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Thomas Proffen Diffraction Group Leader tproffen@ornl.gov

Total Scattering The Key to Understanding disordered, nano -crystalline and amorphous materials. Tutorial 9 th Canadian Powder Diffraction Workshop. Thomas Proffen Diffraction Group Leader tproffen@ornl.gov. Friday 25th May 2012. All cartoons by Julianne Coxe . Modeling

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Thomas Proffen Diffraction Group Leader tproffen@ornl.gov

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  1. Total Scattering The Key to Understanding disordered, nano-crystalline and amorphous materials.Tutorial9th Canadian Powder Diffraction Workshop Thomas Proffen Diffraction Group Leader tproffen@ornl.gov

  2. Friday 25th May 2012 All cartoons by Julianne Coxe.

  3. Modeling Total Scattering

  4. Data modeling ‘PDFFIT’ style

  5. Software: Data modeling PDFgui • Part of DANSE project. • http://www.diffpy.org/ • Calculation and refinement of small model system (< 1000 atoms) • ‘Rietveld’ type parameters: lattice parameters, atomic positions, displacement parameters, .. • New possibilities: Refinements as function of r range ! • Automatic refinement of multiple datasets as function of T or x. • Intuitive GUI. • Engine pdffit2 can also be used in command mode.

  6. Calculating a PDF .. • Calculating a PDF from a structural model: • Thermal motion • Small crystal  convolution of (r-rij) with distribution function (PDFFIT) • Large crystal  actual displacements & ensemble average (DISCUS) • Termination ripples • Multiplication with step function in reciprocal space gives convolution with sin(Qmaxr)/r in real space.

  7. Calculated PDF without “” of InAs PDF analysis: Individual peaks PDF peak width of InAs uncorrelated correlated • Correlated motion results in sharpening of near neighbor PDF peaks. • Empirical correction • Future: Extraction of phonons ?? Jeong et al., J. Phys. Chem. A103, 921 (1999)

  8. Calculating a PDF: PDFfit PDF calculated according to In more detail

  9. Effects of Q resolution on the PDF • Assuming Gaussian resolution function leads to dampening of PDF: • Assuming ΔQ/Q constant leads to PDF peak broadening at high r:

  10. High r PDF refinement – Ni on NPDF • No corrections • Rw = 32% • a = 3.5259Å • Uiso = 0.00852Å2 • Dampening • Rw = 20% • a = 3.5259Å • Uiso = 0.00762Å2 • Damp. & Broadening • Rw = 11% • a = 3.5261Å • Uiso = 0.00506Å2

  11. Example: Local atomic strain in ZnSe1-xTex Simon Billinge (Columbia) Thomas Proffen (LANL) Peter Peterson (SNS)

  12. ZnSe1-xTex : Structure • Zinc blend structure (F43m) • Technological important: Electronic band gap can be tuned by the composition x. • Bond length difference Zn-Se and Zn-Te strain. • Local structural probe required !

  13. Behaves like average structure Behaves like local structure ZnSe1-xTex : Total scattering Peterson et al., Phys. Rev. B63, 165211 (2001)

  14. BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results. ZnSe1-xTex : Nearest neighbors

  15. Data modeling ‘PDFFIT’ style R-dependent refinements

  16. Refinement range – length scales in structure • Simulated structure of 20x20x20 unit cells. • Matrix (M): blue atoms • Domains (D): red atoms, spherical shape, d=15Å. • Simulated using DISCUS. Th. Proffen and K.L. Page, Obtaining Structural Information from the Atomic Pair Distribution Function, Z. Krist.219, 130-135 (2004).

  17. Refinement range – length scales in structure • Top: Single-phase model with blue/red fractional occupancies (O). • Bottom: Refinement of same model for 5Å wide sections. • Extensions: • Multi phase models • Modeling of boundary • R-dependent refinable mixing parameters O=15% O=29% O=16% O=15% O=15% O=15%

  18. Example: Local structure in LaxCa1-xMnO3 Simon Billinge Emil Bozin Xiangyn Qiu Thomas Proffen

  19. LaMnO3: Jahn-Teller distortion • Mn-O bond lengths are invariant with temperature, right up into the R-phase • JT distortions persist locally in the pseudocubic phase • Agrees with XAFS result: M. C. Sanchez et al., PRL (2003). Jahn Teller Long Mn-O bond Local structure Average structure

  20. Refinement as function of atom-atom distance r ! X. Qiu, Th. Proffen, J.F. Mitchell and S.J.L. Billinge, Orbital correlations in the pseudo-cubic O and rhombohedral R phases of LaMnO3, Phys. Rev. Lett.94, 177203 (2005).

