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