1. 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

2. 2Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Friday 25th May 2012 9:00 - 9:45 Beyond the Bragg peaks or why do we care about total scattering? 9:45 - 10:30 Measuring total scattering X-ray and neutron data: where and how? 10:30 - 11:15Break 11:15-12:30 What to do with your PDF: Modeling of disordered structures ? 12:30 - 1:30Lunch 1:30 - 5:00Practical Sessions All cartoons by Julianne Coxe.

3. 3Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Modeling Total Scattering

4. 4Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Data modeling ‘PDFFIT’ style

5. 5Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Software: Data modeling PDFgui  Part of DANSE project.  http://www.diffpy.org/ 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. 6Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Calculating a PDF.. Calculating a PDF from a structural model: Thermal motion – Small crystal  convolution of  (r-r ij ) with distribution function ( PDFFIT ) – Large crystal  actual displacements & ensemble average ( DISCUS ) Termination ripples – Multiplication with step function in reciprocal space gives convolution with sin(Q max r)/r in real space.

7. 7Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. PDF analysis: Individual peaks uncorrelated correlated PDF peak width of InAs Calculated PDF without “  ” of InAs  Correlated motion results in sharpening of near neighbor PDF peaks.  Empirical correction  Future: Extraction of phonons ?? Jeong et al., J. Phys. Chem. A 103, 921 (1999)

8. 8Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Calculating a PDF: PDFfit PDF calculated according to In more detail

9. 9Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Effects of Q resolution on the PDF

10. 10Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. High r PDF refinement – Ni on NPDF No corrections – Rw = 32% – a = 3.5259Å – Uiso = 0.00852Å 2 Dampening – Rw = 20% – a = 3.5259Å – Uiso = 0.00762Å 2 Damp. & Broadening – Rw = 11% – a = 3.5261Å – Uiso = 0.00506Å 2

11. 11Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Simon Billinge (Columbia) Thomas Proffen (LANL) Peter Peterson (SNS) Example: Local atomic strain in ZnSe 1-x Te x

12. 12Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. ZnSe 1-x Te x : 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. 13Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. ZnSe 1-x Te x : Total scattering Behaves like local structure Behaves like average structure Peterson et al., Phys. Rev. B63, 165211 (2001)

14. 14Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results. ZnSe 1-x Te x : Nearest neighbors

15. 15Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Data modeling ‘PDFFIT’ style R-dependent refinements

16. 16Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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. 17Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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=29%O=16%O=15%

18. 18Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Simon Billinge Emil Bozin Xiangyn Qiu Thomas Proffen Example: Local structure in La x Ca 1-x MnO 3

19. 19Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. LaMnO 3 : 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). Average structure Local structure Jahn Teller Long Mn-O bond

20. 20Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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). Refinement as function of atom-atom distance r !

21. 21Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. LaMnO 3 : T-dependence of orbital clusters from PDF Diameter of orbitally ordered domains above T JT is 16Ǻ Appears to diverge close to T JT Red lines are a guide to the eye (don’t take the fits too seriously!) r max (Ǻ)

22. 22Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. LaMnO 3 : Simplicity of the PDF approach 30s Distortions persist locally! 700 K data (blue) vs 750 K data (red)

23. 23Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon.

24. 24Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. PDF Refinements (nano particles)

25. 25Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Software: Data modeling DISCUS  Disordered materials simulations  Refinement via DIFFEV / RMC  http://discus.sourceforge.net/ http://discus.sourceforge.net/ Oxford University Press, October 2008

26. 26Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Enhanced local dipoles in 5nm BaTiO 3 K. Page, T. Proffen, M. Niederberger, and R. Seshadri, Enhanced local dipoles in BaTiO 3 nanoparticles, Chem Mater., in press Total scattering clearly supports local polar symmetry (P4mm) symmetry. In addition the ligand structure can be readily observed. Rietveld analysis for ferroelectric bulk BaTiO 3 unambiguosly supports tetragonal (polar) symmetry. For the nanoparticle data, tetragonal (P4mm) and cubic (Pm-3m) perovskite models are indistinguishable. Are small BaTiO 3 particles polar?

27. 27Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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/ 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.

28. 28Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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 50 nm 2nm

29. 29Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Gold nanoparticles: First NPDF data Bulk gold Gold nanoparticles Average diameter ~3.6nm 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).

