Total Scattering
The Key to
Understanding
disordered, nanocrystalline and
amorphous materials.
Tutorial
9th Canadian Powder
Diffraction Workshop
Thomas Proffen
Diffraction Group Leader
tproffen@ornl.gov
Friday 25th May 2012
9:00 - 9:45
9:45 - 10:30
Beyond the Bragg peaks or why do we care about total
scattering?
Measuring total scattering X-ray and neutron data: where
and how?
10:30 - 11:15
Break
11:15-12:30
What to do with your PDF: Modeling of disordered
structures ?
12:30 - 1:30
Lunch
1:30 - 5:00
Practical Sessions
All cartoons by
Julianne Coxe.
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Measuring
Total
Scattering
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Experimental
Considerations
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
How to obtain high quality PDFs ?
The PDF (similar to the Patterson) is obtained via
Fourier transform of the normalized total
scattering S(Q):
G(r ) 
2

Q[ S (Q )  1]sin(Qr )dQ


0
Requirements to obtain ‘good’ PDF:
High maximum momentum transfer, Qmax.
High Q-resolution.
Good counting statistics @ high Q.
Low instrument background
Where ?
Synchrotron sources
(high energy X-rays)
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or
spallation neutron sources
(reactor neutron energies are too low)
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
NPDF: the key to high quality, high r PDFs
The PDF (similar to the Patterson) is obtained
via Fourier transform of the normalized total
scattering S(Q):
G (r ) 
2

Q[S (Q)  1]sin(Qr )dQ


0
Requirements to obtain ‘good’ PDF:
 High maximum momentum transfer, Qmax.
 High Q-resolution.
 Good counting statistics @ high Q.
 Low and stable instrument background.
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
DISCUS - http://discus.sourceforge.net/
3 day DISCUS workshop
in Spring 2012 in Erlangen, Germany ..
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Q resolution
Ni data from GLAD (IPNS) and high resolution NPDF (Lujan)
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Q resolution ..
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University of Saskatchewan, Saskatoon.
Nanoparticles: Particle size
Nanogold
Spherical particle envelope
3
3 r 1 r 
1
  
2 R 2 R
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Experimental
Facilities
or
Where to measure a good PDF
?
Neutrons
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Facility overview
• Spallation Neutron Sources
–
–
–
–
–
Lujan Neutron Scattering Center, Los Alamos, USA
ISIS Pulsed Neutron and Muon Facility, Didcot, UK
IPNS, Argonne, USA – closed
Spallation Neutron Source, Oak Ridge, USA
Japan Proton Accelerator Research Complex, Tokai, Japan
• Synchrotron Sources
– Advanced Photon Source, Argonne, USA
– ESRF, Grenoble, France
– Many more ..
• Links
– http://neutron.anl.gov/facilities.html
– http://www-als.lbl.gov/als/synchrotron_sources.html
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Facility Access
• Most facilities in the US
(and Europe) run a open
user program.
• Peer reviewed proposals.
• Tips for success:
– Check the facilities web sites.
– Contact the instrument scientist
before submitting a proposal
online !
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutrons ?
Neutrons show where the atoms are….
The 1994 Nobel Prize in
Physics – Shull &
Brockhouse
…and what the atoms do.
Wave nature of neutron:
de Broglie relation: =h/p
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutrons vs. X-rays
• Sensitive to light atoms
(e.g. H)
• Contrast by isotope
substitution
X-ray and neutron scattering
Lengths for selected elements.
• Easy sample
environment (T,p,..)
• No ‘formfactor’ (good for
PDF)
• Weak  large samples
& long measuring times
..
Scattering from single atom
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Time of Flight Diffraction
I
ki
 res =  bw
kf
Neutron
Source Spectrum

