Characterization of Materials using the PDF

1. Characterization of Materialsusing the PDF Thomas Proffen Manuel Lujan Jr. Neutron Scattering Center Los Alamos National Laboratory tproffen@lanl.gov LA-UR 05-0111

2. Why do we care about the atomic structure? • Diamond • hard • transparent • insulating • expensive • Graphite • soft • black • metallic • cheap The atomic structure has a profound influence on the properties of materials. Consider carbon ...

3. Bragg’s world The average atomic structure

4. Bragg’s world: Structure of crystals Bragg’s law • Assumes periodicity • Average structure from Bragg peak positions and intensities

5. Bragg’s world: Theory The condition for a Bragg-peak to appear is: or The intensity of the Bragg peak is given by the square of the “Structure factor”: The sum running over atoms in the unit cell.

6. Bragg’s world: Powder Diffraction (220) (200) (111) Sample Incident beam x-rays or neutrons All orientations of crystallites possible. Powder Diffraction gives Scattering on Debye-Scherrer Cones

7. Rietveld refinement technique Ic = Io{SkhF2hmhLhP(Dh) + Ib} Io - incident intensity - variable for fixed 2Q kh - scale factor for particular phase F2h - structure factor for particular reflection mh - reflection multiplicity Lh - correction factors on intensity - texture, etc. P(Dh) - peak shape function – includes instrumental resolution, crystallite size, microstrain, etc.

8. Structure from powder diffraction • Determination of the atomic structure using diffraction has revolutionized our knowledge about how materials work .. • Zn insulin structure (> 1600 atoms in unit cell) determined from powder diffraction data (R.B. van Dreele) • Average structure determined using Bragg reflections.

9. Bragg’s world: Information beyond the average structure • Bragg profiles: size,size distribution and shapeof crystallites, and strain. • Intensity along powder rings: texture and preferred orientation. • Accessible using modern Rietveld refinement programs. Texture of Ti wire plate (Lujan Center) From Ungár, et al, Carbon40, 929 (2002)

10. Diffuse scattering Local atomic structure

11. The challenge of real materials: Knowing the local structure Nanostructures: Science (290) 2000 • Traditional crystallographic approach to structure determination is insufficient or fails for • 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 (-> badly defined Bragg peaks) • A new approach to determine local and nano-scale structures is needed.

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

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

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

15. See http://www.totalscattering.org/teaching/

16. How about powder diffraction ?

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

18. Theory again – no periodicity this time ! Elastic Scattering amplitude (from quantum mechanics) The potential is given by Where the sum is over all atoms in the sample and

19. More theory .. “Form factor” “Structure factor” Rewrite the scattering factor equation substituting Ra and change the order of integration: For neutrons: and

20. Even more theory .. The atomic pair distribution function, G(r) is the Fourier couple of S(Q):

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

22. What is a PDF? Intra-domain Inter-domain Example: C60 - ‘Bucky balls’ The PDF (similar to the Patterson) is obtained via Fourier transform of the normalized total scattering S(Q):

23. Examples

24. Local atomic strain in ZnSe1-xTex Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) Facilities: IPNS, Lujan Funding: DOE, NSF

25. 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 ! ¯

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

27. ZnSe1-xTex : Nearest neighbors and Z-plots .. BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results. Local bond length Average bond length

28. ZnSe1-xTex : Potential based “supercell” modeling Kirkwood potential

29. Local structure of WS2 Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) Valeri Petkov (CMU) Facilities: Chess Funding: DOE, NSF

30. WS2 : Structure of the “restacked” material S Pristine WS2 W “Restacked” WS2 ? • 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 …

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

32. Domain structures Katharine Page Thomas Proffen Facilities: Lujan Funding: DOE, NASA

33. Domain structures : Simulated example • Simulated structure of 20x20x20 unit cells. • Matrix (M): blue atoms • Domains (D): red atoms, spherical shape, d=15Å. • Simulated using DISCUS. Proffen & Page, Z. Krist. (2004), in press

34. Domain structures : Pair Distribution Function r > Domain size: NO D-D contribution. r < Domain size: Mainly D-D and M-M pairs M-M M-M D-D

35. Domain structures : R-dependent refinements • Top: Refinement of 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% Domain radius

36. High temperature local structure of LaMnO3 Xiangyun Qiu Simon Billinge Thomas Proffen Facilities: Lujan Funding: DOE-BES, NSF

37. LaMnO3 : Local structure vs. electronic state • JT orbitals are ordered at low-temperature in a checker-board pattern:

38. LaMnO3 : Crystallography Rhombohedral No JT distortion Less-Orthorhombic-O‘ Virtually no JT distortion Orthorhombic-O Large JT distortion JT distortion disappears at the O-O’ transition

39. LaMnO3 : T-dependence of Mn-O bond distribution • Two Mn-O peaks persist up to the highest T measured • Thermal broadening appears to be the ONLY contributor to peak profile changes • Local JT distortion exists in both high T orthorhombic (pseudo-cubic) and rhombohedral phase • Two Gaussian curves fit the data very well Xiangyun Qiu, Th. Proffen, J. F. Mitchell and S. J. L. Billinge, Phys. Rev. Lett.94, 177203 (2005).

40. LaMnO3 : T-dependence of Mn-O bond distribution • 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). Long-bonds Short-bonds Average structure Local structure

41. LaMnO3 : Crossover from local to average structure • Varying range refinement • Fix rmin • Vary rmax • x axis is rmax O O' Local Average Intermediate??? R

42. LaMnO3 : Crossover from local to average structure • Assume the PDF “form-factor” for a sphere • Take asymptotic values to be low-r result from peak fitting and the high-r result from Rietveld • Three curves are self-consistently fit with one parameter – the diameter of the spherical domain

43. LaMnO3 : T-dependence of orbital clusters from PDF rmax(Ǻ) • 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!) Xiangyun Qiu, Th. Proffen, J. F. Mitchell and S. J. L. Billinge, Phys. Rev. Lett.94, 177203 (2005).

44. “Complete” Structure of Gold Nanoparticles Katharine Page Thomas Proffen Ram Seshadri Tony Cheetham Facilities: Lujan Funding: DOE, NASA

45. Au nanoparticles : Why PDF ? 2nm 50 nm • 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

46. Au nanoparticles : Nano vs. bulk 100Å Experimental PDFs of gold nanoparticles and bulk gold, measured on NPDF.

47. Au nanoparticles : Structural refinements • PDF from nano- and bulk gold refined using PDFFIT. • Nanoparticles show “normal” gold structure. • No indication of surface relaxations. • abulk < anano • Indication of Au-cap distances Au-capping layer distance (Au-S) 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. , accepted (2004).

48. Local structure in sandstone Katharine Page Christina Herrera Thomas Proffen Sylvia McLain Tim Darling Jim TenCate Facilities: Lujan Funding: DOE, NSF

49. 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

50. Sandstone: Local structure • Refinement of single phase quartz model. • Good agreement above r > 3Å. • Missing “intensity” in first two PDF peaks corresponding to Si-O and O-O NN distances.