Thomas Proffen Diffraction Group Leader tproffen@ornl.gov

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. About your instructor .. PDF Master of the Universe

4. Why Total Scattering ? S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science316, 561 (2007).

5. Bragg’s law Bragg’s world: Structure of crystals • Assumes periodicity • Average structure from Bragg peak positionsand intensities

6. The challenge : Knowing the local structure • Traditional crystallographic approach to structure determination is insufficient or fails for • Non crystalline materials • Disordered materials: The interesting properties are often governed by the defects or local structure ! • Nanostructures: Well defined local structure, but long-range order limited to few nanometers (-> poorly defined Bragg peaks) • A new approach to determine localand nano-scale structures is needed. S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science316, 561 (2007).

7. Idea / drawing by Emily Tencate Emily’s corner soon coming to http://totalscattering.lanl.gov Judging by the average .. • Analysis of Bragg intensities yields the average structure of materials which can be deceiving ! • Consider going to a party where all you know is the average age is 40 ... ?

8. Total scattering ? Cross section of 50x50x50 u.c. model crystal consisting of 70% black atoms and 30% vacancies ! Properties might depend on vacancy ordering !!

9. Bragg peaks are blind .. Bragg scattering: Information about the average structure, e.g. average positions, displacement parameters and occupancies.

10. Diffuse scattering to the rescue .. Diffuse scattering: Information about two-body correlations, i.e. chemical short-range order or local distortions.

11. How about powder diffraction ?

12. Finally the Pair Distribution Function • The PDF is the Fourier transform of the total scattering diffraction pattern ! Proffen, Z. Krist, 215, 661 (2000)

13. 4.26Å 2.84Å 1.42Å 2.46Å 3.76Å 4.92Å 5.11Å What is a PDF? Pair distribution function (PDF) gives the probability of finding an atom at a distance “r” from a given atom.

14. Bulk BaTiO3– average vs. local structure RT NPDF data The PDF at room temperature shows R3m bond distances at low r, instead of P4mm character expected from the average structure. R3m P4mm

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

16. 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 !

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

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

19. Example: Local structure of WS2 Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) ValeriPetkov (CMU) Facilities: Chess Funding: DOE, NSF

20. S Pristine WS2 W “Restacked” WS2 ? WS2: Structure of “restacked” material • WS2 useful as a lubricant, catalyst, solid-state electrolyte. • Exfoliated and restacked WS2 has a metastable disordered structure. Disorder precluded a full structural solution. • PDF can help …

21. S Pristine WS2: Hexagonal P63/mmc W “Restacked” WS2: Monoclinic P1121 (disordered derivative of WTe2) WS2 : PDF to the rescue Petkov et al., J. Am. Chem. Soc. 122, 11571(2001)

22. Example: Local atomic in sandstone Katharine Page Thomas Proffen Sylvia McLain Tim Darling Jim TenCate Facilities: Lujan Funding: DOE, NSF

23. Sandstone: Crystalline quartz ? • Measured on NPDF • High statistics data (24 hrs) • Solid rock sample • Ambient conditions – sealed to avoid taking up of water • Motivation: Structural explanation for non-linear acoustic properties

24. PDFfit: Refinement of a small model • “Real space Rietveld” • Refinement of structural parameters: lattice parameters, atom positions, occupancies, adp’s, .. • Small models (<200 atoms). • Corrections for Qmax, instrument resolution, correlated motion. • Software: PDFfit, PDFfit2 and PDFGui. Example: Is sandstone simply quartz ? K.L. Page, Th. Proffen, S.E. McLain, T.W. Darling and J.A. TenCate, Local Atomic Structure of Fontainebleau Sandstone: Evidence for an Amorphous Phase ?, Geophys. Res. Lett.31, L24606 (2004).

25. Sandstone: Local structure • Refinement of two phases : • Crystalline quartz • “Amorphous” quartz up to 3Å • Good agreement over complete range • Amorphous regions “stress formed” by point like contacts at grain contacts ?

26. Example: Elastic properties of bulk metallic glasses Katharine Page Thomas Proffen Bjorn Clausen ErsanUstundag Seung-Yub Lee Facilities: Lujan Funding: DOE, NSF

27. BMG : Properties • High Specific Strength • Light Weight • High Elastic Strain • High Hardness • Excellent Wear Resistance • Excellent Corrosion Resistance • BMG’s are prone to catastrophic failure during unconstrained loading due to the formation of macroscopic shear bands • Crystalline reinforcements to suppress the formation of macroscopic shear bands http://www.its.caltech.edu/~matsci/wlj/wlj_research.html

28. BMG: Phases in composite sample • Ability to distinguish between phases - Difference between measured composite PDF and calculated Tungsten PDF agrees well with measured BMG PDF

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

30. 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

31. 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).

32. 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!)

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

35. PI FM La1-xCaxMnO3: Phase diagram • Phase diagram draws itself from the parameters. • Unexpected detail emerges and demands interpretation. Atomic displacement parameter (ADP) for Oxygen (measure for thermal and static deviations from site)

36. La1-xCaxMnO3: Phase diagram Local structure Average structure Mn-O long bond ADP Oxygen

37. Example: “Complete” structure of Gold Nanoparticles Katharine Page Ram Seshadri Tony Cheetham Thomas Proffen

38. 2nm 50 nm Gold nanoparticles • 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

39. 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

40. Nanoparticles: Particle size Nanogold Instrument resolution Spherical particle envelope

41. Au nanoparticles: Particle size We’re dealing with a length scale that can be simulated on an atom by atom basis, perhaps opening the door to extremely detailed refinements.