 bw   T
ki
kf
I
I
 res   T


Angle dispersive: Vary scattering angle in Bragg’s law
Energy dispersive: Vary wavelength (TOF – wavelength)
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University of Saskatchewan, Saskatoon.
Neutrons at Oak Ridge National Lab.
ORNL hosts two neutron sources:
• Spallation Neutron Source
• High Flux Isotope Reactor
• Both are DOE User Facilities
• Also hosts the Joined Institute for
Neutron Sciences
http://neutrons.ornl.gov
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SNS – how does it work ?
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University of Saskatchewan, Saskatoon.
Spallation Neutron Source
Powder diffractometers
• POWGEN : High resolution
• NOMAD: Total scattering
• VULCAN: Engineering
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NOMAD
contact
• Total scattering instrument
• Science of disordered
materials, glasses and nanomaterials
• Commissioning – partial user
program
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Jorg Neuefeind
neuefeindjc@ornl.gov
Mikhail Feygenson
feygensonm@ornl.gov
NOMAD opens the door to ‘x-ray size’
samples of less than 1mg.
Overnight run on
NOMAD
Diffraction of small Samples
• Studies of rare and/or expensive samples
Example Na35Cl
• Isotopic labeling for local structure
• High cost for stable isotopes
• Well-defined structure with less than 1mg
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
NOMAD: Isotope
substitution experiment
CaSiO3 melt
L. Skinner, C.J. Benmore, J.K.R. Weber, S. Tumber, L. Lazareva, J. Neuefeind, L.
Santodonato, J. Du, J.B. Parise
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
LANSCE: Multiple experimental areas
Isotope production
Facility
Proton Radiography
Ultracold Neutrons
Materials
Test Station
PSR
Target 1L
Target 2
Target 4
(WNR)
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Lujan Center
ER-1/2
Lujan Center: Powder diffractometers
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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NPDF: Overview
• Specifications
– Upgrade finished Sep. 2002
– L1: 32m, Qmax=50Å-1, d/d=0.15%
– Typical PDF measurement 1 - 4 hrs
– Sample amounts down to 200 mg
– Ancillary: 10K-1500K, soon: 0.5K, 11T
• Science
– 95% PDF studies, hard matter
– Many users new to PDF
• Software
– Web based instrument interface
– Automatic creation of PDF
– Integration in SNS data portal (soon)
• http://www.lansce.lanl.gov
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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The ISIS Neutron Facility
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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ISIS: Powder diffractometers
• GEM
• POLARIS
Sample tank
• SANDALS
Incident Polychromatic
Neutron Beam
Bank 6
142-169o
Bank 1
6-13o
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Bank 2
14-21o
Bank 3
25-45o
Bank 4
50-75o
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Bank 5
79-104o
Instrument: NOVA at J-PARC
NPDF at LANSCE is a high
resolution total scattering
instrument.
NOVA constructed at J-PARC as
part of the HYDRO-STAR project
is a high flux total scattering
spectrometer.
January 2010: Yumiko
Nakamura opens
shutter of NOVA shutter
during first joined LANLAIST experiment.
The instruments provide
complementary total scattering
data.
LANL collaborators are the first
external users of NOVA (January
2010)
Instrument scientist: T. Otomo
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Experimental
Facilities
or
Where to measure a good PDF ?
X–rays
