NNATUREATURE OFOF THETHE M MONOCLINICONOCLINIC TOTO

CCUBICUBIC P PHASEHASE T TRANSITIONRANSITION IN THE IN THE FFAST AST

OOXYGEN XYGEN IION ON CCONDUCTOR LaONDUCTOR La22MoMo22OO99

(LAMOX) (LAMOX)

Lorenzo MalavasiLorenzo Malavasi, , Simon J.L. Billinge,Simon J.L. Billinge, Gaetano Gaetano Chiodelli, Giorgio Flor, Chiodelli, Giorgio Flor, Hyunjeong J. Kim,Hyunjeong J. Kim, Cristina Cristina

TealdiTealdi

Dipartimento di Chimica Fisica “M. Rolla” – Dipartimento di Chimica Fisica “M. Rolla” –

Università di PaviaUniversità di Pavia

Dipartimento di Chimica Fisica “M.Rolla” e IENI-CNR, Università di Pavia, ITALY

Department of Physics and Astronomy, Michigan State University, USAVI Convegno Nazionale sulla Scienza e Tecnologia dei Materiali – Perugia –

12-15 Giugno 2007

General ConsiderationsGeneral ConsiderationsWHAT IS THE ATOMIC PAIR DISTRIBUTION FUNCTION (PDF)

Atomic Pair Atomic Pair

Density FunctionDensity Function

Atomic Pair Atomic Pair

Distribution Distribution FunctionFunction

gg((rr) GIVES THE PROBABILITY OF FINDING TWO ATOMS ) GIVES THE PROBABILITY OF FINDING TWO ATOMS SEPARATED BY THE DISTANCE SEPARATED BY THE DISTANCE rr

‘g(r) is like a distance map of the inside of the solid’

This is a method of “local” This is a method of “local” crystallography crystallography

Which is the interest for the crystalline Which is the interest for the crystalline solids?solids?

General ConsiderationsGeneral ConsiderationsTHROUGH THE PDF WE CAN STUDY THETHROUGH THE PDF WE CAN STUDY THE LOCAL DEVIATIONSLOCAL DEVIATIONS OF OF

THETHE AVERAGEAVERAGE STRUCTURESTRUCTURE

TRADITIONAL CRYSTALLOGRAPHIC TRADITIONAL CRYSTALLOGRAPHIC METHODSMETHODS

Analysis of Bragg Analysis of Bragg PeaksPeaks

Diffuse ScatteringDiffuse Scattering

TOTAL SCATTERING TECHNIQUETOTAL SCATTERING TECHNIQUE

Bragg Peaks -Bragg Peaks - Diffuse ScatteringDiffuse Scattering

TOTAL SCATTERING STRUCTURE FUNCTION S(Q)

CONTAINS INFORMATION ABOUT THE SHORT-RANGE CONTAINS INFORMATION ABOUT THE SHORT-RANGE AND INTERMEDIATE ORDERAND INTERMEDIATE ORDER

It has a weak dependence with Q and forms a It has a weak dependence with Q and forms a continuous backgroundcontinuous background

Diffuse Scattering is usually discarded in Diffuse Scattering is usually discarded in crystallographic analysiscrystallographic analysis

General ConsiderationsGeneral Considerations

TOTAL SCATTERING STRUCTURE FUNCTION TOTAL SCATTERING STRUCTURE FUNCTION SS(Q) (Q) AND THE AND THE PDFPDF

DIRECTLY MEASURED QUANTITYDIRECTLY MEASURED QUANTITY

Reduced PairReduced Pair

Distribution FunctionDistribution Function

In principle it requires a measure up to Q infinite

5 10 15 20-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

r (Å )

G (

Å -2

)

High Q-range of measure:

HIGH RESOLUTION AND ACCURACY OF THE PDF

General ConsiderationsGeneral ConsiderationsThrough the PDF analysis we can obtain information on:Through the PDF analysis we can obtain information on:

Direct Information from the PDFDirect Information from the PDF

Atom-Pair Separation from Peak Positions

Coordination Number from Peak Integrated Intensity

Atom-Pair Probability Distribution from the Peak-Shape

Additional Information and Advanced ModellingAdditional Information and Advanced Modelling

Joint Real- and Reciprocal-Space Refinements

Difference Modelling

Experimental Details – Data Experimental Details – Data CollectionCollection

Neutron Scattering ExperimentNeutron Scattering Experiment

SPALLATION NEUTRON SOURCESSPALLATION NEUTRON SOURCES

Large Flux of EPITHERMAL Neutrons Large Flux of EPITHERMAL Neutrons Short-wavelength Short-wavelength High-Q (up to 100 ÅHigh-Q (up to 100 Å-1-1))

