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Advances in Single Crystal Diffuse Scattering Ray Osborn, Stephan Rosenkranz Neutron and X-‐ray Sca0ering GroupMaterials Science DivisionArgonne Na;onal Laboratory
Acknowledgements‣ Ray Osborn, John Paul Castellan, Rich Vi;, Bob Kleb,
Ma; Krogstad, Keith Taddei, Jared AllredMaterials Science Division, Argonne Na4onal Laboratory
‣ Feng Ye, Georg Rennich, Ross WhiGield, Yaohua Liu, Luke Heroux, Andrei Savici,Mariano Ruiz-‐Rodriguez, Loren Funk, Rick ReidelNeutron Sciences Directorate, Oak Ridge Na4onal Laboratory
‣ JusMn Wozniak, Michael Wilde, Ben Blaiszik, Ian FosterMathema4cs and Computer Science Division, Argonne Na4onal Laboratory
‣ Branton Campbell Brigham Young University
‣ Funding by the U. S. Department of Energy, Office of Basic Energy SciencesMaterials Science and Engineering Division and the Scien4fic User Facili4es Division
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21st NSRRC Users’ Mee;ng and Workshops
Corelli
‣ This is the first dedicated diffuse sca0ering diffractometer on a pulsed neutron source ‣ Commissioning started last year
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21st NSRRC Users’ Mee;ng and Workshops
Feng Ye, Luke Heroux, Yaohua Liu
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Arcangelo Corelli was the greatest violinist of his age and an influential composer who became known as the "Father of the Concerto Grosso". This musical form contrasts music from a small ensemble of solo musicians with the full orchestra. Similarly, the properties of many materials are enriched by the interactions between both short and long-range ordering motifs that the Corelli instrument is designed to explore.
Outline
‣ What is diffuse sca0ering? • What does it look like? • What causes it? • Who started it?
‣ What is it good for? • A random walk through disordered materials
‣ Case Study 1: Diffuse sca0ering from vacancies in mullite ‣ Case Study 2: Huang sca0ering in bilayer manganites ‣ Why neutrons?
• Elas;c Discrimina;on -‐ sta;c vs dynamic disorder • Corelli -‐ Diffuse sca0ering with elas;c discrimina;on
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21st NSRRC Users’ Mee;ng and Workshops
21st NSRRC Users’ Mee;ng and Workshops
Bragg Scattering vs Diffuse Scattering
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Bragg ScatteringAverage Structure
Diffuse ScatteringDeviations from the Average Structure
21st NSRRC Users’ Mee;ng and Workshops
Single Crystal Diffuse Scattering in 3D
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Simple Example of Disorder
‣ In these examples, 30% of atoms (blue dots) have been replaced by vacancies (green dots) • Le^-‐Hand-‐Side: random subs;tu;on • Right-‐Hand-‐Side: high probability of vacancy clusters
-‐ Thanks to Thomas Proffen
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21st NSRRC Users’ Mee;ng and Workshops
Bragg Scattering
‣ Bragg sca0ering is determined by the average structure. • Since the average vacancy occupa;on is iden;cal, both examples have iden;cal Bragg peaks
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21st NSRRC Users’ Mee;ng and Workshops
Diffuse Scattering
‣ The diffuse sca0ering is quite different in the two examples • Random vacancy distribu;ons lead to a constant background (Laue monotonic sca0ering) • Vacancy clusters produce rods of diffuse sca0ering connec;ng the Bragg peaks
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21st NSRRC Users’ Mee;ng and Workshops
21st NSRRC Users’ Mee;ng and Workshops
An Ultra-Short History of Advances in Diffuse Scattering
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Yttria-Stabilized Zirconia
T. Proffen and T. R. Welberry J. Appl. Cryst. 31, 318 (1998)
21st NSRRC Users’ Mee;ng and Workshops
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What is it good for?
