1. 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 Institute
Stony Brook University

2. Why X-ray total scattering?
Why do conventional crystallographic techniques fail?
Size effects
Severely peak broadening
Reduced structural coherence
No/reduced long range order
Surface effects
Short-range order
Diffuse scattering
Redfern et al Phys. Chem. Min. 2005
 Conventional structure solution techniques fail!
Jørgensen et al J. Appl. Cryst. 36, 2003

3. Why X-ray total scattering?
Redfern et al Phys. Chem. Min. 2005
Large amount of diffuse scattering
Deviation from the 3D ordered average structure
TiO2 nano-crystals

4. Total scattering 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

5. Data collection High Energy X-rays Area detector Collection
E~100 keV  Large Q
Area detector
Collection
Background
Sample container
Sample +container
2D1D Fit2D
Polarization correction
Masking of contributions from sample container
X-ray

6. Programs PDFgetX2 PDFGui
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)
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, (2007)

7. Experimental parameters
Platform independent
IDL virtual Machine
Python routines
Data input
Experimental parameter
Wavelength
Polarization (done in Fit2D)
In-house
Monochromator
Analyzer
Notes  Header of output files

8. Sample Information Sample geometry Sample Additional information
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

9. Data Normalization Corrections for normalization Corrections
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

10. 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

11. Fourier Transformation
Automatic S(Q) optimization
Needs good starting values
Fourier Transformation
Choose data range
Different transformation routines

12. Visualization
Monitoring the effect of corrections

13. And Now? Pair Distribution Function: Glasses: Journey ends here!
Nanocrystalline and crystalline materials:
Move on to next program!

14. Fitting the PDF Refinement of PDF Least-squares fit in real space
6 nm
7 nm
8 nm
Fitting the PDF
Refinement of PDF
Least-squares fit in real space
Structural model
Global parameters
Sample Parameter
Spdiameter
Instrument resolution
Qdamp
Qbroad

15. Structural Model Structural model Correlated motion Sharpening delta1
sratio
rcut

16. Results

17. Take home message
Valuable structural information of nanocrystalline materials from total X-ray scattering experiments
6 nm