1. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Characterization of Materials using the PDF Thomas Proffen Manuel Lujan Jr. Neutron Scattering Center Los Alamos National Laboratory tproffen@lanl.gov LA-UR 05-0111

2. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Why do we care about the atomic structure? n Diamond –hard –transparent –insulating –expensive n Graphite –soft –black –metallic –cheap The atomic structure has a profound influence on the properties of materials. Consider carbon...

3. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Bragg’s world The average atomic structure

4. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Bragg’s world: Structure of crystals n Assumes periodicity n Average structure from Bragg peak positions and intensities Bragg’s law

5. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen 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. Bragg’s world: Theory

6. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen All orientations of crystallites possible. Powder Diffraction gives Scattering on Debye-Scherrer Cones Incident beam x-rays or neutrons Sample (111) (200) (220) Bragg’s world: Powder Diffraction

7. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen I o - incident intensity - variable for fixed 2Q k h - scale factor for particular phase F 2 h - structure factor for particular reflection m h - reflection multiplicity L h - correction factors on intensity - texture, etc. P(D h ) - peak shape function – includes instrumental resolution, crystallite size, microstrain, etc. I c = I o {  k h F 2 h m h L h P(  h ) + I b } Rietveld refinement technique

8. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Structure from powder diffraction Determination of the atomic structure using diffraction has revolutionized our knowledge about how materials work.. n Zn insulin structure (> 1600 atoms in unit cell) determined from powder diffraction data (R.B. van Dreele) n Average structure determined using Bragg reflections.

9. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Bragg’s world: Information beyond the average structure n Bragg profiles: size, size distribution and shape of crystallites, and strain. n Intensity along powder rings: texture and preferred orientation. n Accessible using modern Rietveld refinement programs. From Ungár, et al, Carbon 40, 929 (2002) Texture of Ti wire plate (Lujan Center)

10. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Diffuse scattering Local atomic structure

11. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen n 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 ) n A new approach to determine local and nano-scale structures is needed. Nanostructures: Science (290) 2000 The challenge of real materials: Knowing the local structure

12. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen 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. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Bragg peaks are blind.. Bragg scattering: Information about the average structure, e.g. average positions, displacement parameters and occupancies.

14. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Diffuse scattering to the rescue.. Diffuse scattering: Information about two-body correlations, i.e. chemical short-range order or local distortions.

15. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen See http://www.totalscattering.org/teaching/

16. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen How about powder diffraction ?

17. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen 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. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen 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. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen More theory.. Rewrite the scattering factor equation substituting R  and change the order of integration: For neutrons: and “Structure factor” “Form factor”

20. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Even more theory.. The atomic pair distribution function, G(r) is the Fourier couple of S(Q):

21. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen What is a PDF? 5.11Å 4.92Å 4.26Å 3.76Å 2.84Å 2.46Å 1.42Å Pair distribution function (PDF) gives the probability of finding an atom at a distance “r” from a given atom.

22. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen What is a PDF? Example: C 60 - ‘Bucky balls’ The PDF (similar to the Patterson) is obtained via Fourier transform of the normalized total scattering S(Q): Intra-domain Inter-domain

23. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Examples

24. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) Facilities: IPNS, Lujan Funding: DOE, NSF Local atomic strain in ZnSe 1-x Te x

25. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen ZnSe 1-x Te x : Structure n Zinc blend structure (F43m) n Technological important : Electronic band gap can be tuned by the composition x. n Bond length difference Zn- Se and Zn-Te  strain. n Local structural probe required ! ¯

26. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen ZnSe 1-x Te x : Total scattering Behaves like local structure Behaves like average structure Peterson et al., Phys. Rev. B63, 165211 (2001)

27. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results. ZnSe 1-x Te x : Nearest neighbors and Z-plots.. Local bond length Average bond length

28. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen ZnSe 1-x Te x : Potential based “supercell” modeling Kirkwood potential

29. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) Valeri Petkov (CMU) Facilities: Chess Funding: DOE, NSF Local structure of WS 2

30. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen W S WS 2 : Structure of the “restacked” material n WS 2 useful as a lubricant, catalyst, solid-state electrolyte. n Exfoliated and restacked WS 2 has a metastable disordered structure. Disorder precluded a full structural solution. n PDF can help … ? Pristine WS 2 “Restacked” WS 2

31. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen WS 2 : PDF to the rescue W S Pristine WS 2 : Hexagonal P6 3 /mmc Petkov et al., J. Am. Chem. Soc. 122, 11571 (2001) “Restacked” WS 2 : Monoclinic P112 1 (disordered derivative of WTe 2 )

32. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Katharine Page Thomas Proffen Facilities: Lujan Funding: DOE, NASA Domain structures

33. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Domain structures : Simulated example n Simulated structure of 20x20x20 unit cells. n Matrix (M): blue atoms n Domains (D): red atoms, spherical shape, d=15Å. n Simulated using DISCUS. Proffen & Page, Z. Krist. (2004), in press

34. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Domain structures : Pair Distribution Function M-M D-D r < Domain size: Mainly D-D and M-M pairs r > Domain size: NO D-D contribution.

35. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Domain structures : R-dependent refinements n Top: Refinement of single-phase model with blue/red fractional occupancies (O). n Bottom: Refinement of same model for 5Å wide sections. n Extensions: –Multi phase models –Modeling of boundary –R-dependent refinable mixing parameters Domain radius O=29%O=16%O=15%

36. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Xiangyun Qiu Simon Billinge Thomas Proffen Facilities: Lujan Funding: DOE-BES, NSF High temperature local structure of LaMnO 3

37. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : Local structure vs. electronic state n JT orbitals are ordered at low-temperature in a checker- board pattern:

38. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : Crystallography Orthorhombic-O Large JT distortion Less-Orthorhombic-O‘ Virtually no JT distortion Rhombohedral No JT distortion JT distortion disappears at the O-O’ transition

39. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : T-dependence of Mn-O bond distribution n Two Mn-O peaks persist up to the highest T measured n Thermal broadening appears to be the ONLY contributor to peak profile changes n Local JT distortion exists in both high T orthorhombic (pseudo-cubic) and rhombohedral phase n 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. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : T-dependence of Mn-O bond distribution n Mn-O bond lengths are invariant with temperature, right up into the R-phase n JT distortions persist locally in the pseudocubic phase n Agrees with XAFS result: M. C. Sanchez et al., PRL (2003). Short-bonds Long-bonds Average structure Local structure

41. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : Crossover from local to average structure n Varying range refinement –Fix r min –Vary r max –x axis is r max Local Average Intermediate??? O R O'

42. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : Crossover from local to average structure n Assume the PDF “form-factor” for a sphere n Take asymptotic values to be low-r result from peak fitting and the high- r result from Rietveld n Three curves are self-consistently fit with one parameter – the diameter of the spherical domain

43. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen LaMnO 3 : T-dependence of orbital clusters from PDF n Diameter of orbitally ordered domains above T JT is 16Ǻ n Appears to diverge close to T JT n 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). r max (Ǻ)

44. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Katharine Page Thomas Proffen Ram Seshadri Tony Cheetham Facilities: Lujan Funding: DOE, NASA “Complete” Structure of Gold Nanoparticles

45. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Au nanoparticles : Why PDF ? n Nanoparticles often show different properties compared to the bulk. n Difficult to study via Bragg diffraction (broadening of peaks). n PDF reveals “complete” structural picture – core and surface. n This study: –5nm monodisperse Au nanoparticles –1.5 grams of material –Neutron measurements on NPDF 50 nm 2nm

46. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Au nanoparticles : Nano vs. bulk Experimental PDFs of gold nanoparticles and bulk gold, measured on NPDF. 100Å

47. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Au nanoparticles : Structural refinements n PDF from nano- and bulk gold refined using PDFFIT. n Nanoparticles show “normal” gold structure. n No indication of surface relaxations. n a bulk < a nano n 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. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Katharine Page Christina Herrera Thomas Proffen Sylvia McLain Tim Darling Jim TenCate Facilities: Lujan Funding: DOE, NSF Local structure in sandstone

49. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Sandstone: Crystalline quartz ? n Measured on NPDF n High statistics data (24 hrs) n Solid rock sample n Ambient conditions – sealed to avoid taking up of water n Motivation: Structural explanation for non-linear acoustic properties

50. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Sandstone: Local structure n Refinement of single phase quartz model. n Good agreement above r > 3Å. n Missing “intensity” in first two PDF peaks corresponding to Si-O and O-O NN distances.

51. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Sandstone: Local structure n Refinement of two phases : n Crystalline quartz n “Amorphous” quartz up to 3Å n Good agreement over complete range n Amorphous regions “stress formed” by point like contacts at grain contacts ? 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 ?, Geophysical Research Lett. 31, L24606 (2004)

52. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Katharine Page Thomas Proffen Bjorn Clausen Ersan Ustundag Seung-Yub Lee Facilities: Lujan Funding: DOE, NSF Elastic properties of Bulk-Metallic-Glasses

53. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen BMG : Properties http://www.its.caltech.edu/~matsci/wlj/wlj_research.html n High Specific Strength n Light Weight n High Elastic Strain n High Hardness n Excellent Wear Resistance n Excellent Corrosion Resistance n BMG’s are prone to catastrophic failure during unconstrained loading due to the formation of macroscopic shear bands n Crystalline reinforcements to suppress the formation of macroscopic shear bands

54. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen BMG : Experiment n The amorphous BMG matrix does not give rise to Bragg peaks => PDF ! n Experiment on SMARTS n The BMG is compressed along one axis, causing atoms along the other to expand n Detector Banks at +90 and –90 degrees receive scattering from separate distortions BMG Beam +90 ° -90°

55. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen BMG : Result +90° -90° 10 MPa 500 MPa 1500 MPa Work in progress..

56. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen BMG: Phase analysis on composite sample n Ability to distinguish between phases –Difference between measured composite PDF and calculated Tungsten PDF agrees well with measured BMG PDF

57. 7th Canadian Powder Diffraction Workshop, May 2007 Characterizing materials using the PDF – Thomas Proffen Summary and more information n Analysis of total scattering gives valuable insight in structure  properties relationship n High-resolution instruments open the door to medium-range order investigations n Obtain structural information from disordered crystalline, amorphous of composite materials n Fast powder measurements allow systematic exploration of local structure as function of T, x, P http://www.totalscattering.org