Science Impacted by Diffuse Scattering
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‣ Subjects iden;fied at the Workshop on Single Crystal Diffuse ScaIering at Pulsed Neutron Sources • Stripes in cuprate superconductors • Orbital correla;ons in transi;on metal oxides (including CMR) • Nanodomains in relaxor ferroelectrics • Defect correla;ons in fast-‐ion conductors • Geometrically frustrated systems • Cri;cal fluctua;ons at quantum phase transi;ons • Orienta;onal disorder in molecular crystals • Rigid unit modes in framework structures • Quasicrystals • Atomic and magne;c defects in metallic alloys • Molecular magnets • Defect correla;ons in doped semiconductors • Microporous and mesoporous compounds • Host-‐guest systems • Hydrogen-‐bearing materials • So^ ma0er -‐ protein configura;onal disorder using polariza;on analysis of spin-‐incoherence • Low-‐dimensional systems • Intercalates • Structural phase transi;ons in geological materials
Diffuse Scattering from Metallic Alloys
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Short-range Order in Null Matrix 62Ni0.52Pt0.52
J. A. Rodriguez, S. C. Moss, J. L. Robertson, J. R. D. Copley, D. A. Neumann, and J. MajorPhys. Rev. B 74, 104115
0 2 40
2
4
0 qy
0 (r
.l.u.
) qx 0 0 (r.l.u)
Diffuse Scattering from a Fast-Ion Conductor
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M. T. Hutchings et al J. Phys. C 17, 3903 (1984)
CaF2
Diffuse Scattering from Molecular Solids
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T. R. Welberry et al J. Appl. Cryst. 36, 1400 (2003)
Diffuse Scattering from Relaxor Ferroelectrics
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T. R. Welberry et al J. Appl. Cryst. 38, 639 (2005)
Lead Zinc-Niobate
G. Xu, P. M. Gehring, G. Shirane, Phys. Rev. B 72, 214106 (2005).
Lead Magnesium-Niobate
E=0 E||[111]
Magnetic Diffuse Scattering from Geometric Frustration
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21st NSRRC Users’ Mee;ng and Workshops
S.-H. Lee et al Nature 418, 856 (2002)
ZnCr2O4
Thermal Diffuse Scattering
‣ Lakce vibra;ons produce devia;ons from the average structure even in perfect crystals
‣ X-‐ray sca0ering intensity is given by the integral over all the phonon branches at each Q
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M. Holt, et al, Phys Rev Le0 83, 3317 (1999).
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How do I model it?
A Few Equations
‣ Laue Monotonic Diffuse Sca;ering
‣ Cowley Short-‐Range Order
‣ Warren Size Effect
‣ Borie and Sparks CorrelaMons
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21st NSRRC Users’ Mee;ng and Workshops
I =
X
i
X
j
bibjexp(iQ · rij)
I =
¯b2X
ij
exp(iQ · rij) +N(b2 � ¯b2); b̄2 = (cAbA + cBbB)2; b2 = cAcB(bB � bA)
2
Idiffuse = NcAcB(bB � bA)2+
X
ij
↵icBcA(bB � bA)2exp(iQ · rij) ↵i =
✓1� pi
cA
◆;
J. M. Cowley, J. Appl. Phys. 21, 24 (1950)
I =
X
i
X
j
bibjexp (iQ · (Ri �Rj))
1 + iQ · (ui � uj)�
1
2
(Q · (ui � uj))2+ ...
�
V. M. Nield and D. A. Keen Diffuse Neutron Scattering From Crystalline Materials (2001) T. R. Welberry Diffuse X-ray Scattering and Models of Disorder (2004)
Idiffuse = NcAcB(bB � bA)2
0
@1 +
X
ij
↵iexp(iQ · rij +X
ij
�iexp(iQ · rij
1
A �i = f(✏iAA, ✏iBB);
Three-Dimensional Pair Distribution Functions
‣ The ability to measure three-‐dimensional S(Q) over a wide range of reciprocal space provides the 3D analog of PDF measurements. • Total PDFs if Bragg peaks and diffuse sca0ering
can be measured simultaneously • Δ-‐PDFs if the Bragg peaks are eliminated
-‐ using the punch and fill method
‣ This would allow a model-‐independent view of the measurements in real space.
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Case Study 1: Mullite
Mullite - A Case Study‣ Mullite is a ceramic that is formed by adding O2+ vacancies to Sillimanite
• Sillimanite has alterna;ng AlO4 and SiO4 tetrahedra • Mullite has excess Al3+ occupying Si2+ sites for charge balance
‣ This results in strong vacancy-‐vacancy correla;ons
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Sillimanite: Al2SiO5 Mullite: Al2(Al2+2xSi2-2x)O10+x
AlO6 Octahedra
AlO4 Tetrahedra
SiO4 Tetrahedra
B. D. Butler, T. R. Welberry, & R. L. Withers, Phys Chem Minerals 20, 323 (1993)
Measuring X-ray Diffuse Scatteringwith Continuous Rotation Method
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Pilatus 2M Detector
‣ The sample is con;nuously rotated in shu0erless mode at 1° per second ‣ A fast area detector (e.g., a Pilatus 2M) acquires images at 10 frames per second
• i.e., 3600 x 8MB frames ~ 30GB every 6 minutes
‣ The detector needs low background, high dynamic range, and energy discrimina;on • Ideally, this is performed with high-‐energy x-‐rays, e.g., 80 to 100 keV
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• Group data based on use and features, not location/filename– Logical grouping to organize, search, and
describe• Operate on datasets as units• Tag datasets with characteristics
that reflect content• Share/move datasets for
collaboration• Interact with via REST API, Python
API, GUI, and CLI
Vs.
