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Jamie NoëlUniversity of Western Ontario, London, Ontario, Canada
Neutron Scattering and Reflectivity for Depth-Profiled Information
Introduction: The Neutron• A unique probe for materials and interfaces
• Discovered in 1932 by James Chadwick
• Mass = 1.009 amu (= 1.675 x 10-27kg)
• Charge = 0 Spin = ½ (polarizable, magnetism)
• Made of 3 charged quarks (2d+1u). 2(-1/3)+1(2/3) = 0
• Half-life (outside atomic nucleus) = 611 s
• Interacts with atomic nuclei via strong nuclear force
• Strength of interaction and direction (attractive/repulsive) are independent of atomic number (depend on properties of nucleus, differ with isotope)
Neutrons vs Photons
• Both treated with similar principles of “optics”
• Photons interact with electrons (Z-dependent), neutrons interact with the nucleus (not Z-dependent; see D very different from H)
• Photon speed 3 x 108 m/s, neutrons 2 x 103 m/s
• Photon energy eV (visible) to MeV (gamma); Thermal neutron energy ~27 meV (kBT): non-destructive
• Both refract, interfere, diffract, have a wavelength (λ= h/mv), can be absorbed, etc.
Neutron Sources
• Stored in atomic nuclei and released by fission or spallation
• Continuous or pulsed sources
Neutron Attenuation
Polarized Neutrons• To determine magnetic order in a sample we probe
it with polarized neutrons
• A polarized neutron beam is made by throwing away all neutrons whose spins are not parallel to the polarization vector we choose– Scattering filters
– Absorption filters
– Bragg reflection
– ‘Optical’ reflection
Neutron Techniques
• Radiography
• Diffraction (single crystal, powder, strain mapping)
• Spectrometry
• Small Angle Scattering (SANS)
• Reflectometry
• Cold Neutron Depth Profiling
Radiography: Take Advantage of Contrast
Neutron Diffraction
• Interatomic distances on the order of Å
• Ideally suited to X-rays, electrons and thermal neutrons
•Nobel Prize 1929 for “for his discovery of the
wave nature of electrons.”
Louis de Broglie1892-1987
Zeillinger et al, Rev. Mod. Phys. 60 (1988) 1067
Double slit diffraction of neutrons
Diffraction
Bragg’s Law: 2d sin θ = nλ
Crystal Structure Determination
• Single crystal diffraction gives specific diffracted beams in (θ,φ)
• Powder diffraction has grains in all orientations, resulting in conic solutions to scattering for each hkl
• Same analysis methods as used for X-ray diffraction
•Cartoon from: Neutron Scattering -A primer by Roger Pynn
Neutron Spectrometry
Inelastic Neutron Scattering
Nobel Prize: Bertram Brockhouse, Clifford Shull, 1994
‘for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter ’
Instruments
Triple-Axis Neutron Spectrometer
Small Angle Scattering (SANS)• Since scattering is a reciprocal space method, smaller
scattering vector yields information about larger structures
• Two ways to see smaller scattering vector: long wavelength (cold neutrons) or small angle (detector far from sample)
• SANS is a valuable tool for structural biophysics allowing in situ measurements of systems between 10 to 2000 Å
• Overall morphology can be obtained through model independent approach, while model-based analysis provides further details on various structural parameters
• Contrast variation (H2O/D2O) and specific labeling greatly enhances resolution of determined structures
SANS Setup
Neutron Reflectometry
Neutron Reflectometry
Surface analytical technique that measures specularly reflected neutrons.
