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Analysis of X-ray total scattering data: from raw data to pair

distribution functions

Lars Ehm

National Synchrotron Light Source

Brookhaven National Laboratory

Mineral Physics InstituteStony Brook University

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Conventional structure solution techniques fail!

• Size effects– Severely peak broadening

• Reduced structural coherence– No/reduced long range order– Surface effects

• Short-range order– Diffuse scattering

Why X-ray total scattering?

Jørgensen et al J. Appl. Cryst. 36, 2003

Redfern et al Phys. Chem. Min. 2005

• Why do conventional crystallographic techniques fail?

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Why X-ray total scattering?

• Large amount of diffuse scattering– Deviation from the 3D ordered average structure

Redfern et al Phys. Chem. Min. 2005

TiO2 nano-crystals

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Total scattering

S(Q, )

1

2hG(r, t)exp{(i(Q r t)} dr dt

Experimentally observable total structure factor:

Total scattering Bragg and diffuse scattering

Fourier transform Pair Distribution Function

What do we get from PDF?

– Probabilities of finding atom pairs separated by distance r

•Short, intermediate, and long-range structure

Nanocrystalline materials

•Fit structural models

•Crystal size

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Data collection • High Energy X-rays

– E~100 keV Large Q • Area detector• Collection

– Background– Sample container– Sample +container

• 2D1D Fit2D– Polarization correction– Masking of

contributions from sample container

X-ray

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Programs

• PDFgetX2– X. Qiu, J. W. Thompson, and S. J. L. Billinge,

PDFgetX2: A GUI driven program to obtain the pair distribution function from X-ray powder diffraction data, J. Appl. Cryst. 37, 678 (2004)

• http://www.pa.msu.edu/cmp/billinge-group/programs/PDFgetX2/

• PDFGui– C. L. Farrow, P. Juhas, J. W. Liu, D. Bryndin, E. S. Bozin,

J. Bloch, Th. Proffen and S. J. L. Billinge, PDFfit2 and PDFgui: computer programs for

studying nanostructure in crystals, J. Phys.: Condens. Matter 19, 335219 (2007)

• http://www.diffpy.org/

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• Data input

• Experimental parameter– Wavelength– Polarization (done in

Fit2D)– In-house

• Monochromator • Analyzer

• Notes Header of output files

Experimental parameters• Platform independent

– IDL virtual Machine• Python routines

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Sample Information• Sample geometry

– Many options– Absorption correction

• Sample– Stoichiometry– Linear attenuation

coefficient– Scattering factors

• Tabulated (neutral, ions)• Dispersion parameter

f1,f2• User input

• Additional information– Not used in normalization

• Data setup

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Data Normalization• Corrections for normalization

– I(Q) S(Q)

• Corrections– Ruland width:

• energy width of diffracted beam, only used when energy discrimination is used

– Breit-Dirac recoil function: • Q > 25 Å-1

– 2- photon counter– 3- intensity measurement

• Energy dependence: – E dependent detector

performance

• Sample Self-Absorption– No effect at high E beams

• Oblique Incidence: – Intensity differences on Debye-

Scherrer ring due to detector tilt

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Data Normalization

• Normalization I(Q) S(Q)– Scaling background– Choose Q range for scaling– Corrections for Sample – Corrections for Instrument– High Q region normalizes to

1

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Fourier Transformation

• Automatic S(Q) optimization– Needs good starting values

• Fourier Transformation– Choose data range– Different transformation routines

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Visualization

• Monitoring the effect of corrections

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And Now?Pair Distribution Function:

Glasses: Journey ends here!

Nanocrystalline and crystalline materials:

Move on to next program!

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Fitting the PDF

• Refinement of PDF– Least-squares fit in real space– Structural model

– Global parameters– Sample Parameter

• Spdiameter

– Instrument resolution• Qdamp

• Qbroad

6 nm

7 nm

8 nm

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Structural Model

• Structural model• Correlated

motion– delta1

• Sharpening– sratio– rcut

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Results

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Take home message– Valuable structural information of

nanocrystalline materials from total X-ray scattering experiments

6 nm