Globus CatalogCatalog à Datasets à Members
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NeXpy Remote Data Access
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NeXpy&Data&Service&
NeXpy&user&at&APS&
NeXpy&Display&And&UI&
...&
Exp&Archive&
NeXpy&remote&user&
NeXpy&Display&And&UI& Live&
Experiment&Data&
~TB
~KB
~MB
Python remote objects
~GB
Catalog& SwiB&Workflow&
NeXpy - a Python toolbox for big data
‣ A toolbox for manipula;ng and visualizing arbitrary NeXus data of any size
‣ A scrip;ng engine for GUI applica;ons ‣ A portal to Globus Catalog ‣ A demonstra;on of the value of combining:
• a flexible data model • a powerful scrip;ng language
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http://nexpy.github.io/nexpy/$ pip install nexpy
+=
Data Reduction Workflows
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Peak SearchRefinement and Orientation
Coordinate Transformation Data Projections
NeXus Wrapper Files
‣ The data from the whole experiment can be encapsulated in a few “wrapper” files.
‣ Large arrays are stored externally to ensure data integrity.
‣ All other metadata is available with a single NeXus file load.
‣ These files can include: • Raw data arrays from mul;ple detector
configura;ons • Transformed data • Sample and instrument calibra;on parameters • Derived data, e.g., peak coordinates • Provenance informa;on • Imported SPEC files • Simula;on results
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21st NSRRC Users’ Mee;ng and Workshops
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3D Diffuse Scattering in Mullite
‣ There is strong diffuse sca0ering throughout reciprocal space ‣ The shape of the diffuse sca0ering is strongly dependent on the value of Ql ‣ There are incipient superlakce peaks at Q = 0.5 c* + 0.31 a*
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Ql=0.16 Ql=0.5 Ql=0.75
Monte Carlo Analysis‣ In a classic analysis, Richard Welberry and
colleagues developed a set of interac;on energies to model mullite disorder
‣ Interac;on energies were ini;alized: ‣ insights from chemical intui;on ‣ insights from the measured diffuse sca0ering
‣ The diffuse sca0ering was calculated using a Monte Carlo algorithm to generate vacancy distribu;ons first in 2D slices and then in 3D
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B. D. Butler, T. R. Welberry, & R. L. Withers, Phys Chem Minerals 20, 323 (1993)
21st NSRRC Users’ Mee;ng and Workshops
Monte Carlo Analysis Results
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0 5 10 15 200
20
40
60
80
100
120
0 2 4 6 8 10 12
-40
-20
0
20
40
V-V pair(a)
Diffe
renc
e w
ith ra
ndom
stru
ctur
e
G(r)
[ 1 1
0 ]< 0
1 0
>
1/2
< 1
1 2>
< 1
0 0
>
1/2
< 1
1 0
>
< 0
0 1>
(b)
r (A) r (A)
21st NSRRC Users’ Mee;ng and Workshops
Vacancy Short-Range Order in MulliteA First-Principles Approach
35
Lowest Energy 3:2 Mullite Structurefrom Kinetic Monte Carlo Calculation
Peter Zapol & Anh Ngo
21st NSRRC Users’ Mee;ng and Workshops
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Case Study 1: Bilayer Manganites
Diffuse Scattering from Jahn-Teller Polarons
0 1-1-2 2
1.7
2.0
2.3
l
h
0
28
29
212
214
216
210
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21st NSRRC Users’ Mee;ng and Workshops
4+4+ 4+3+
t2g
eg
ΔCF
ΔJTdMn
T = 115 K
d(3x2-r2)d(3y2-r2)
T = 300 K
Huang Scattering
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21st NSRRC Users’ Mee;ng and Workshops
ℑ3
ℑ3
ℑ1
ℑ1
ℑ2
ℑ2
€
I(Q) = eiQ ⋅(R m −R n ) fm fne−Wm e−Wn
m, n∑ (Q ⋅ um )(Q ⋅ u n )
qx
qzTDS
POL
TotalB. Campbell et al Phys. Rev. B. 67, 020409 (2003)
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21st NSRRC Users’ Mee;ng and Workshops
500 K
h (r.l.u)
275 K
h (r.l.u)
l (r.l
.u.)
