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Total Scattering The Key to Understanding disordered, nano -crystalline and amorphous materials. Tutorial 9 th Canadian Powder Diffraction Workshop. Thomas Proffen Diffraction Group Leader [email protected]. Friday 25th May 2012. All cartoons by Julianne Coxe . About your instructor . - PowerPoint PPT Presentation
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Total Scattering The Key to Understanding
disordered, nano-crystalline and amorphous materials.
Tutorial9th Canadian Powder Diffraction Workshop
Thomas ProffenDiffraction Group Leader
2 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Friday 25th May 2012
9:00 - 9:45 Beyond the Bragg peaks or why do we care about total scattering?
9:45 - 10:30 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 byJulianne Coxe.
3 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
About your instructor ..
PDF Master of theUniverse
4 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Why Total Scattering ?
S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science 316, 561 (2007).
5 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Bragg’s world: Structure of crystals
Assumes periodicity
Average structure from Bragg peak positions and intensities
sin2dn Bragg’s law
6 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
The challenge : Knowing the local structureTraditional crystallographic approach to
structure determination is insufficient or fails for
Non crystalline materials Disordered materials: The interesting
properties are often governed by the defects or local structure !
Nanostructures: Well defined local structure, but long-range order limited to few nanometers (-> poorly defined Bragg peaks)
A new approach to determine local and nano-scale structures is needed.
S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science 316, 561 (2007).
7 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
?Idea / drawing by Emily Tencate
Emily’s corner soon coming to http://totalscattering.lanl.gov
Judging by the average ..• Analysis of Bragg intensities yields the average structure of materials which can be deceiving !
• Consider going to a party where all you know is the average age is 40 ...
8 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Total scattering ?
Cross section of 50x50x50 u.c. model crystal consisting of 70% black atoms and 30% vacancies !Properties might depend on vacancy ordering !!
9 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Bragg peaks are blind ..Bragg scattering: Information about the average structure, e.g. average positions, displacement
parameters and occupancies.
10 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Diffuse scattering to the rescue ..Diffuse scattering: Information about two-body
correlations, i.e. chemical short-range order or local distortions.
11 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
How about powder diffraction ?
12 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Finally the Pair Distribution FunctionThe PDF is the Fourier transform of the total scattering diffraction pattern !
Proffen, Z. Krist, 215, 661 (2000)
13 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
What is a PDF?
5.11Å4.92Å
4.26Å
3.76Å
2.84Å
2.46Å
1.42Å
Pair distribution function (PDF) gives the probability of finding an atom at a distance “r” from a given atom.
14 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
The PDF at room temperature shows R3m bond distances at low r, instead of P4mm character expected from the average structure.
RT NPDF data
R3mP4mm
Bulk BaTiO3 – average vs. local structure
15 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Simon Billinge (Columbia)Thomas Proffen (LANL)Peter Peterson (SNS)
Example:Local atomic strain in ZnSe1-xTex
16 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
ZnSe1-xTex : StructureZinc blend structure (F43m)
Technological important : Electronic band gap can be tuned by the composition x.
Bond length difference Zn-Se and Zn-Te strain.
Local structural probe required !
17 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
ZnSe1-xTex : Total scattering
Behaves like local structure
Behaves like average structure
Peterson et al., Phys. Rev. B63, 165211 (2001)
18 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results.
ZnSe1-xTex : Nearest neighbors
19 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Simon BillingeThomas Proffen (LANL)
Peter Peterson (SNS)Valeri Petkov (CMU)
Facilities: ChessFunding: DOE, NSF
Example:Local structure of WS2
20 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
W
S
WS2: Structure of “restacked” material• WS2 useful as a lubricant,
catalyst, solid-state electrolyte.
• Exfoliated and restacked WS2 has a metastable disordered structure. Disorder precluded a full structural solution.
• PDF can help …
?
0 10 20 30 40 50 60 70 80 900
5
10
15
20
25NSLS, =0.413 Å
Inte
nsity
, a.u
.
Bragg angle, 2
40 50 60 700
1
2
3
Pristine WS2
10 20 30 40 50 60 70 80 900
2
4
6
8
10CHESS, =0.202 Å
Inte
nsity
, a.u
.
Bragg angle, 2
40 50 60 700.0
0.1
0.2
0.3
0.4
0.5
“Restacked” WS2
21 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
WS2 : PDF to the rescue
0 2 4 6 8 10 12 14 16 18-1.0
-0.5
0.0
0.5
1.0
1.5
Distance r (Å)
G(Å
-2)
0 2 4 6 8 10 12 14 16 18
-1
0
1
2
3G
(Å-2)
Distance r (Å)
W
SPristine WS2:
HexagonalP63/mmc
Petkov et al., J. Am. Chem. Soc. 122, 11571 (2001)
“Restacked” WS2:
MonoclinicP1121
(disordered derivative of WTe2)
22 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Katharine Page
Thomas ProffenSylvia McLainTim DarlingJim TenCate
Facilities: LujanFunding: DOE, NSF
Example:Local atomic in sandstone
23 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Sandstone: Crystalline quartz ?
