7th canadian powder diffraction workshop, may 2007 characterizing materials using the pdf – thomas...

$: 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Characterization of Materials using the PDF$
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

[email protected]

LA-UR 05-0111



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 ...



Bragg’s worldThe average atomic structure



Bragg’s world: Structure of crystals

Assumes periodicity

Average structure from Bragg peak positions and intensities

sin2dn Bragg’s law



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.



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



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



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.



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)



Diffuse scatteringLocal atomic structure



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



Total scattering ?

Cross section of 50x50x50 u.c. model crystal consisting of 70% black atoms and 30% vacancies !Properties might depend on vacancy ordering !!



Bragg peaks are blind ..

Bragg scattering: Information about the average structure, e.g. average positions, displacement

parameters and occupancies.



Diffuse scattering to the rescue ..

Diffuse scattering: Information about two-body correlations, i.e. chemical short-range order or

local distortions.



See http://www.totalscattering.org/teaching/



How about powder diffraction ?



Finally the Pair Distribution Function (PDF)

The PDF is the Fourier transform of the total scattering diffraction pattern !

Proffen, Z. Krist, 215, 661 (2000)



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



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



Even more theory ..

The atomic pair distribution function, G(r) is the Fourier couple of S(Q):

0

sin]1)([2

)( QrdQQSQrG



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.



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



Examples



Simon BillingeThomas Proffen (LANL)

Peter Peterson (SNS)

Facilities: IPNS, LujanFunding: DOE, NSF

Local atomic strain in ZnSe1-xTex



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 !

¯



ZnSe1-xTex : Total scattering

Behaves like local structure

Behaves like average structure

Peterson et al., Phys. Rev. B63, 165211 (2001)



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



ZnSe1-xTex : Potential based “supercell” modeling

Kirkwood potential



Simon BillingeThomas Proffen (LANL)

Peter Peterson (SNS)Valeri Petkov (CMU)

Facilities: ChessFunding: DOE, NSF

Local structure of WS2



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



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)



Katharine Page

Thomas Proffen

Facilities: LujanFunding: DOE, NASA

Domain structures



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



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.



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%



Xiangyun QiuSimon Billinge

Thomas Proffen

Facilities: LujanFunding: DOE-BES, NSF

High temperature local structure of

LaMnO3



LaMnO3 : Local structure vs. electronic state

JT orbitals are ordered at low-temperature in a checker-board pattern:



LaMnO3 : Crystallography

Orthorhombic-OLarge JT distortion

Less-Orthorhombic-O‘Virtually no JT distortion

RhombohedralNo JT distortion

JT distortion disappears at the O-O’ transition



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).



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



LaMnO3 : Crossover from local to average structure

Varying range refinement– Fix rmin

– Vary rmax

– x axis is rmax

Local

Average

Intermediate???

O

R

O'



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



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)



Katharine Page

Thomas Proffen

Ram SeshadriTony Cheetham

Facilities: LujanFunding: DOE, NASA

“Complete” Structure of Gold Nanoparticles



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



Au nanoparticles : Nano vs. bulk

Experimental PDFs of gold nanoparticles and bulk gold, measured on NPDF.

100Å



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).



Katharine PageChristina Herrera

Thomas ProffenSylvia McLain

Tim DarlingJim TenCate

Facilities: LujanFunding: DOE, NSF

Local structure in sandstone



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



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.



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)



Katharine Page

Thomas ProffenBjorn Clausen

Ersan UstundagSeung-Yub Lee

Facilities: LujanFunding: DOE, NSF

Elastic properties of Bulk-Metallic-Glasses



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



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°°



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 ..



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

PDF



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

7th canadian powder diffraction workshop, may 2007 characterizing materials using the pdf – thomas...

Documents

powder diffraction slide

pdf thomas proffen structure

characterizing materials

powder diffraction data

h structure factor

powder rings

average atomic structure

structure of crystals