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

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

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

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

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

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) 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/

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

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

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

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

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

Visualization Monitoring the effect of corrections

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

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

Structural Model Structural model Correlated motion Sharpening delta1 sratio rcut

Results

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