The D3 Reflectometer SetupChalk River
Reflectivity Fundamentals•
Key parameter: “coherent bound neutron scattering length”, b
Reflectivity of an Interface
•
Where b(z) is the compositional:density depth profile we are seeking
Neutron Scattering Lengths and Cross Sections
Ti --- -3.438 --- 1.485 2.87 4.35 6.09
46Ti 8.2 4.93 0 3.05 0 3.05 0.59
47Ti 7.4 3.63 -3.5 1.66 1.5 3.2 1.7
48Ti 73.8 -6.08 0 4.65 0 4.65 7.84
49Ti 5.4 1.04 5.1 0.14 3.3 3.4 2.2
50Ti 5.2 6.18 0 4.8 0 4.8 0.179
O --- 5.803 --- 4.232 0.0008 4.232 0.00019
16O 99.762 5.803 0 4.232 0 4.232 0.0001
17O 0.038 5.78 0.18 4.2 0.004 4.2 0.236
18O 0.2 5.84 0 4.29 0 4.29 0.00016
Isotope Abund. Coh b Inc b Coh xs Inc xs Scatt xs Abs xs
H --- -3.7390 --- 1.7568 80.26 82.02 0.3326
1H 99.985 -3.7406 25.274 1.7583 80.27 82.03 0.3326
2H 0.015 6.671 4.04 5.592 2.05 7.64 0.000519
3H (12.32 a) 4.792 -1.04 2.89 0.14 3.03 0
(%) (fm) (fm) (barn) (barn) (barn) (barn)
Neutron Reflectometry
• Intensity profile of reflectivity yields composition of surface layers
• Interference pattern allows determination of layer thickness (0.5-300 nm)
• Non-destructive nature and ability to see hydrogen and buried interfaces are other rare qualities that make this an invaluable technique.
bQc 162
sin2d
What Do We Get from Neutron Reflectometry?
• Intensity profile of reflectivity yields composition of surface layers.
where Qc is the critical momentum transfer for total external reflection
• b may be + or – (e.g., bH = -3.7 fm, but bD = 6.7 fm).
• If b < 0, then Qc is imaginary (and therefore unobservable)
bQc 162
Element,
Compound, or
Functional Group
(Effective)
Coherent
Neutron
Scattering
Lengtha, b (fm)
Number
Densityb,
(Å-3)
SLD,
b (Å-2)
Si 4.1491 4.996 10-2 2.07 10-6
Ti -3.438 5.670 10-2 -1.95 10-6
O 5.803 N/A N/A
H -3.7390 N/A N/A
Na 3.63 N/A N/A
Cl 9.5770 N/A N/A
Fe 9.45 N/A N/A
H2O -1.675 3.343 10-2 -0.56 10-6 @ 20C
SiO2
(cristobalite)
15.7551 2.325 10-2 3.66 10-6
SiO2
(amorphous)
15.7551 2.205 10-2 3.47 10-6
SiO2 (quartz) 15.7551 2.666 10-2 4.20 10-6
TiO2 (rutile) 8.168 3.211 10-2 2.62 10-6
TiO2 (anatase) 8.168 2.894 10-2 2.40 10-6
TiO2 (brookite) 8.168 3.143 10-2 2.56 10-6
TiH2 -10.916 4.705 10-2 -5.14 10-6
What Else Can We Get from Neutron Reflectometry?• Difference in path lengths
of coherent neutron beam results in interference at the detector.
• Interference pattern allows determination of layer thickness (0.5-300 nm) using Bragg’s Law.
• Can see buried interfaces too.
Oxide
Si
Ti
Oxide
Si
Ti
a)
b)
sin2d
But How Do We Actually Get Sample Composition and Thickness?
• Raw data in momentum space are modeled to yield a real space profile.
• Model is proposed based on other knowledge, then refined by a least squares fitting process.
-1
0
1
2
3
4
5
6
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
Q (Å-1)
Log(
inte
nsity
)
Example: Ti Thin Film• Thin film of Ti deposited on Si single crystal substrate
– Si because it is very flat, transparent to neutrons
– Ti film ~ 50 nm thick (covered with a few nm of native oxide)
– Magnetron sputtering yields flat Ti film, uniform thickness
– Sample size ~ 100 mm Big, eh? Glancing angle = large beam footprint.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
Ti on Si slab through the Air - Stand Alone -Bckg corrected
Qz/A
-1
-- d/A Rho/A-2 ImRho/A-2 Sigma/AAir N/A 0 0 1TiO2 33.16 2.635E-6 0 9.298Ti 605.37 -1.838E-6 0 10.207SiO2 31.83 3.354E-6 4.056E-7 29.366Si N/A 2.073E-6 2.376E-11 14.37
0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
1E-6
1E-5
1E-4
1E-3
0.01
0.1
Ti on Si slab through the Si - Stand Alone -Bckg corrected
Qz/A-1
-- d/A Rho/A-2 ImRho/A-2 Sigma/ASi N/A 2.073E-6 5.711E-11 1SiO2 32.02 3.35E-6 0 12.129Ti 602.6 -1.824E-6 0 29.512TiO2 36.29 2.634E-6 1.93E-6 10.06Air N/A 0 0 10.926
Neutrons incident from air Neutrons incident from Si
Refle
ctiv
ity
Refle
ctiv
ity
In Situ Reflectometry Example
D. Wiesler and C. Majkrzak, Physica B: Condensed Matter Volume 198, Issues 1-3, 1 April 1994, Pages 181-186
•Oxide-covered Ti film in sulphuric acid for 2 days
•Oxide becomes hydrated and thins
•Metal also thins and eventually corrodes away
•Corrosion rate of a few Å/h measured directly!
