Sung-Min Choi

NCNR Summer School

Neutron Small Angle Scattering andReflectometry from Submicron Structures

June 5 - 9 2000

SANS Experimental Methods

• Procedure of SANS Measurements- From the initial planning

to SANS data in absolute scale - Sample preparation- What to measure

• Further consideration- Effects of Q-resolution- Multiple Scattering

• Summary

Outline

1) Initial planning

2) Sample preparation

3) Setup proper SANS configurations

4) Sample scattering

5) Additional measurements for correction

6) Absolute scaling

Procedure of SANS measurements

• What information do I want to measure ?

• Is it accessible with SANS ?- Length scale of interest (~10 Å - ~5000 Å) - Sample size- Neutron scattering contrast- Sample environment

(Temperature, Pressure, Magnetic field and etc.)- How long would it take ?

• Use NCNR Web based tools

• Consultation with SANS staff members

dΣ(Q)dΩ

sample

Initial Planning

• SANS can handle various forms of samples.Liquid, Gel, and Solid

• How much sample do I need ?- Depends on sample- Neutron transmission

• Prepare proper neutron contrast

• Standard SANS sample cell

• Custom made sample cell

0.1 ~ 10 mm

1.0 ~ 2.5 cm (beam diameter)

Sample Preparation

Typical size

d1) Transmitted beam, IIncident beam, Io

2) Coherent Scattering

4) Absorption

5) Multiple Coherent Scattering

3) Incoherent Scattering

T =IIo

= exp(−ΣTd) Σ T = Σ coh + Σ inc + Σ abs• Transmission where

• Scattered Intensity Is ∝ d T dΣcoh

dΩ

∝ d exp −ΣTd( )

What Should Sample Thickness Be?

• To decide the sample thickness, we need to understand what is happeningin the sample

Is

d

d = 1/ ΣT

d exp −ΣTd( )• Is is maximum

when d = 1/ ΣT

• When ΣT ≈ Σcoh d = 1/ ΣT is too large.will have multiple scattering problem

T ≥ 90%want

, T = 37%• When Σcoh << ΣT ≈ Σ inc + Σabs d = 1/ ΣT

= 1/e = 37%

T = exp −ΣTd( )

Optimal Sample Thickness

• When λ = 5Å

H2O 1 mm, T = 52 %

1.5 mm, T = 38 % *3 mm, T = 14 %

ΣT ≈ Σcoh

Silica 0.5 mm, T = 96 %

1 mm, T = 92 %*3 mm, T = 78 %

Σcoh << ΣT ≈ Σabs + Σinc

(want T > 90%) (T = 1/e = 37 % is optimal)

σσσσcoh = 10.62 barnsσinc = 0.005 barnsσabs = 0.17 barns

σcoh = 7.75 barnsσσσσinc = 164 barnsσabs = 0.66 barns

Examples of Sample Thickness

• Neutron cross-section depends on neutron wavelength λ.• Total cross-section increases as the neutron wavelength increases.

0

0.2

0.4

0.6

0.8

1

4 6 8 10 12 14 16

1mm Silica1mm H

2O

Tran

smis

sion

Wavelength λ (Å)

Wavelength Dependence of Transmission

- bound coherent scattering length (10-13 cm-1) bH = -3.74 bD = 6.67 bO = 5.80

SLD

(10

10cm

-2)

0

H2O-0.56

D2O6.65

H2O + D2O(1:1 volume)

2.88ρSLD =

bii

n

∑V

= NAρmass

Mw

Σ

ibi( )

molecule

N A = Avogadro' s number = 6 ×1023

Mw = molecular weightbi = bound coherent scattering length of atom i

• H2O

• D2O

ρSLD ,H2O = (6 ×10 23 / mol ) 1.0g / cm 3

18g / mol

2 × bH + bO( )

= −0.56 × 10 10 cm −2

ρSLD , D2O = (6 × 10 23 / mol ) 1.1g / cm 3

20 g / mol

2 × bD + bO( )

= 6.32 × 1010 cm −2

• H2O + D2O mixture (1:1 volume)ρSLD , Mixture = xH2 O × ρSLD ,H 2O + (1− xH2 O) × ρSLD , D2O

= 0.5 × (−0.56 × 1010cm−2 ) + 0.5 × (6.32 ×1010cm−2 ) = 2.88 × 1010cm−2

Calculation of Scattering Length Density

• Coherent scattering contains the structural information of sample• Incoherent scattering is flat background.• Examples

H2O or Hydrocarbons ~ 1 cm-1 ster-1

D2O or Deuterated sample ~ 0.1 cm-1 ster-1

SiO2 (amorphous) ~ 0.02 cm-1 ster-1

• Large incoherent scattering reduce the dynamic range of measurement.• Use deuterated solvent whenever it is possible.