  21. rmax(Ǻ) LaMnO3 : T-dependence of orbital clusters from PDF • Diameter of orbitally ordered domains above TJT is 16Ǻ • Appears to diverge close to TJT • Red lines are a guide to the eye (don’t take the fits too seriously!)

  22. LaMnO3: Simplicity of the PDF approach 700 K data (blue) vs 750 K data (red) 30s Distortions persist locally!

  23. PDF Refinements (nano particles)

  24. Software: Data modeling DISCUS • Disordered materials simulations • Refinement via DIFFEV / RMC • http://discus.sourceforge.net/ Oxford University Press, October 2008

  25. Enhanced local dipoles in 5nm BaTiO3 Rietveld analysis for ferroelectric bulk BaTiO3unambiguosly supports tetragonal (polar) symmetry. For the nanoparticle data, tetragonal (P4mm) and cubic (Pm-3m) perovskite models are indistinguishable. Are small BaTiO3 particles polar? Total scattering clearly supports local polar symmetry (P4mm) symmetry. In addition the ligand structure can be readily observed. K. Page, T. Proffen, M. Niederberger, and R. Seshadri, Enhanced local dipoles in BaTiO3 nanoparticles, Chem Mater., in press

  26. Modeling of nanoparticle data / current • Using PDFgui • Calculation and refinement of small model system (< 1000 atoms) • ‘Rietveld’ type parameters: lattice parameters, atomic positions, displacement parameters, .. • New possibilities: Refinements as function of r range ! • http://www.diffpy.org/ • Nanoparticle case • Nanoparticle is modeled as bulk with a formfactor for the limited shape. • Ligands are modeled as single molecules in box and no particle/ligand correlations are included.

  27. 2nm 50 nm Gold nanoparticles (revisited) • Nanoparticles often show different properties compared to the bulk. • Difficult to study via Bragg diffraction (broadening of peaks). • PDF reveals “complete” structural picture – core and surface. • This study: • 5nm monodisperse Au nanoparticles • 1.5 grams of material • Neutron measurements on NPDF

  28. Gold nanoparticles: First NPDF data K.L. Page, Th. Proffen, H. Terrones, M. Terrones, L. Lee, Y. Yang, S. Stemmer, R. Seshadri and A.K. Cheetham, Direct Observation of the Structure of Gold Nanoparticles by Total Scattering Powder Neutron Diffraction, Chem. Phys. Lett.393, 385-388 (2004). Bulk gold Gold nanoparticles Average diameter ~3.6nm

  29. Modeling Au structure only • 300 K: Rw = 33.8 % • scale = 0.2121(5) • a = 4.0753(1) • uiso(Au) = 0.01267(6) • δ1 = 1.980(7) • d = 26.13(7) Å • 15 K: Rw = 27.8 % • scale = 0.2070(4) • a = 4.06515(5) • uiso(Au) = 0.0044(2) • δ1 = 2.257(5) • d = 25.54(4) Å This is the conventional PDF nanoparticle approach… no ligand modeling.

  30. Modeling Au structure & ligand + CF3(CF2 )5(CH2 )2S- Au-S • 300 K: Rw = 31.4 % • scale (Au) = 0.2082(5) • scale (molecule) = 0.0485(6) • a (Au) = 4.0755(1) • a(molecule) = 49.40(3) • uiso(Au/molec) = 0.01227(5) • δ1 (Au) = 1.953(7) • srat (molecule)= 0.02(3) • 15 K: Rw = 24.7 % • scale (Au) = 0.2054(4) • scale (molecule) = 0.0604(6) • a (Au) = 4.06500(5) • a(molecule) = 49.23(2) • uiso(Au/molec) = 0.00433(2) • δ1 (Au) = 2.256(6) • srat (molecule)= 0.03(14) ~1 Mol./110 Å2 particle surface U N C L A S S I F I E D

