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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 Institute Stony Brook University. Redfern et al Phys. Chem. Min. 2005. Why X-ray total scattering?.
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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 Institute Stony Brook University
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
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
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 • 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
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/
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 • 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 • 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!
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
Structural Model • Structural model • Correlated motion • delta1 • Sharpening • sratio • rcut
6 nm Take home message • Valuable structural information of nanocrystalline materials from total X-ray scattering experiments