Total Scattering The Key to Understanding disordered, nano- crystalline and amorphous materials. Tutorial 9 th Canadian Powder Diffraction Workshop Thomas Proffen Diffraction Group Leader

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 :00 - 9:45 Beyond the Bragg peaks or why do we care about total scattering? 9: :30 Measuring total scattering X-ray and neutron data: where and how? 10: :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.

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. About your instructor.. PDF Master of the Universe

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. Why Total Scattering ? S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science 316, 561 (2007).

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

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. 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 local and nano-scale structures is needed. S.J.L. Billinge and I. Levin, The Problem with Determining Atomic Structure at the Nanoscale, Science 316, 561 (2007).

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. ? Idea / drawing by Emily Tencate Emily’s corner soon coming to 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...

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

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

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

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. How about powder diffraction ?

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

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. 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.

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. The PDF at room temperature shows R3m bond distances at low r, instead of P4mm character expected from the average structure. RT NPDF data R3m P4mm Bulk BaTiO 3 – average vs. local structure

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. Simon Billinge (Columbia) Thomas Proffen (LANL) Peter Peterson (SNS) Example: Local atomic strain in ZnSe 1-x Te x

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. 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 !

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. ZnSe 1-x Te x : Total scattering Behaves like local structure Behaves like average structure Peterson et al., Phys. Rev. B63, (2001)

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. BLUE: XAFS from Boyce et al., J. Cryst. Growth. 98, 37 (1989); RED: PDF results. ZnSe 1-x Te x : Nearest neighbors

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. Simon Billinge Thomas Proffen (LANL) Peter Peterson (SNS) Valeri Petkov (CMU) Facilities: Chess Funding: DOE, NSF Example: Local structure of WS 2

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. W S WS 2 : Structure of “restacked” material WS 2 useful as a lubricant, catalyst, solid-state electrolyte. Exfoliated and restacked WS 2 has a metastable disordered structure. Disorder precluded a full structural solution. PDF can help … ? Pristine WS 2 “Restacked” WS 2

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. WS 2 : PDF to the rescue W S Pristine WS 2 : Hexagonal P6 3 /mmc Petkov et al., J. Am. Chem. Soc. 122, (2001) “Restacked” WS 2 : Monoclinic P112 1 (disordered derivative of WTe 2 )

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

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. 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

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. 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 Q max, instrument resolution, correlated motion. Software: PDFfit, PDFfit2 and PDFGui. 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). Example: Is sandstone simply quartz ?

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. 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 ?

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

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. 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

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. 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

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. Simon Billinge Emil Bozin Xiangyn Qiu Thomas Proffen Example: Local structure in La x Ca 1-x MnO 3

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. 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

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. 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, (2005). Refinement as function of atom-atom distance r !

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. 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)

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. LaMnO 3 : Simplicity of the PDF approach 30s Distortions persist locally! 700 K data (blue) vs 750 K data (red)

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.

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. La 1-x Ca x MnO 3 : Phase diagram Phase diagram draws itself from the parameters. Unexpected detail emerges and demands interpretation. FM PI Atomic displacement parameter (ADP) for Oxygen (measure for thermal and static deviations from site)

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. Local structureAverage structure Mn-O long bond ADP Oxygen La 1-x Ca x MnO 3 : Phase diagram

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

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. 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 50 nm 2nm

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. 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, (2004).

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. Nanoparticles: Particle size Nanogold Instrument resolution Spherical particle envelope

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. 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. Au nanoparticles: Particle size