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Synchrotron sources
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http://www.esrf.eu/AboutUs/GuidedTour/
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray PDF: The traditional way
100
(2% ~) C om pton + Elastic (~98% )
80
60
40
In te n s ity (a .u .)
20
Intensity, a.u.
25
20
-1
Q = 2 (Å )
0
80
(85% ~) C om pton
60
Elastic (~15% )
40
20
-1
Q = 25 (Å )
0
15
C om pton
(~97% )
80
10
60
40
5
-1
Q = 40 (Å )
0
0
0
5
10
15
20
25
30
35
40
-1
Q (Å )
31
Elastic (~3% )
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University of Saskatchewan, Saskatoon.
60
70
80
90
100
E [keV]
Valeri Petkov
X-ray PDF: The traditional way
• Energy dispersive
detector
• Step scans in Q
• Long counting
times, especially at
high Q.
• Typical collection
time: 12-24 h
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray PDF: The fast way
Exposure: 25 sec !
Image plate
detector
P.J. Chupas, X. Qiu, J.C. Hanson, P.L. Lee, C.P. Grey and S.J.L.
Billinge, Rapid-acquisition pair distribution function (RAPDF) analysis, J. Appl. Cryst. 36, 1342-1347 (2003).
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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11ID-B at the Advanced Photon Source
Application of a large-area, highsensitivity, fast readout,
flat-panel GE detector based on
amorphous silicon.
PDF acquisition at 30Hz !
Time-resolved PDF measurements:
Reduction of PtIV
Pt0
P. Chupas et al, J. Appl. Cryst. 40, 463-470 (2007).
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
11ID-B at the Advanced Photon Source
Beamline Specs
Source
2.3 Undulator
Monochromator Type
Si(511)
Energy Range
90-91 keV
Resolution (ΔE/E)
1 x 10 -3
Flux (photons/sec)
1 x 10 11 @90 keV
Beam Size (HxV)
Unfocused 1mm x 1mm
Monochromator Type
Si(311)
Energy Range
58-60 keV
Resolution (ΔE/E)
1 x 10 -2
Flux (photons/sec)
1 x 10 11 @58 keV
Beam Size (HxV)
Unfocused 1mm x 1mm
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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Agreement between LANL and ANL ..
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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MgCo – the power of neutrons and x-rays
PDF peak intensity ∝
where bi is the scattering length of the ith atom.
37
bi for x-ray
bi for neutron
Mg
12
3.631
Co
27
0.779
bmbn
Mg-Mg
Mg-Co
Co-Co
x-ray
144
324
729
neutron
13.18
2.83
0.607
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray PDF: In house measurements
fci-Ho-Mg-Zn
Huber Gunier diffractometer
Qmax = 13.5Å-1
Brühne et al., Z. Kristallogr.
219 (2004) 245-258
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray PDF: In house measurements
•
STOE STADI-P diffractometer
•
Cu Kα1 radiation (Qmax = 6.5 A-1)
•
Data collection time: 27 h
•
Why Cu?
– Information on average structure
(→ Structure solution)
Naphthalene:
2.8 Å
≈ 7Å
Raw data:
PDF:
C10H8
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
2.4 Å
Buy your own PDF diffractometer ..
Exhibit at the EPDIC meeting 2008
(Photo by Nadine Rademacher)
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Data
Reduction
How difficult is the
processing of total scattering
data ?
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron data processing
Corrections
Cylindrical Time-Of-Flight geometry
(energy dispersive)
Typical characterization runs
Empty instrument (B)
Empty Container (C)
Empty Container background (CB)
Vanadium (V)
Vanadium background (VB)
Sample (S)
Scorr=[(S-SB)-(C-CB)]/[V-VB]
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
G (r ) 
2



