SANS%20investigation%20of%20materials%20for%20%20%20high-temperature%20applications

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Neutron Reflectometry

• measurement of the intensity reflected by a
  planar surface and/or interfaces
• neutrons at thermal energies incident on a
  surface at a grazing angle of less than 3
• at these small angles, the potential for
  scattering approximated by a continuous value
  called the scattering length density (SLD)

• sensitive to the difference of the refractive
  index (or contrast) across surfaces and
  interfaces gt
• near surface structure of materials

NG7 HORIZONTAL NEUTRON REFLECTOMETER (NIST)
The data measured as intensity versus wave-vector
transfer, Qz or Q? (difference between the final
(kf) and initial (ki) wave-vectors elastic
scattering assumed kfki When ?i ?f,
specular scattering used to determine the
structure of the material in the z-direction
(perpendicular to the surface)
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Specular Reflectivity (? ?i ?f)
Qz 4 p sin ?/?
Above the critical angle ?c for total reflection,
the data show finite-size fringes whose
separation are inversely related to the film
layer thickness After subtraction of the
off-specular background, these data can be fit
(or inverted) to obtain a real-space profile of
the scattering length density as a function of
depth.
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Off-Specular Reflectivity
information about the length scale of in-plane
structural correlations
For transverse-Qx scans (rocking curve), 2? is
held constant while ?i and ?f are varied equally
in opposite directions (?i ?f const).
Typically a narrow specular peak, evident at
Qx0, can be separated from the underlying
diffuse scattering which is broad. The width of
the diffuse peak is indirectly related to the
inverse of the coherence length ? of the in-plane
roughness.
Interpretation difficult gt the study of diffuse
scattering from rough surfaces has not made much
headway. The theory (Distorted Wave Born
Approximation) works in some cases only. gt Not
discussed in this introductory course
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Goal of reflectivity measurements to infer
a density profile perpendicular to a flat
interface
In general the results are not unique, but
independent knowledge of the system often makes
them very reliable Frequently, layer models are
used to fit the data Advantages of neutrons
include Contrast variation (using H and D, for
example) Low absorption probe buried
interfaces, solid/liquid interfaces etc
Non-destructive Sensitive to magnetism
Thickness length scale 10 5000 Å
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Three basic features of reflectivity data
(specular)
1) the critical wave-vector transfer. Neutrons
are totally reflected below. Given by SLD (for a
non-uniform layer roughly a function of the
average SLD). Important Below the critical
angle, neutrons are perfectly reflected from a
smooth surface This is NOT weak scattering and
the Born approximation is not applicable to this
case (neither near the critical angle)
The position of this transition to total
reflection yields information about the average
SLD of the material. The reflectivity away from
the total reflection angle holds information
about the change in scattering length density
with depth. It can be analyzed to determine a
film's total thickness, material composition,
periodicity, and even roughness.
2) second feature the decrease in reflectivity
with Qz which, for a smooth sample, becomes
proportional to Qz-4. If the surface is not
smooth, faster decrease is observed. 3) A thin
film can also show oscillations around the
continuously decreasing reflectivity the result
of an interference effect between the air/film
and film/substrate interfaces. The amplitude
proportional to the SLD difference between the
film and substrate (SLD contrast). An estimate
of the film's thickness given by the oscillation
period.
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Specular reflectivity

• The quantity measured in a neutron reflectometry
  experiment the intensity reflected from the
  surface
• To calculate the reflectivity of an interface
  the time-independent Schrödinger equation
• a solution for the wave function, ?, representing
  the neutron wave inside and outside of the
  reflecting sample.