Approach
• Neutron reflectometry is easily performed in situ with samples in various environments, including electrodes in solution under electrochemical control.
• We used a combination of electrochemical techniques and neutron reflectometry to probe anodic oxide film growth on Ti and then hydrogen absorption by cathodically polarized Ti.
Sample Preparation
•Sample must be flat, uniform, LARGE
Example: Electrochemical Behaviours of Ti and Zr
P-doped Si slab
Ti film
Pt electrode
glas
s
NaCl soln
PotentiostatWE CE RE
SCE
neutrons
glass
In situ reflectometry. Neutrons enter from the back.
Electrochemical Cell
Experimental
• Pure Zr or Pure Ti film, 500 Å• Sputtered on 4” Si slab• Zr 0.1 mol/L Na2SO4 | Ti 0.27 mol/L NaCl
• Neutral pH, Argon deaerated• SCE reference• Neutron scans on dry sample, then in cell at
Eoc and under potentiostatic control at a series of more positive potentials.
• EIS recorded during neutron scans.
Real Space Profiles –Ti Film
• As-prepared film on Si in air, with 461 Å of Ti metal and 47 Å of rutile-like oxide
• Note the negative SLD of Ti
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600 700 800
Depth (Å)
Scat
terin
g le
ngth
den
sity
b
× 10
6 (Å
-2)
Si
Ti
oxide
air
0.05 0.10 0.15
1E-5
1E-4
1E-3
0.01
0.1
1
0 100 200 300 400 500 6000.0
1.0x10-6
2.0x10-6
3.0x10-6
4.0x10-6
5.0x10-6
SLD (A-2)
Z (A)
Qz (Å-1)
Zr Film with Native Oxide•R
efle
ctiv
ity
Si
SiO2Zr
ZrO2
Air
•Raw Data (red circles)•Fitted Model (black curve)
•Real Space Profile•with layer compositions indicated
As-prepared Zr film in air, neutrons from Si side
Layer Thickness (Å)
SiO2 49
Zr 444
ZrO2 53
Anodic Film Growth
•As prepared, in air.•461 Å of Ti Metal•47 Å of rutile-like oxide
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600 700 800
Depth (Å)
Scat
terin
g le
ngth
den
sity
b
× 10
6 (Å
-2)
Si
Ti
oxide
air
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
De n
sity
, pb
x 10
^ 6 (Å
²)
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
De n
sity
, pb
x 10
^ 6 (Å
²)
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
De n
sity
, pb
x 10
^ 6 (Å
²)
Eoc
E = +1 V
E = +3 V
Titanium Zirconium
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600 700 800
Depth (Å)
Sca
tterin
g le
ngth
den
sity
b
× 10
6 (Å
-2)
Open-circuit
Anodized to 2V
No change upon immersion at Eoc.Upon anodization to 2 V:Metal thins (38Å), oxide thickens (65 Å).PB = 1.72
Bilayer oxide formed.
No change upon immersion at Eoc.Upon anodization:PB = 1.52-1.63 Metal and oxide SLDs decrease, but oxide does not form bilayer. Cracks?