AACCURACY IN THE CCURACY IN THE DDETERMINATION OFETERMINATION OF QQ--VVALUESALUES

AACCURACY IN THE CCURACY IN THE DDETERMINATION OF ETERMINATION OF INTENSITYINTENSITY

SOURCE LOCATION INSTRUMENT

Intense pulsed neutron

source (IPNS) Argonne National Lab. - USA SEPD, GLAD, GPPD

ISIS Rutherford Appleton Lab - UK POLARIS, GEM

KENS Tsukuba, JP HTT-II

Spallation Neutron Source (SNS) Los Alamos National Lab. – USA HIPD, HIPPO, NPDF

X-ray Scattering ExperimentX-ray Scattering Experiment

LABORATORY SOURCESLABORATORY SOURCES

Experimental DetailsExperimental Details

SOURCE SOURCE EE00 (keV) (keV) λλ ( (Å)Å) QQmaxmax (Å (Å-1-1))

Cu 8.05 1.538 8.0Mo 17.48 0.708 17.5Ag 22.16 0.559 22.0W 59.32 0.209 59.0

Short Q-range -Short Q-range - Long acquisition timeLong acquisition time - Relatively - Relatively low-resolutionlow-resolution

SYNCHROTRON SOURCESSYNCHROTRON SOURCES

Second Generation Sources Can Be Used (relatively low real-space resolution)

TTHIRD HIRD GGENERATION ENERATION SSOURCES (CHESS, ESRF; APS and Spring8) OURCES (CHESS, ESRF; APS and Spring8) QQ-max 50 -max 50 ÅÅ-1-1

Experimental DetailsExperimental Details

RREQUIREMENTS:EQUIREMENTS:

Time-stable incident fluxTime-stable incident flux

Low Background (collimation and shielding)Low Background (collimation and shielding)

Stable Detectors and Detectors ElectronicStable Detectors and Detectors Electronic

Stable Beam MonitorStable Beam Monitor

Stable ModeratorStable Moderator

Solid State Detectors (preferred – X-rays)Solid State Detectors (preferred – X-rays)

Care in the instrument alignement Care in the instrument alignement

Experimental Details – Data Experimental Details – Data AnalysisAnalysis OBTAIN THE NORMALIZED TOTAL OBTAIN THE NORMALIZED TOTAL

SCATTERING STRUCTURE FUNCTION SCATTERING STRUCTURE FUNCTION S(Q)S(Q)

Measured Intensity Measured Intensity Scattering from the Sample and Scattering from the Sample and from the “Addenda”from the “Addenda”

Addenda is Modified by Sample Absorption

Multiple Scattering (in the sample and apparatus)

Normalization to the Incident Flux

Polarization Effects

Sample Absorption ...

ANY IMPERFECTION IN THE CORRECTION WILL AFFECT THE ANY IMPERFECTION IN THE CORRECTION WILL AFFECT THE OUTCOMEOUTCOME

Good News:Good News: Most of the Corrections Can Be Reliably EstimatedMost of the Corrections Can Be Reliably Estimated

The structural Information in the PDF is “fairly The structural Information in the PDF is “fairly robust” with respect to robust” with respect to analysys errors (slowly varying analysys errors (slowly varying with Q)with Q)

Experimental Details – Data Experimental Details – Data AnalysisAnalysisOOBTAIN THE BTAIN THE PDFPDF FROM THE FROM THE DDIFFRACTION IFFRACTION EEXPERIMENT XPERIMENT

(PDFgetX(PDFgetX11 – PDFgetN – PDFgetN22))

[1] Peterson, P. F. et al., [1] Peterson, P. F. et al., J. Applied CrystallographyJ. Applied Crystallography (2000), (2000), 3333, 1192., 1192.[2] Jeong, I. K. et al., [2] Jeong, I. K. et al., J. Applied CrystallographyJ. Applied Crystallography (2001), (2001), 3434, 536., 536.[3] Proffen, Th. Et al., J. Applied CrystallographyJ. Applied Crystallography (1999), (1999), 3232, 572., 572.[4] Proffen, Th. Et al., J. Applied CrystallographyJ. Applied Crystallography (1997), (1997), 3030, 171., 171.

