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

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. Redfern et al Phys. Chem. Min. 2005 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  Conventional structure solution techniques fail! Jørgensen et al J. Appl. Cryst. 36, 2003

3. Redfern et al Phys. Chem. Min. 2005 Why X-ray total scattering? • 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 • 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 • 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. Matter19, 335219 (2007) • http://www.diffpy.org/

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 • 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 • 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. 8 nm 7 nm 6 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 • delta1 • Sharpening • sratio • rcut

16. Results

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