0.01

0.1

1

10

100

0.01 0.1

d Σ(Q

)/dΩ

(cm

-1)

Q (Å-1)

0.01

0.1

1

10

100

0.01 0.1

d Σ(Q

)/dΩ

(cm

-1)

Q (Å-1)

Large Σinc Small Σinc

Coherent and Incoherent Scattering

Liquid Gel or Polymer Melt Solid

Path length (Volume)1 mm (0.3 ml) 2 mm (0.6 ml)5 mm (1.5 ml)

Path length (Volume)1 mm (0.3 ml) 2 mm (0.6 ml)4 mm (1.2 ml)

Glue on a Cd maskSize mountable on a standard

Sample changerwidth < 3.5 cmheight < 5 cmthickness < 2cmDiameter = 2.0 cm Diameter = 2.0 cm

SANS Sample Holders

- neutron wavelength (5 - 20Å)- wavelength spread (∆λ/λ=10−30%)- source to sample distance (L1, #of guide, 4-15m)- sample to detector distance ( L2, 1-15m)- detector offset ( 0 - 25 cm)- sample ( 1- 2.5cm) and source(1.5-5cm) aperture sizes- position of beam attenuator during transmission measurement (0-8)

• Q-range cover : (1, 2, or 3 configuration)• Q-resolution needed• Beam intensity available, I ∝ Qmin

4

Qmin to Qmax

Use SASCAL or Web Based Tools

Set up SANS Configuration

Velocity selector

2D detector

sampleL1 L2

Neutron GuideBeam

attenutator

SampleAperture, A2

SourceAperture, A1

1) Scattering from sample2) Scattering from other than sample (neutrons still go through sample)3) Stray neutrons and electronic noise (neutrons don’t go through sample)

• We need MORE measurements

Stray neutronsand Electronic noise

Incident beam

aperture

air

sample

cell

• Contribution to detector counts

ISAM = (Count Rate)sample t

σ ISAM= ISAM

Counting time

σ ISAM/ ISAM

Sample Scattering

• Detector sensitivity

Source 1) Detector dark current2) Stray neutrons3) Cosmic radiation

- Measure a blocked beam(6Li or Boronated material)

• Blocked Beam

Source 1) Scattering from empty cell2) Scattering from windows

and collimation slits3) Air scattering

- Minimize air in beam path- Carefully choose cell and

window materials- Measure an empty cell

• Empty Beam

Why ?1) Sensitivity of each pixel is

slightly different (~ 1%)

- Use isotropic scattering material(Plexiglass or water)

- We calibrate each reactor cycle

• Counting time tbackground

tsample

= Count Ratebackground

Count Ratesample

Additional Measurements

Tsample +cell Tcelland

ISAM = CO Tsample +cell dΣ (Q)

dΩ

sample+

dΣ (Q)dΩ

EMP

+ IBlocked Beam

IEMP = CO Tcell dΣ(Q)

dΩ

EMP

+ IBlocked Beam

IBGD = IBlocked Beam

CO = φ A d∆Ω ε t ∆Ω = solid angle of each pixelε = detector efficiencyt = counting time

φ = incident neutron fluxA = sample aread = sample thickness

Data CorrectionMeasured Raw Data

ICOR = (ISAM − IBGD) −Tsample+ cell

Tcell

IEMP − IBGD( )

Corrected SANS data

• The corrected SANS data is then calibrated with detector sensitivity.

ICAL = ICOR /(Normalized Detector Sensitivity)

I(Q)CAL = φ A d Tsample+ cell dΣ(Q)

dΩ

sample ∆Ω ε t

• This is what we have

• Direct Beam Flux Method- Measure a direct beam with nothing in the beam except an attenuator.

IDirect = φ A Tatten. ∆Ω ε t

• Standard Sample Calibration - Use a sample with known absolute scattering cross-section at Q=0.- Measure the standard sample with the exactly same configuration

dΣ(Q)dΩ

sample=

I(Q)CAL

IDirect

1d

Tatten .