• Measured on NPDF
• High statistics data (24 hrs)• Solid rock sample• Ambient conditions – sealed to avoid taking up of water
• Motivation: Structural explanation for non-linear acoustic properties
24 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
PDFfit: Refinement of a small model• “Real space Rietveld”
• Refinement of structural parameters: lattice parameters, atom positions, occupancies, adp’s, ..
• Small models (<200 atoms).
• Corrections for Qmax, instrument resolution, correlated motion.
• Software: PDFfit, PDFfit2 and PDFGui.
K.L. Page, Th. Proffen, S.E. McLain, T.W. Darling and J.A. TenCate, Local Atomic Structure of Fontainebleau Sandstone: Evidence for an Amorphous Phase ?, Geophys. Res. Lett. 31, L24606 (2004).
Example: Is sandstone simply quartz ?
25 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Sandstone: Local structure
Refinement of two phases : Crystalline quartz “Amorphous” quartz
up to 3Å
Good agreement over complete range
Amorphous regions “stress formed” by point like contacts at grain contacts ?
26 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Katharine Page
Thomas ProffenBjorn Clausen
Ersan UstundagSeung-Yub Lee
Facilities: LujanFunding: DOE, NSF
Example:Elastic properties of bulk metallic glasses
27 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
BMG : Properties
http://www.its.caltech.edu/~matsci/wlj/wlj_research.html
High Specific Strength Light Weight High Elastic Strain High Hardness Excellent Wear Resistance Excellent Corrosion Resistance
BMG’s are prone to catastrophic failure during unconstrained loading due to the formation of macroscopic shear bands
Crystalline reinforcements to suppress the formation of macroscopic shear bands
28 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
BMG: Phases in composite sample
• Ability to distinguish between phases - Difference between measured composite PDF and calculated Tungsten PDF agrees well with measured BMG PDF
29 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Simon BillingeEmil Bozin
Xiangyn Qiu
Thomas Proffen
Example:Local structure in LaxCa1-xMnO3
30 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
LaMnO3: Jahn-Teller distortion
• Mn-O bond lengths are invariant with temperature, right up into the R-phase
• JT distortions persist locally in the pseudocubic phase
• Agrees with XAFS result: M. C. Sanchez et al., PRL (2003).
Average structureLocal structure
Jahn Teller Long Mn-O bond
31 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
X. Qiu, Th. Proffen, J.F. Mitchell and S.J.L. Billinge, Orbital correlations in the pseudo-cubic O and rhombohedral R phases of LaMnO3, Phys. Rev. Lett. 94, 177203 (2005).
Refinement as function ofatom-atom distance r !
32 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
LaMnO3 : T-dependence of orbital clusters from PDF
• Diameter of orbitally ordered domains above TJT is 16Ǻ
• Appears to diverge close to TJT
• Red lines are a guide to the eye (don’t take the fits too seriously!)
rmax(Ǻ)
33 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
LaMnO3: Simplicity of the PDF approach
30s
Distortions persist locally!
700 K data (blue) vs 750 K data (red)
34 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
35 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
La1-xCaxMnO3: Phase diagram
• Phase diagram draws itself from the parameters.
• Unexpected detail emerges and demands interpretation.
FM
PI
Atomic displacement parameter (ADP) for Oxygen(measure for thermal and static deviations from site)
36 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Local structureAverage structure
Mn-O long bond
ADPOxygen
La1-xCaxMnO3: Phase diagram
37 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Example:“Complete” structure of
Gold Nanoparticles
Katharine PageRam Seshadri
Tony Cheetham
Thomas Proffen
38 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Gold nanoparticles• Nanoparticles often show different
properties compared to the bulk.
• Difficult to study via Bragg diffraction (broadening of peaks).
• PDF reveals “complete” structural picture – core and surface.
• This study:– 5nm monodisperse Au nanoparticles– 1.5 grams of material– Neutron measurements on NPDF
50 nm
2nm
0
10
20
30
40
50
1 - 1.9 2 - 2.9 3 - 3.9 4 - 4.9 5 - 5.9 6 - 6.9
Num
ber
Grain size [nm]
Total = 148Average grain size = 3.6 nm
39 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Gold nanoparticles: First NPDF data
Bulk gold
Gold nanoparticles
Average diameter ~3.6nm
K.L. Page, Th. Proffen, H. Terrones, M. Terrones, L. Lee, Y. Yang, S. Stemmer, R. Seshadri and A.K. Cheetham, Direct Observation of the Structure of Gold Nanoparticles by Total Scattering Powder Neutron Diffraction, Chem. Phys. Lett. 393, 385-388 (2004).
40 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
Nanoparticles: Particle size
33 112 2r rR R
NanogoldInstrument resolution
Spherical particle envelope
41 Managed by UT-Battellefor the U.S. Department of Energy 9th Canadian Powder Diffraction Workshop – May 23-25, 2012
University of Saskatchewan, Saskatoon.
We’re dealing with a length scale that can be simulated on an atom by atom basis, perhaps opening the door to extremely detailed refinements.
Au nanoparticles: Particle size
