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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
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