchen.de/research/sackmann.htmhttp://cell.e22.physik.tu-muenchen.de/research/sackmann.htm


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Total external reflection of neutrons from surfaces is also the operating principleofneutron mirrors. Since the core of a research reactor has to be protected byheavy concrete against impacts from the outside world (e.g. airplane crashes)and vice versa, there is not much room for neutron scattering instruments in theconfinement building housing the core. One therefore uses neutron guides

coated with neutron mirrors to guide the neutrons outside the confinementbuilding into a much larger guide hall built from standard building materials.

neutron mirror

FRM-II Research Reactor

Atomic Egg Neutron Guide HallExperimentalHall inside the

Reactor

EasternExperimental

Hall

4


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Since the critical angle decreases with decreasing neutron wavelength , thisworks best for cold neutrons with sub-thermal energies and wavelength

.12

Recently, so-called supermirrors with larger critical angles were developed.

They consist of multilayers of elements such as and Ti which are chemicallysimilar, but whose indices of refraction are very different:

Ni

Supermirrors

http://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdf

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http://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdf


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If one chooses the layer sequence judiciously, Bragg reflections from amultilayer can extend the effective critical angle by up to a factor of 4 comparedto pure :

/Ni Ti

Ni

Bragg peaks

c(Ni)=0.099(/) () c(mirror)=mc(Ni)

http://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdf

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http://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdfhttp://www.sns.gov/users/instrument_systems/pdfs/optical/new/OCT-Presentation-Analysisofsupermirrordesign.pdf

neutron reflectivity (2)

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