50
(2,0,0)l (r.l
.u.)
125 K
l (r.l
.u.)
200 K
100 K
single crystal synchrotron x-ray scattering 11-ID-D, APS@Argonne
this allows us to subtract background from thermal diffuse scattering!
TDS + Huang scattering
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+=
TDS polaron
Cooperative Jahn-Teller Distortions
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21st NSRRC Users’ Mee;ng and Workshops
ab
ac
O(3a) O(3b)
O2
O1
ξ ~ 6aB. J. Campbell, R. Osborn, D. N. Argyriou, L. Vasiliu-Doloc, J. F. Mitchell, S. K. Sinha, U. Ruett, C. D. Ling, Z. Islam, and J. W. Lynn, Physical Review B 65, 014427 (2001)
X-ray SCD data (115 keV 11-ID-C)
Origins of Stripe Formation
‣ Stripe forma;on is a very common mo;f of disordered systems
‣ It is the response of a system with interac;ons that compete on different length scales • e.g., long-‐range repulsion vs short-‐range a0rac;on
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21st NSRRC Users’ Mee;ng and Workshops
a0 6-18 18-12 12-6
0
12
-12
-6
6 Γ⊥
Γ||
b
q ≈ (0.3, 0, 0)
C. Reichhardt, C. J. Olsen, I. Martin & A. Bishop, EPL 61, 221–227 (2003).
Wigner Lattice Phase SeparationStripes
21st NSRRC Users’ Mee;ng and Workshops
Huang Scattering as a Function of (Qh, Qk, Ql)
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21st NSRRC Users’ Mee;ng and Workshops
Expanding the Concept of a Data Set
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44
0 1-1-2 2
1.7
2.0
2.3
l
h
0
28
29
212
214
216
210
Phase Diagram
Total Data: S(Q, T, x)
Correlated Data Analysis/ Machine Learning
21st NSRRC Users’ Mee;ng and Workshops
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Why neutrons?
Importance of Elastic Discrimination
‣ X-‐rays measure the instantaneous (t=0) pair correla;on func;ons • i.e., integra;ng sta;c and dynamic disorder
‣ Neutrons have lower incident energies so it is possible, in principle, to separate sta;c (t=∞) pair correla;ons from dynamic correla;ons.
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21st NSRRC Users’ Mee;ng and Workshops
+=
TDS polaron
neutrons
-1 0 1 2 3 4
50
100
150
coun
ts / 5min
energy transfer (meV)
300K200K125K100K 10K
phonon
polaron
x-‐rays
Measuring Large Volumes of Reciprocal Space Conventional Time-of-Flight Neutron Methods
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21st NSRRC Users’ Mee;ng and Workshops
White Beam: efficient
NO energy discrimination
Fixed ki : energy resolved
NOT efficient
M(t)
Sample with : elastic scattering
TOF Laue Diffractometer •highly efficient data collection •wide dynamic range in Q
Statistical Chopper •elastic energy discrimination •optimum use of white beam
inelastic excitations
Cross Correlation Chopper
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21st NSRRC Users’ Mee;ng and Workshops
16
Efficient Elastic Discrimination
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21st NSRRC Users’ Mee;ng and Workshops
Time-of-Flight
Distance
ω>0
ω=0
ω<0
Statistical Chopper
TOF Laue Diffractometer Intensity at detector when beam transmission is modulated in time by M(t)
L. Pal et al, Neutron Inelastic Scattring, p. 407 (Vienna, 1968) R. Von Jan & R. Scherm, Nucl. Inst. Meth. 80, 69 (1970) P. Pellionicz et al, Nucl. Inst. Meth. 92, 125 (1971) W. Matthes, Neutron Inelastic Scattering, p. 773 (Vienna, 1972) R. K. Crawford et al, ICANS-IX (1986) L. D. Cussen et al, Nucl. Inst. Meth. A314, 155 (1992)
Very efficient for large momentum coverage
€
I t0,t( ) = M τ − t0( )S t,τ( )dτ0
TS
∫ + B t( )
The scattering law can by reconstructed through the cross correlation
if M(t) obeys
€
AMM τ( ) ≡ 1TS
M t( )M t − τ( )dt = c1 ⋅ δ τ( )0
TS
