advances in single crystal diffuse...

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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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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Bragg Scattering vs Diffuse Scattering

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Bragg ScatteringAverage Structure

Diffuse ScatteringDeviations from the Average Structure


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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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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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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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)


12

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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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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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


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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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)


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)


Vacancy Short-Range Order in MulliteA First-Principles Approach

35

Lowest Energy 3:2 Mullite Structurefrom Kinetic Monte Carlo Calculation

Peter Zapol & Anh Ngo


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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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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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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)

39


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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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

42


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


Huang Scattering as a Function of (Qh, Qk, Ql)

43


Expanding the Concept of a Data Set

44

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


45

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.

46


+=

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

47


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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16

Efficient Elastic Discrimination

49


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

50


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


elastic inelastic

Comparison with conventional chopperConventional Chopper

360 Hz N=1 c~1%

51


2500

2000

1500

1000

500

0

incid

ent flig

ht tim

e (µS

)

16000140001200010000800060004000


2500

2000

1500

1000

500

0

inci

dent

flig

ht ti

me

(µS

)

140001200010000800060004000


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

52


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


φ = 90°

161412108642


φ = 90°

harmonic oscillator + Bragg Peaks

corr. chopper

Q

Correla;on method measures all momentum transfers simultaneously


53


54

Internal Stacked Shielding

Control Room

Poured-in-Place Shielding

Mezzanine

Cave Phase 1

Cave Phase 2

Cave Roof

ElectricalPiping

Roll-in Shielding

Beam Stop


Sample Scattering Vessel

55


Inside of Sample Scattering Vessel

56

Radial, oscilla;ng collimatorFeng Ye

Lead Instrument Scien;stYaohua Liu

Instrument Scien;st


Cross correlation chopper disk

57


Instrument commissioning: beam profile

58

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

59


Reconstructed Scattering FunctionCross Correlation

elastic

Raw Data

inelastic 19

First Results

‣ La0.7Ca0.3MnO3

60


‣ 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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