CCALCULATE THE ALCULATE THE PDFPDF FROM A FROM A SSTRUCTURAL TRUCTURAL MMODELODEL

RREAL EAL SSPACE PACE RRIETVELD IETVELD AANALYSISNALYSIS

PDFFITPDFFIT33

RREVERSE MEVERSE MONTE-ONTE-CCARLOARLO

DISCUSSDISCUSS44

IntroductionIntroduction

1. FUORITE TYPE (stabilized zirconia, ceria, δ-Bi2O3)

2. PEROVSKITES (doped LaGaO3)

3. INTERGROWTH PEROVSKITE/BI2O2 LAYERS (BIMEVOX)

4. PYROCHLORES (Gd2Zr2O7, Gd2Ti2O7)

5.LAMOX

OXIDE ION CONDUCTORS

103/T (K-1)

0.9 1.0 1.1 1.2 1.3 1.4

log

[

-1 c

m-1]

-5

-4

-3

-2

-1

T (°C)

400 450 500 550 600 650 700

DT

A (

mW

)

-4

-2

0

4

6

8

10

12

542°C

563°C

αα ββ Transition Transition (monoclinic to cubic) at (monoclinic to cubic) at ~550°C~550°C

Introduction - StructureIntroduction - Structureββ -LAMOX (cubic)-LAMOX (cubic)

Crystal data

Crystal system cubicSpace group P213 (no. 198)Unit cell dimensions a = 7.2421(2) ÅCell volume379.83(1) Å3

Z = 4

Atomic coordinates

Atom Wyck. Occ. x y zLa1 4a 1.00 0.8501(5) 0.8501(5) 0.8501(5)Mo1 4a 1.00 0.1613(8) 0.1613(8) 0.1613(8)O1 4a 1.00 0.3155(8) 0.3155(8) 0.3155(8)O2 12b 0.66 0.9875(9) 0.1724(15) 0.3266(14)O3 12b 0.34 0.9152(28) 0.6213(27) 0.5670(18)

F. Goutenoire et al., J. Mater. Chem. 2001, 11; 119.

Introduction - StructureIntroduction - Structureββ -LAMOX (cubic)-LAMOX (cubic)

• Short O-O bond lenghts;

• Partial Occupancy of O2 and O3 sites

• Very high B-factors in O2 and O3

Bond-lengths J. Mater. Chem. 2001

Mo-O1 1.83(2) [1]

Mo-O2 1.77(3) [3]

Mo-O3 1.73(4) [3]

O1-O3 2.79(2) [3]

O1-O2 2.574(7) [3]

O1-O2 2.789(8) [3]

O2-O3 1.54(3) [1]

O2-O3 2.30(2) [1]

O2-O3 2.86(2) [1]

O2-O3 2.68(2) [1]

O2-O3 1.54(3) [1]

O3-O3 1.74(2) [2]

CONDUCTION MECHANISM CONDUCTION MECHANISM INVOLVING O2 AND O3 SITESINVOLVING O2 AND O3 SITES

Introduction - StructureIntroduction - Structureαα -LAMOX (monoclinic)-LAMOX (monoclinic)

I.R. Evans et al., Chem. Mater. 2005, 17; 4074.

2 3 4 Superstructure Relative to the Cubic

High-temeprature Form and Small Monoclinic

Distortion

Introduction - StructureIntroduction - StructureLaLa22MoMo22OO99 (LAMOX) (LAMOX)

αα ββ Transition Transition (monoclinic to cubic) at (monoclinic to cubic) at ~560°C~560°C

ββ--SnWOSnWO44 ββ--LaLa22MoMo22OO99

ββ--SnWOSnWO44 ββ--LaLa22MoMo22OO9 9 αα--LaLa22MoMo22OO99

I.R. Evans et al., Chem. Mater. 2005, 17; 4074.

LAMOX – Some ResultsLAMOX – Some Results

Neutron Diffraction Reveals Significant Contribution from

Diffuse Scattering

500°500°CC

600°600°CC

NPDF Measurements at 500 and 600°C NPDF Measurements at 500 and 600°C (before and after (before and after the the ααββ transition) transition)

d-space

MMONOCLINICONOCLINIC

CCUBICUBIC

L. Malavasi et al., J. Am. Chem. Soc. 2007, 129, 6903

LAMOX – Some ResultsLAMOX – Some ResultsCCOMPARISONOMPARISON OFOF PDF PDF AT THEAT THE T TWOWO T TEMPERATURESEMPERATURES

THE LOCAL STRUCTURES ARE THE LOCAL STRUCTURES ARE SIMILARSIMILAR, EVEN THOUGH THE , EVEN THOUGH THE

AVERAGE ONES ARE MARKEDLY AVERAGE ONES ARE MARKEDLY DIFFERENTDIFFERENT

G (Å

-2)