∫ + c2Energy discrimination
€
C(t1, t) ≡1TS
M(t1 - t0 )I(t0, t)dt00
TS
∫
= c1 ⋅ S(t1, t) + c2 S(t1 - t', t)dt '0
TS
∫ + B(t) ⋅ θ
= c1 ⋅ S(t1, t) +c2
θI(t0, t)dt0
0
TS
∫ + B(t) ⋅ θ - c2
θTS
&
' (
)
* +
M(t)
Full Experiment Simulations with McStas
Sample : harmonic oscillator E0 = ±2 meV, T = 100K
Reconstructed S(Q,ω)Cross
Correlation
Instrument : Corelli (SNS, high resolution water moderator)
Chopper : N = 255; f = 350 Hz; R = 0.26 cm
Raw Data
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21st NSRRC Users’ Mee;ng and Workshops
250
200
150
100
50
0
Sequence O
ffsett (
Channels
)
16000140001200010000800060004000
total time of flight (µS)
2500
2000
1500
1000
500
0
incid
en
t flig
ht
tim
e (µS
)
16000140001200010000800060004000
total time of flight (µS)
elastic inelastic
Comparison with conventional chopperConventional Chopper
360 Hz N=1 c~1%
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21st NSRRC Users’ Mee;ng and Workshops
2500
2000
1500
1000
500
0
incid
ent flig
ht tim
e (µS
)
16000140001200010000800060004000
total time of flight (µS)
2500
2000
1500
1000
500
0
inci
dent
flig
ht ti
me
(µS
)
140001200010000800060004000
total time of flight (µS)
10-9
10-8
10-7
10-6
Inte
nsity
(arb
. uni
ts)
-10 -5 0 5 10energy transfer (meV)
Disc Chopper Ei = 39.6meV Correlation Chopper
Correlation Chopper 350 Hz N=255 c=50%
Gain in efficiency: influence of Bragg Peaks
➡ Gain factor < 1 : less efficient
➡ Gain factor is for a single channel but the correla;on chopper covers many channels simultaneously
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21st NSRRC Users’ Mee;ng and Workshops
1.0
0.8
0.6
0.4
0.2
0.0
norm
aliz
ed in
tens
ity
161412108642
momentum transfer (Å-1)
φ = 90°
76543
momentum transfer (Å-1)
φ = 90°
161412108642
momentum transfer (Å-1)
φ = 90°
harmonic oscillator + Bragg Peaks
corr. chopper
Q
Correla;on method measures all momentum transfers simultaneously
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Internal Stacked Shielding
Control Room
Poured-in-Place Shielding
Mezzanine
Cave Phase 1
Cave Phase 2
Cave Roof
ElectricalPiping
Roll-in Shielding
Beam Stop
21st NSRRC Users’ Mee;ng and Workshops
Sample Scattering Vessel
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Inside of Sample Scattering Vessel
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Radial, oscilla;ng collimatorFeng Ye
Lead Instrument Scien;stYaohua Liu
Instrument Scien;st
21st NSRRC Users’ Mee;ng and Workshops
Cross correlation chopper disk
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21st NSRRC Users’ Mee;ng and Workshops
Instrument commissioning: beam profile
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measured
λ <0.1 A λ ~ 1.2 ± 0.1 A λ ~ 2 ± 0.1 A
λ ~ 3 ± 0.1 A
simulated
λ~ 0.9 Å (100 meV)λ~ 2.85 Å (10 meV)
Cross Correlation in Action
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Reconstructed Scattering FunctionCross Correlation
elastic
Raw Data
inelastic 19
First Results
‣ La0.7Ca0.3MnO3
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‣ PbMn1/3Nb2/3O3-‐30%PbTiO3
The Future
‣ Co-‐refinement of Neutrons and X-‐rays • Complementarity of sca0ering lengths • Sta;c vs dynamic disorder
‣ Increasing use of ab ini4o computa;onal modeling • Allowing more complex systems to be inves;gated • Less dependence on intui;on in modeling
‣ Enhanced analysis tools • Machine learning • Correlated data analysis
‣ High-‐Energy X-‐rays • Absorp;on similar to neutrons • Need high efficiency detectors
e.g. CdTe ‣ Micro-‐diffuse sca0ering
• Benefi;ng from increased brightness of, e.g., APS Upgrade
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