0
Q[ S (Q)  1] sin QrdQ
Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
Conversion from time of flight to Q depends
on path lengths. Can be refined, e.g. GSAS:
TOF = DIFC d + DIFA d2 + T0
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering

DIFC  252 .816  2 sin  L1  L22  L23 / 16
L1: primary flight path (source – sample)
L2: secondary flight path (sample – detector)
L3: detector height
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.

Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering
 After an event is recorded the
detector generally needs some time
to reset itself and the detector
electronics to process the pulse.
Neutrons arriving during this deadtime are not recorded.
 Count-rate dependent.
 Important at high count-rates.
 Corrected analytically.
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
 Depends on wavelength and
elements present.
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering
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 Depends on path sample 
PDFgetN corrects for cylindrical
geometry !
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering
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 Neutrons that are scattered twice or
more in the sample need to be
corrected.
 Effect can be as big as 10% !
 Corrected theoretically.
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron corrections
• TOF  Q conversion
• Deadtime correction
 Incident beam is monitored to
normalize for the total neutron flux.
• Absorption
 Incident neutron spectrum is
corrected via vanadium
characterization run.
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering
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 The condition S(Q)  1 for high Q
is used to normalize for sample
size and density.
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
 Inelastically scattered neutrons are
counted in the incorrect Q-bin in the
time of flight neutron method.
• Multiple scattering
 Corrected theoretically (?)
• Normalization
• Placzek correction
 Strictly only valid for liquids.
• Parasitic scattering
 Needs new approach !
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Neutron corrections
• TOF  Q conversion
• Deadtime correction
• Absorption
 Measured (background and empty
can) and subtracted after suitable
normalization.
• Multiple scattering
• Normalization
• Placzek correction
• Parasitic scattering
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 Reproducible background key to
success !
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Software: PDFgetN
• Based on GLASS package.
• Graphical users interface &
integrated plotting.
• Supports most TOF neutron
powder file formats.
• Records all processing
parameters as part of output
files G(r) and S(Q).
• Runs on Windows
95/98/NT/2000 and UNIX
http://pdfgetn.sourceforge.net
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P.F. Peterson, M. Gutmann, Th. Proffen and
S.J.L. Billinge, PDFgetN: A User-Friendly
Program .., J. Appl. Cryst. 33, 1192 (2000).
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray data processing
• In house X-ray experiments:
– Easy.
– Low r resolution, slow (and/or poor statistics).
– Mo: Qmax ~ 17Å-1, Ag: Qmax ~ 20Å-1.
– Flat plate transmission or reflection geometry.
Transmission
(transparent samples)
Reflection
(absorbing samples)
• Synchrotron experiments:
– Little precious beamtime.
– High energy X-rays (Qmax > 60Å-1).
– High intensity (x 10,000 times stronger).
– Parallel beam optics.
– Generally flat plate transmission geometry.
– New rapid PDF setup (PDF in seconds).
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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X-ray corrections
• 2  Q conversion
• Deadtime correction
• Absorption
• Multiple scattering
• Normalization
• Compton scattering
• Polarization correction
 Data from some diffractometers
might require a conversion from
scattering angle 2 to
momentum transfer Q !
 Uncertainties: Offset 2,
wavelength
• Parasitic scattering
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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X-ray corrections
• 2  Q conversion
• Deadtime correction
• Absorption
• Multiple scattering
• Normalization
• Compton scattering
• Polarization correction
• Parasitic scattering
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 Incident beam is monitored to
normalize for the total X-ray flux
(especially at the synchrotron).
 Normalization for angle
depended change of illuminated
sample volume.
 The condition S(Q)  1 for high
Q is used to normalize for sample
size and density.
9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray corrections
• 2  Q conversion
• Deadtime correction
• Absorption
 Compton scattering is inelastic
incoherent scattering.
• Multiple scattering
• Normalization
• Compton scattering
 Calculated theoretically or
measured and subtracted.
• Polarization correction
• Parasitic scattering
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray corrections
• 2  Q conversion
• Deadtime correction
• Absorption
• Multiple scattering
• Normalization
• Compton scattering
• Polarization correction
 Intensity depends on beam
polarization which depends on
beamline optics
(monochromators etc.) and
angle.
• Parasitic scattering
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X-ray corrections: Removal of Compton
scattering
 Energy sensitive detector (e.g. Ge
detector) allows separation of
Compton scattering at higher Q.
Q=40Å-1
 Modes:
 SCA: Electronic windows to
separate elastic channel
 MCA: recording of complete
spectrum at each measured
point  software integration.
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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Software: PDFgetX2
X. Qiu, J.W. Thompson, S.J.L. Billinge, J. Appl. Cryst. 37, 678-678 (2004)
• Use Fit2D for area detector
integration.
• Reads SPEC files.
• Supports MCA and SCA data.
• Integrated plotting of various
corrections applied.
• Tools for merging scans.
• Runs on Windows and UNIX.
Based on IDL (download free
runtime environment).
http://www.pa.msu.edu/cmp/billinge-group/programs/PDFgetX2/
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9th Canadian Powder Diffraction Workshop – May 23-25, 2012
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