Tsample+cell

I(Q = 0)STD = φ A dSTD TSTD+cell dΣ(Q = 0)

dΩ

STD

∆Ω ε t .

dΣ(Q)dΩ

sample=

I(Q)CAL

I(Q = 0)STD

dSTD

d

TSTD+cell

Tsample+cell

dΣ(Q = 0)dΩ

STD

Absolute Scaling

0

200

400

600

800

1000

1200

0 0.02 0.04 0.06 0.08

d Σ(Q

)/dΩ

(cm

-1)

Q (Å-1)

• Take average over annulus

• Each annulus corresponds to one data point in reduced 1D SANS data

Circular 1D Average

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

10

20

30

40

50

60

70

80

Q (Å-1)

collimationdominated

∆λ/λdominated

Q-Resolution Functionin Gaussian Approximation

R(Q,Qo) = A exp( -(Q-Qo)2/δQ2)

Q = 4πλ

sinθ2

≈

2πλ

θ

collimation wavelength spread

δQQ

2

= δθθ

2

+ δλλ

2

δ Q/Q

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

10

20

30

40

50

60

70

80

Q (Å-1)

collimationdominated

∆λ/λdominated

30%

5 %

δQ/Q

• Collimation : L1, L2, A1, A2, δD (detector resolution)

Q-Resolution Function

• The magnitude of smearing effect is proportional tothe curvature of scattering function

Ismeared (Qo ) ≅ I(Qo ) + Aσ Q2 d 2 I(Q)

dQ2Q=Qo

+ ⋅⋅ ⋅

Sharp features are smeared the most.

10 -1

10 0

10 1

10 2

10 3

0.01 0.1

No smearingHigh resolutionMedium resolutionLow resolution

I(Q

) (cm

-1 st

er-1

)

Q (Å -1 )

Form factor of a monodisperse sphere

(R=200Å)

Smearing Effect

Large A1, A2,Short L1, L2Large ∆λ/λSmall λ

Small A1, A2,Long L1, L2Small ∆λ/λLarge λ

High resolution

Low Resolution

• When sample has a strong coherent scattering X-section and thick.• Final scattering angle is added incoherently• To reduce the multiple scattering, we need to reduce d.

Incident beam

sampled

(J.G. Barker)

10 -1

10 0

10 1

10 2

10 3

10 4

10 5

0 0.005 0.01 0.015 0.02

Im(0) T=0.9Im(0) T=0.5Im(0) T=0.1I(q)

I m(Q

) (c

m-1

ster

-1)

Q (Å -1 )

When attenuation is only due to coherent scattering

Multiple Scattering

• Now We have a whole picture of SANSExperiment.

- Sample preparation- Optimization of configuration.- What to measure.

• To get good quality of data,Initial Planning is VERY Important.

• Use Beamtime Efficiently

Summary

• Align the center of sample with neutron beam- laser beam and neutron camera

• Align beamstop- 1, 2, 3, 4 inch diameter- NO attenuator

• Measure a beam center - Q = 0 position- Use a proper beam attenuator

Beam center(65.94, 63.87)

128 x 128 pixels

(Beamstop needs to move down and left)

Appendix Beam Alignment and Initial Measurements

• Neutron cross-section depends on neutron wavelength λ.

• Absorption Cross-Section • Scattering Cross-Section

(B10, ΣΤ ~ Σabs)

where vn = neutron velocity

( Hydrogen, )σbound = 4 σ free

For light element σbound > σ free

σbound ≈ σ freeFor heavy element

Σabs ∝1/ vn ∝ λ

σ bound =A + 1

A

2

σ free

σ free

Neutron Energy/Chemical Binding Energy

A=atomic number

- Scattering lengths, b, listed in table are bound scattering length.

At T=0K

Wavelength Dependence of Cross-SectionAppendix

• Q-resolution Function R(Q,Qo) is determined by :1) Beam collimation 2) Detector resolution 3) Wavelength 4) Wavelength spread

Qx

Qy

collimation ∆λ/λ+ collimation

σ θ2 =

116

A1

L1

2

+A2

2

161L1

+1L2

2

+σ d

L2

2

1) 2) 3) 4)

σQ2 = 2π

λ

2

σθ2 + Q2 ∆λ

λ

2

Ismeared (Qo ) = R(Q,Qo )I(Q)dQ∫

Q-Resolution FunctionAppendix

• The measured scattering intensity is I(Q) of sample convolutedwith a resolution function R(Q,Qo).