-2

-1

0

1

2600°C 500°C

r (Å)

2 4 6 8 10 12 14 16 18 20

G (Å

-2)

-2

-1

0

1

2

3Monoclinic ModelCubic Model

EXPECTED CHANGE TO THE EXPECTED CHANGE TO THE PDFPDF FOR A CHANGE IN THE FOR A CHANGE IN THE LOCAL STRUCTURE FROM LOCAL STRUCTURE FROM MONOCLINIC TO CUBICMONOCLINIC TO CUBIC

The use of “reasonable “ a.d.p. leads to sharp peaks in the

calculated PDF

LAMOX – Some ResultsLAMOX – Some Results

-2

-1

0

1

2

G (Å

-2)

-2

-1

0

1

2

r (Å)5 10 15 20

-4

-2

0

A

B

C

500°C Data Fitted with 500°C Data Fitted with the Monoclinic Modelthe Monoclinic Model

RRwpwp 14.7% 14.7%

600°C Data Fitted with 600°C Data Fitted with the Monoclinic Modelthe Monoclinic Model

RRwpwp 15.5% 15.5%

600°C Data Fitted with 600°C Data Fitted with the Cubic Modelthe Cubic Model

RRwpwp 38.4% 38.4%

Fit Parameters: a, b, c, γ, and

LAMOX – Some ResultsLAMOX – Some Results

5 10 15 20-3

-2

-1

0

1

G (Å

-2)

r (Å)

RRwpwp 20.0% 20.0%

Fit Parameters: a, b, c, γ, and and Atomic

Positions and a.d.p.Parameter

Rietveld Refinement Fit of Figure 4

Lattice parameter 7.21788(8) 7.2220(3)

La, x 0.8543(3) 0.8575(2)

Uiso 0.065(7) 0.1004(8)

Mo, x 0.1682(2) 0.1754(2)

Uiso 0.057(6) 0.0750(4)

O1, x 0.3147(4) 0.3103(2)

Uiso 0.093(3) 0.0578(6)

O2, x 0.9933(5) 0.9859(2)

O2, y 0.1875(9) 0.1615(3)

O2, z 0.3438(5) 0.3455(2)

Uiso 0.088(4) 0.0614(5)

O3, x 0.894(1) 0.9830(3)

O3, y 0.698(6) 0.7531(3)

O3, z 0.553(1) 0.4950(3)

Uiso 0.33(3) 0.0310(7)

Rwp (%) 2.99 18.7

Meaningless Occupancies…

SOME DEFICIENSIS IN THE SOME DEFICIENSIS IN THE MODELMODEL

The Local Structure of the Cubic Model is Basically the Same as in The Local Structure of the Cubic Model is Basically the Same as in the Monoclinic Structurethe Monoclinic Structure

The Monoclinic Cubic Phase Transition is a transition from long-range ordered to a dynamic short range-ordered distribution of

the oxygen defects while preserving the monoclinic local structure

LAMOX – ConclusionLAMOX – Conclusion

Monoclinic Structure = Mo-O Monoclinic Structure = Mo-O polyhedra with coordination 4, 5 and polyhedra with coordination 4, 5 and

66

Cubic Structure = 4.5Cubic Structure = 4.5

Local change with time of the Mo-O Local change with time of the Mo-O coordinationcoordination

Conduction Mechanims from a Conduction Mechanims from a “donor” to an “acceptor” polyhedra“donor” to an “acceptor” polyhedra

Mo-O-Vo-Mo distance is roughly the Mo-O-Vo-Mo distance is roughly the same as Mo-O2-O3-Mo same as Mo-O2-O3-Mo

LAMOX – ConclusionLAMOX – Conclusion

First application of the atomic-pair distribution function analysis to the study of an oxygen fast-oxide ion conductor

A clear and reliable description of the local atom arrangement in LAMOX structure can be only achieved through the application of a local probe such as the PDF

We directly determined that the transition from the monoclinic to the cubic phase of LAMOX is a transition from a static to a dynamic distribution of the oxygen defects while preserving the monoclinic local structure

Useful tool to study the solid state ionics materials in order to obtain a more detailed description of their local structure which can lead to a better comprehension of the structure-property correlation