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Theory for perfect surface
The neutron obeys Schrodinger's equation The
average potential inside the medium is Then in
vacuo where k0 is neutron wavevector in vacuo
and similarly k is the wavevector in a
material Since k/k0 n refractive index
(definition), and since ? is very small (10-6
Å-2 ) Since generally nlt1, neutrons are
externally reflected from most materials. The
surface cannot change the neutron velocity
parallel to the surface gt neutrons obey Snell's
Law Then
gtthe critical value of k0z for
total external reflection is
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Theory for perfect surface
Continuity of ? and derivative of ? at z 0
gt
and
? component perpendicular ? to the surface
gt reflectance
gt reflectivity
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perfect surface
neutron beam reflecting from a perfectly smooth
silicon substrate (surrounded by air). The
neutron scattering length density for Si is ?Si
2.07 x10-6 Å-2
reflectivity
solid curve the calculated reflectivity for the
interface (a) dashed curve a reflectivity curve
calculated using the Born approximation The
dynamical calculation in the region of Q? 0.1
Å-1 similar to that obtained by the Born
approximation (kinematical case) In the large
Q? regime, the decay of the curve scales as Q?-4
(Fresnel decay)
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Thin layer
More interesting and realistic cases involve
reflection from stratified media thin layer on
top of the substrate gt interference fringes
reflectivity
red curve surface of material with ?4.10-6 Å-2
green curve added thin layer with larger ? The
fringe spacing at large k0z is p/t (a 250 Å
film used) Ability to measure layer thickness
with high precision (3)
The critical edge for neutron reflectivity often
determined by the substrate and not the thin film
owing to the fact that a neutron beam is a highly
penetrating
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diffuse scattering is caused by surface
roughness or inhomogeneities in the reflecting
medium a smooth surface reflects radiation in a
single (specular) direction a rough surface
scatters in various directions
specular scattering is damped by surface
roughness treat as graded interface. For a
single surface with r.m.s roughness s
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Listing the information yielded by the
measurements
Measurement feature Information obtained from a sample of cm2 size
Position of critical edge, Qc Nuclear (chemical) composition of the neutron-optically thick part of the sample, often the substrate.
Intensity for Q lt Qc Unit reflectivity provides a means of normalization to an absolute scale.
Periodicity of the fringes Provides measurement of layer thickness. Thickness measurement with uncertainty of 3 is routinely achieved. Thickness measurement to less than 1 nm can be achieved.
Amplitude of the fringes Nuclear (chemical) contrast across an interface.
Attenuation of the reflectivity Roughness of an interface(s) or diffusion across an interface(s). Attenuation of the reflectivity provide usually establishes a lower limit (typically of order 1-2 nm) of the sensitivity of reflectometry to detect thin layers.
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Polarized neutron reflectometry
tool to investigate the magnetization profile
near the surfaces of crystals, thin films and
multilayers.

• applied to important problems such as
• the influence of frozen or pinned magnetization
  on the origin of exchange bias,
• the influence of exchange coupling on magnetic
  domain structures,
• the identification of spatially inhomogeneous
  magnetism in nanostructured systems.

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Polarized neutron reflectometry
Applications n Multilayers n Non colinear
magnetism n Interface magnetism Allows the study
of the magnetic configuration of a multilayer
system access to the magnetisation amplitude and
direction in each layer. n Determination of
in-depth magnetic profiles n Absolute measurement
of the magnetic moment in µB per f.u. (sum of the
spin and orbital moment) n But sensitivity only
to the in-plane moment. n Resolution of the order
of 0.1µB (better on simple systems) n No
sensitivity to the substrate para/dia-magnetism. n
No absorption, no phenomenological parameter,
absolute normalisation.
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Neutron Reflectivity Links
http//www.ncnr.nist.gov/instruments/ng1refl/Fitz.
pdf http//www.mrl.ucsb.edu/pynn/Lecture_4_Reflec
tivity.pdf http//pathfinder.neutron-eu.net/idb/m
ethods/reflectometry http//neutronreflectivity.ne
utron-eu.net/main/Lectures http//www.ncnr.nist.g
ov/programs/reflect/index.html http//www.ncnr.nis
t.gov/programs/reflect/NR_article/index.html http
//www.ncnr.nist.gov/programs/reflect/measurements/
reflweb1.pdf