7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Characterization of Materialsusing the PDF
Thomas ProffenManuel Lujan Jr. Neutron Scattering Center
Los Alamos National Laboratory
LA-UR 05-0111
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Why do we care about the atomic structure?
Diamond– hard– transparent– insulating– expensive
Graphite– soft– black– metallic– cheap
The atomic structure has a profound influence on the properties of materials. Consider carbon ...
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Bragg’s worldThe average atomic structure
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Bragg’s world: Structure of crystals
Assumes periodicity
Average structure from Bragg peak positions and intensities
sin2dn Bragg’s law
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
The condition for a Bragg-peak to appear is:
or
The intensity of the Bragg peak is given by the square of the “Structure factor”:
The sum running over atoms in the unit cell.
Bragg’s world: Theory
sin2dn
hklKkkQ '
ii
iiebF rQ
K.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
All orientations of crystallites possible.
Powder Diffraction gives Scattering on Debye-Scherrer Cones
Incident beamx-rays or neutrons
Sample
(111)
(200)
(220)
Bragg’s world: Powder Diffraction
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Io - incident intensity - variable for fixed 2Q
kh - scale factor for particular phase
F2h - structure factor for particular reflection
mh - reflection multiplicity
Lh - correction factors on intensity - texture, etc.
P(Dh) - peak shape function – includes
instrumental resolution,
crystallite size, microstrain, etc.
Ic = Io{khF2hmhLhP(h) + Ib}
Rietveld refinement technique
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Structure from powder diffraction
Determination of the atomic structure using diffraction has revolutionized our knowledge about how materials work ..
Zn insulin structure (> 1600 atoms in unit cell) determined from powder diffraction data (R.B. van Dreele)
Average structure determined using Bragg reflections.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Bragg’s world: Information beyond the average structure
Bragg profiles: size,size distribution and shapeof crystallites, and strain.
Intensity along powder rings: texture and preferred orientation.
Accessible using modern Rietveld refinement programs. From Ungár, et al, Carbon 40, 929 (2002)
Texture of Ti wire plate(Lujan Center)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Diffuse scatteringLocal atomic structure
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Traditional crystallographic approach to structure determination is insufficient or fails for
– 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 (-> badly defined Bragg peaks)
A new approach to determine local and nano-scale structures is needed.
Nanostructures: Science (290) 2000
The challenge of real materials: Knowing the local structure
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Total scattering ?
Cross section of 50x50x50 u.c. model crystal consisting of 70% black atoms and 30% vacancies !Properties might depend on vacancy ordering !!
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Bragg peaks are blind ..
Bragg scattering: Information about the average structure, e.g. average positions, displacement
parameters and occupancies.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Diffuse scattering to the rescue ..
Diffuse scattering: Information about two-body correlations, i.e. chemical short-range order or
local distortions.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
See http://www.totalscattering.org/teaching/
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
How about powder diffraction ?
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Finally the Pair Distribution Function (PDF)
The PDF is the Fourier transform of the total scattering diffraction pattern !
Proffen, Z. Krist, 215, 661 (2000)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Theory again – no periodicity this time !
Elastic Scattering amplitude (from quantum mechanics)
The potential is given by
Where the sum is over all atoms in the sample and
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
More theory ..
Rewrite the scattering factor equation substituting R and change the order of integration:
For neutrons:
and
“Structure factor” “Form factor”
ji
iji
c jiebbNd
d
,
.1 rrQ
2
22
2
1)(
b
bb
d
d
bS c
Q
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Even more theory ..
The atomic pair distribution function, G(r) is the Fourier couple of S(Q):
0
sin]1)([2
)( QrdQQSQrG
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
What is a PDF?
Example: C60 - ‘Bucky balls’
The PDF (similar to the Patterson) is obtained via Fourier transform of the normalized total scattering S(Q):
/sin4Q
Intra-domain
Inter-domain
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Examples
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Simon BillingeThomas Proffen (LANL)
Peter Peterson (SNS)
Facilities: IPNS, LujanFunding: DOE, NSF
Local atomic strain in ZnSe1-xTex
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
ZnSe1-xTex : Structure
Zinc 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 !
¯
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
ZnSe1-xTex : Total scattering
Behaves like local structure
Behaves like average structure
Peterson et al., Phys. Rev. B63, 165211 (2001)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results.
ZnSe1-xTex : Nearest neighbors and Z-plots ..
Local bond length
Average
bond length
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
ZnSe1-xTex : Potential based “supercell” modeling
Kirkwood potential
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Simon BillingeThomas Proffen (LANL)
Peter Peterson (SNS)Valeri Petkov (CMU)
Facilities: ChessFunding: DOE, NSF
Local structure of WS2
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
W
S
WS2 : Structure of the “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
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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
S
Pristine WS2:
HexagonalP63/mmc
Petkov et al., J. Am. Chem. Soc. 122, 11571 (2001)
“Restacked” WS2:
MonoclinicP1121
(disordered derivative of WTe2)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Katharine Page
Thomas Proffen
Facilities: LujanFunding: DOE, NASA
Domain structures
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Domain structures : Simulated example
Simulated structure of 20x20x20 unit cells.
