SANS Experimental Methods - NIST Center for Neutron Research · Neutron Small Angle Scattering and...
Transcript of SANS Experimental Methods - NIST Center for Neutron Research · Neutron Small Angle Scattering and...
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).