Anodic Film Thickness
-1 0 1 2 3 4 5Potential (V vs. SCE)
0
50
100
150
Oxi
de T
hick
n ess
( Å)
-1 0 1 2 3 4Potential (V vs. SCE)
40
60
80
100
120
140
160
180
Oxi
de L
aye r
Thi
c kne
s s (Å
)-1 0 1 2 3 4
Potential (V vs. SCE)
40
60
80
100
120
140
160
180
Oxi
de L
aye r
Thi
c kne
s s (Å
)
Titanium Zirconium
= 25 Å/V = 34 Å/V
• Z as a function of the sinusoidal frequency is modeled using electrical equivalent circuits consisting of passive circuit elements (resistors, capacitors, etc.)
• Sinusoidal potential input yields phase-shifted sinusoidal current output
• Impedance (Z) is obtained using expression analogous to Ohm’s Law
( ) sin( )( ) sin( )o
E t tZ ZI t t
Input potential Output
current
ior E
Electrochemical Impedance Spectroscopy
Electrochemical Impedance Spectroscopy Modeling
Rs R film
C film
Simple equivalent circuit with one time constant fit EIS spectra from anodically polarized Ti and Zr.
Constant phase element accounts for non-ideal capacitance.
Anodic Film ResistanceTitanium Zirconium
-1 0 1 2 3 4Potential (V vs. SCE)
0
1
2
3
4
5
6
7
8
9
10
Film
Re s
ista
n ce
(MO
hms·
cm²)
6000 ·cm²
-1 0 1 2 3 4 5Potential (V vs. SCE)
0
5
10
15
20
25
Film
Res
ista
n ce
(MO
hm·c
m²)
8000 ·cm²
Specific ResistivityTitanium Zirconium
-1 0 1 2 3 4 5Potential (V vs. SCE)
0
10
20
30
40
50
Spe
cific
Res
istiv
ity (T
Oh m
s·cm
)
-1 0 1 2 3 4Potential (V vs. SCE)
0
2
4
6
8
10
12
Spec
ific
Res
i stiv
ity (T
Oh m
s·cm
)
Band Bending During Polarization
Film CapacitanceTitanium Zirconium
-1 0 1 2 3 4Potential (V vs. SCE)
1
2
3
4
5
6
7
Film
Cap
a cita
n ce
(µF/
cm²)
-1 0 1 2 3 4 5Potential (V vs. SCE)
0
5
10
15
20
Cap
acita
nce
(µF /
cm² )
p
Dielectric Constant
Titanium Zirconium
-1 0 1 2 3 4Potential (V vs. SCE)
30
35
40
45
50
App
aren
t Die
lect
ric C
onst
ant
Cd
-1 0 1 2 3 4 5Potential (V vs. SCE)
0
20
40
60
80
100
Die
lect
ric C
ons t
ant
Reflectivity Profiles During Cathodic Polarization
TitaniumZirconium
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600 700 800
Scat
terin
g le
ngth
den
sity
b
× 10
6 (Å
-2)
Depth (Å)
0 volt
-1.4 volt
b(Ti) beforeanodization
b(Ti) at +2Vanodization potential
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
Den
sit y
, pb
x 10
^ 6 (Å
²
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
Den
sit y
, pb
x 10
^ 6 (Å
²
0 200 400 600 800Depth (Å)
-1
0
1
2
3
4
5
6
Sca
tterin
g Le
n gth
Den
sit y
, pb
x 10
^ 6 (Å
²
+3 V, -1 V, -2.5 V
-2
-1
0
1
2
3
0 200 400 600 800-2
-1
0
1
2
3
0 200 400 600 800
-2
-1
0
1
2
3
0 200 400 600 800
Sca
tterin
g le
ngth
den
sity
b
× 10
6 (Å
-2)
Depth (Å)
-2
-1
0
1
2
3
0 200 400 600 800
0 V -0.4V
-0.8V -1.2V
Cathodic EIS on Zirconium
10- 3 10-2 10-1 100 101 102 103 104 105102
103
104
105
Frequency (Hz)
|Z|
-1 V-1.5 V-2 V-2.5 V
10- 3 10-2 10-1 100 101 102 103 104 105
-100
-50
0
50
Frequency (Hz)
thet
a
•Impedance decreases significantly with decreasing applied potential.
•Band bending makes oxide degenerate conductor.