30. 30Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Modeling Au structure only 300 K: R w = 33.8 % scale = 0.2121(5) a = 4.0753(1) u iso (Au) = 0.01267(6) δ1 = 1.980(7) d = 26.13(7) Å 15 K: R w = 27.8 % scale = 0.2070(4) a = 4.06515(5) u iso (Au) = 0.0044(2) δ1 = 2.257(5) d = 25.54(4) Å This is the conventional PDF nanoparticle approach… no ligand modeling.

31. 31Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. U N C L A S S I F I E D Modeling Au structure & ligand + CF 3 (CF 2 ) 5 (CH 2 ) 2 S - 300 K: R w = 31.4 % scale (Au) = 0.2082(5) scale (molecule) = 0.0485(6) a (Au) = 4.0755(1) a(molecule) = 49.40(3) u iso (Au/molec) = 0.01227(5) δ1 (Au) = 1.953(7) srat (molecule)= 0.02(3) 15 K: R w = 24.7 % scale (Au) = 0.2054(4) scale (molecule) = 0.0604(6) a (Au) = 4.06500(5) a(molecule) = 49.23(2) u iso (Au/molec) = 0.00433(2) δ1 (Au) = 2.256(6) srat (molecule)= 0.03(14) ~1 Mol./110 Å 2 particle surface Au-S

32. 32Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Modeling of nanoparticle data - future ! Using DISCUS/DIFFEV  http://discus.sourceforge.net/ http://discus.sourceforge.net/  Approach : The particle is modeled as a whole.  Current work on gold nanoparticles: An fcc Au 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

33. 33Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Nanoparticle builder Page, K., Hood, TC, Proffen, T, Neder, RB, J. Appl. Cryst., 44 (2), 327 - 336 (2011)

34. 34Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Work in progress … Things to consider Particle size distribution Variations in ligands Ligand-ligand interactions ? Ligand floppiness... r(A)

35. 35Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. nano crystal as narrow as crystal broader than crystal Example: ZnSe nanoparticles nanocrystalline ZnSe crystalline ZnSe

36. 36Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. structural coherence loss of coherence due to stacking faults Example: ZnSe nanoparticles

37. 37Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Calculate PDF / powder pattern Repeat and average create a large single Wurtzite layer A/B Stack along c (with faults) Cut to proper size {110} and {001} Repeat with new set of parameter using a Differential Evolutionary Scheme Software: DISCUS and DIFFEV Example: ZnSe nanoparticles - Model

38. 38Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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 ZnS nanoparticles: Direct modeling of synchrotron-radiation diffraction data, J. Chem. Phys. 123, 224707 (2005).

39. 39Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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 http://discus.sourceforge.net CdSe - ZnS core-shell (R. Neder, U Erlangen) Locally epitaxial Random placement Neder et al.; Chory et al.; Niederdraenk et al. Physica Status Solidi C 4, (2007)

40. 40Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Nanoparticle builder http://totalscattering.lanl.gov/nano/

41. 41Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Nanoparticle builder – in action..

42. 42Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. RMC Shaking a big box of atoms. Courtesy of M. Tucker, ISIS

43. 43Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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).

44. 44Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. RMC: How does it work ? Initial fit to data with starting values Change a variable at random Calculate new fit to data χ 2 Repeat until an acceptable fit is obtained If worse Keep change with a certain probability If better Keep change R everse M onte C arlo algorithm

45. 45Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Adding constraints + anything else you can calculate from the configuration of atoms

46. 46Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Include Bragg intensities.. Use GSAS to fit : Peak shape Background Lattice parameters RMCProfile calculates the intensities and then produces the profile.

47. 47Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Example: SF 6 (010) Section of SF 6 at 50K (010) Section of SF 6 at 190K

48. 48Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Polyhedral Restraints Tetrahedra Octahedra Tetrahedra & Octahedra Chains Triangles Tether and more Weighting is weak to hold things together while the data chooses the final shape Over restrainedNormal

49. 49Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. RMC: Examples SF 6 ZrW 2 O 8 AuCN SrTiO 3

50. 50Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. 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/RMChttp://www.isis.rl.ac.uk/RMC

51. 51Managed by UT-Battelle for the U.S. Department of Energy 9 th Canadian Powder Diffraction Workshop – May 23-25, 2012 University of Saskatchewan, Saskatoon. Nanoparticle modeling tutorial at ACA meeting: July 28, 2012 in Boston. http://totalscattering.lanl.govhttp://totalscattering.lanl.gov DISCUS workshop: Sep. 10-13,2012 U Erlangen (Germany). http://discus.sourceforge.net http://discus.sourceforge.net DISCUS workshop 2010 Erlangen