  31. Modeling of nanoparticle data - future ! Using DISCUS/DIFFEV • http://discus.sourceforge.net/ • Approach: The particle is modeled as a whole. • Current work on gold nanoparticles: An fccAu particle is constructed in DISCUS, we select a cuboctahedron. • Ligands (with ‘internal’ structure as constructed with DFT minimization) are located randomly at the particle surface with a defined surface density and defined Au-S distance, orientated out from the particle center. • Evolutionary algorithm is used to refine model parameters above (CPU intensive). Oxford University Press, October 2009

  32. Nanoparticle builder Page, K., Hood, TC, Proffen, T, Neder, RB, J. Appl. Cryst., 44 (2), 327 - 336 (2011)

  33. Work in progress … • Things to consider • Particle size distribution • Variations in ligands • Ligand-ligand interactions ? • Ligand floppiness • ... r(A)

  34. as narrow as crystal nano crystal broader than crystal Example: ZnSe nanoparticles nanocrystallineZnSe crystalline ZnSe

  35. loss of coherence due to stacking faults Example: ZnSe nanoparticles structural coherence

  36. Example: ZnSe nanoparticles - Model create a large single Wurtzite layer A/B Stack along c (with faults) Cut to proper size Calculate PDF / powder pattern Repeat and average Repeat with new set of parameter using a Differential Evolutionary Scheme Software: DISCUS and DIFFEV {110} and {001}

  37. exp calc Example: ZnSe nanoparticles - Results • Results: • a=3.973Å, c=6.494Å • Diameter ~26Å • Stacking fault prob. 70% C. Kumpf, R.B. Neder et al., Structure determination of CdS and ZnSnanoparticles: Direct modeling of synchrotron-radiation diffraction data, J. Chem. Phys.123, 224707 (2005).

  38. Neder et al.; Chory et al.; Niederdraenk et al. Physica Status Solidi C 4, (2007) What is next ?? • Systematic studies (samples !) • Extensions • Anisotropic shapes • Complex architectures (core-shell) • Software • Nanoparticle Builder • Other refinement strategies • Using more complementary data • http://discus.sourceforge.net Locally epitaxial Random placement CdSe - ZnS core-shell (R. Neder, U Erlangen)

  39. Nanoparticle builder http://totalscattering.lanl.gov/nano/

  40. Nanoparticle builder – in action ..

  41. RMC Shaking a big box of atoms. Courtesy of M. Tucker, ISIS

  42. Reverse Monte Carlo • Commonly used to model glasses and liquids (no long range order). • Recently applied to disordered crystalline materials. • Large model structures. • Importance of constrains. • Uniqueness of solution ? R.L. McGreevy and L. Pusztai, Reverse Monte Carlo Simulation: a New Technique for the Determination of Disordered Structures , Mol. Simul.1, 359-367 (1988). M.G. Tucker, M.T. Dove and D.A. Keen, Application of the Reverse Monte Carlo Method to Crystalline Materials , J. Appl. Cryst.34, 630-638 (2001).

  43. Change a variable at random Initial fit to data with starting values Calculate new fit to data χ2 If better If worse Keep change with a certain probability Keep change Reverse Monte Carlo algorithm Repeat until an acceptable fit is obtained RMC: How does it work ?

  44. Adding constraints • anything else you can calculate from the configuration of atoms

  45. Include Bragg intensities .. RMCProfile calculates the intensities and then produces the profile. Use GSAS to fit : Peak shape Background Lattice parameters

  46. (010) Section of SF6 at 50K (010) Section of SF6 at 190K Example: SF6

  47. Tetrahedra Octahedra Tetrahedra & Octahedra Chains Triangles Tether and more Over restrained Normal Polyhedral Restraints Weighting is weak to hold things together while the data chooses the final shape

  48. RMC: Examples SF6 SrTiO3 ZrW2O8 AuCN

  49. Software: RMCprofile • RMCprofile • Atomic configurations ~600 to 20000+ atoms • Fit both X-ray and neutron F(Q) • Fit G(r) • Fit Bragg profile (GSAS tof 1,2 & 3) • Polyhedral restraints • Coordination constraints • Closest approach constraints • Produce a static 3-D model of the structure (a snap-shot in time) • Link: http://www.isis.rl.ac.uk/RMC

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