Band Bending in Zirconium
Conclusions
• Two-layer anodic film
• Outer film incorporates hydrogen/water.
• Pilling-Bedworth Ratio = 1.72
• Anodization Ratio = 25 Å/V.
• Metal seems to absorb oxygenduring anodization.
• Single-layer film.
• Hydrogen/ water distributed uniformly across oxide. Cracks?
• Pilling-Bedworth Ratio = 1.52 to 1.63
• Anodization Ratio = 34 Å/V.
• Metal seems to absorb hydrogenduring anodization.
Titanium Zirconium
• Hydrogen absorption into oxide, then metal, under cathodic polarization
• Film properties consistent up to 4 V or more. Band bending yields lower resistance at high E.
• No hydrogen absorption under cathodic polarization
• Film properties improve up to 1 V, decline at higher E Evidence: resistance, resistivity, impedance response, dielectric constant, anodic current, corrosion.
ConclusionsTitanium Zirconium
Hydrogen Absorption into Ti• Unanodized Ti
film in 0.27 M NaCl (in D2O)
• Polarized to successively lower E, held for ~16 h.
• Sudden jump in H content between -300 mV and -400 mV, and again between -600 mV and -650 mV, consistent with previous results (Shibata and Zhu, Noël, Zeng).
Hydrogen Content
4 at.%
9 at.%
Metal Layer Thickness Changes
-100 0 100 200 300 400 500 600
0.0
1.0x10-6
2.0x10-6
3.0x10-6
4.0x10-6
5.0x10-6
pH = 5.6 E = -1.6 VSCE
pH = 3 E = -1.6 VSCE
pH = 2 E = -1.6 VSCE
pH = 2 E = Eoc = 0.03 VSCE
SLD
(Å-2)
z (Å)
pH Effect on H Absorption into Zr
56
Metal and oxide SLD values decreased as pH decreased under -1.6 V polarization, but rebounded significantly at pH 2 after applied polarization was halted.
Layer thickness values did not change.
H entry
Layer Thickness (Å)SiO2 49Zr 444
ZrO2 53
Cold Neutron Depth ProfilingUses cold neutrons to generate alpha-particles via nuclear reaction: e.g. 17O + n + 14C
Energy loss of indicates escape depth from surface.
Can use 17O oxide as a tracer layer to track oxygen atom movements during oxide film growth.
Particle Detectors
Beam Stop
Vacuum Chamber
Sample
Cold Neutron
Guide TubeNeutron Monitor
Independent of Chemical State and Ionization
Good Depth Resolution (nm)
Quantitative
Variable Sample Size & Shape &
Topography
Near – Surface Analysis (a few m)
NondestructiveNDP
Metrological Attributes of NDP
0
5
10
15
20
25
697 801 905 1010 1114 1219 1323 1427 1532 1636 1741Energy (keV)
coun
tTi film with 17O oxide (anodized to ~4V)
from B(6%)
from B(94%)
from OLi from B(94%)
Li from B(6%)
10B(n,)7Li
Neutron-Alpha Reactions Limited to Certain Isotopes
R.G. Downing, G.P. Lamaze, and J.K. Langland, J. Res. Natl. Inst. Stand. Technol. 98 (1993) 109.
Accessing Neutrons• In Canada, Canadian Neutron Beam Centre,
NRU Reactor, Chalk River, Ontario.
• Access on basis of peer-reviewed proposal.
C2 High Resolution Powder DiffractometerC5 Polarized Beam Triple-Axis SpectrometerD3 ReflectometerE3 Triple-axis SpectrometerL3 Stress-Scanning DiffractometerN5 Triple-Axis SpectrometerT3 Image-Plate Diffractometer
Apply for beam time http://www.cins.ca/beam.html
Accessing Neutrons• Access and help are free if you publish
• Travel support available for students
• You work with an instrument scientist who knows neutron physics and how to operate the machine –you bring samples, a problem to answer and your expertise. Analyze dataand write paper together.
• Ancillary equipment/facilities available (labs, cells, cryostats, magnets, heaters, etc.)
• International labs also accessible
Acknowledgement
Zin Tun and the staff at CNBC, Chalk River
Greg Downing, NIST, Gaithersburg