Matrix (M): blue atoms
Domains (D): red atoms, spherical shape, d=15Å.
Simulated using DISCUS.
Proffen & Page, Z. Krist. (2004), in press
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Domain structures : Pair Distribution Function
M-M
M-M
D-D
r < Domain size:Mainly D-D and M-M pairs
r > Domain size:NO D-D contribution.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Domain structures : R-dependent refinements
Top: Refinement of single-phase model with blue/red fractional occupancies (O).
Bottom: Refinement of same model for 5Å wide sections.
Extensions:– Multi phase models– Modeling of boundary– R-dependent refinable
mixing parameters
Domain radius
O=29% O=16% O=15% O=15% O=15%
O=15%
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Xiangyun QiuSimon Billinge
Thomas Proffen
Facilities: LujanFunding: DOE-BES, NSF
High temperature local structure of
LaMnO3
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : Local structure vs. electronic state
JT orbitals are ordered at low-temperature in a checker-board pattern:
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : Crystallography
Orthorhombic-OLarge JT distortion
Less-Orthorhombic-O‘Virtually no JT distortion
RhombohedralNo JT distortion
JT distortion disappears at the O-O’ transition
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : T-dependence of Mn-O bond distribution
Two Mn-O peaks persist up to the highest T measured
Thermal broadening appears to be the ONLY contributor to peak profile changes
Local JT distortion exists in both high T orthorhombic (pseudo-cubic) and rhombohedral phase
Two Gaussian curves fit the data very well
Xiangyun Qiu, Th. Proffen, J. F. Mitchell and S. J. L. Billinge, Phys. Rev. Lett. 94, 177203 (2005).
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : T-dependence of Mn-O bond distribution
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).
Short-bonds
Long-bonds
Average structureLocal structure
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : Crossover from local to average structure
Varying range refinement– Fix rmin
– Vary rmax
– x axis is rmax
Local
Average
Intermediate???
O
R
O'
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
LaMnO3 : Crossover from local to average structure
Assume the PDF “form-factor” for a sphere
Take asymptotic values to be low-r result from peak fitting and the high-r result from Rietveld
Three curves are self-consistently fit with one parameter – the diameter of the spherical domain
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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!)
Xiangyun Qiu, Th. Proffen, J. F. Mitchell and S. J. L. Billinge, Phys. Rev. Lett. 94, 177203 (2005).
rmax(Ǻ)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Katharine Page
Thomas Proffen
Ram SeshadriTony Cheetham
Facilities: LujanFunding: DOE, NASA
“Complete” Structure of Gold Nanoparticles
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Au nanoparticles : Why PDF ?
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 nm50 nm
2nm2nm
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
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Au nanoparticles : Nano vs. bulk
Experimental PDFs of gold nanoparticles and bulk gold, measured on NPDF.
100Å
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Au nanoparticles : Structural refinements
PDF from nano- and bulk gold refined using PDFFIT.
Nanoparticles show “normal” gold structure.
No indication of
surface relaxations.
abulk < anano
Indication of Au-cap distances
-4
0
4
8
12
16
2 3 4 5 6 7 8 9 10
r (Å)
G(r
) (
Å-2
)
10 K FCC Model
Au-capping layer distance (Au-S)
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. , accepted (2004).
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Katharine PageChristina Herrera
Thomas ProffenSylvia McLain
Tim DarlingJim TenCate
Facilities: LujanFunding: DOE, NSF
Local structure in sandstone
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Sandstone: Local structure
Refinement of single phase quartz model.
Good agreement above r > 3Å.
Missing “intensity” in first two PDF peaks corresponding to Si-O and O-O NN distances.
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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 ?
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 ?, Geophysical Research Lett. 31, L24606 (2004)
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Katharine Page
Thomas ProffenBjorn Clausen
Ersan UstundagSeung-Yub Lee
Facilities: LujanFunding: DOE, NSF
Elastic properties of Bulk-Metallic-Glasses
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
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
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
BMG : Experiment
The amorphous BMG matrix does not give rise to Bragg peaks => PDF !
Experiment on SMARTS
The BMG is compressed along one axis, causing atoms along the other to expand
Detector Banks at +90 and –90 degrees receive scattering from separate distortions
BMG
BMGBeam
+90+90°°
-90-90°°
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
BMG : Result
-0.5
0
0.5
1
1.5
2
2.5
2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.75 2.8 2.85
r (Å)
G(r
) (Å
-2
)
+90+90°°
-90-90°°10 MPa
500 MPa
1500 MPa
Work in progress ..
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
BMG: Phase analysis on composite sample
Ability to distinguish between phases– Difference between measured composite PDF and calculated Tungsten PDF agrees well with measured BMG
7th Canadian Powder Diffraction Workshop, May 2007
Characterizing materials using the PDF – Thomas Proffen
Summary and more information
Analysis of total scattering gives valuable insight in structure properties relationship
High-resolution instruments open the door to medium-range order investigations
Obtain structural information from disordered crystalline, amorphous of composite materials
Fast powder measurements allow systematic exploration of local structure as function of T, x, P
http://www.totalscattering.org