Modelling the PDF of Crystalline Materials with RMCProfile

Transcription

1 Modelling the PDF of Crystalline Materials with RMCProfile Dr Helen Yvonne Playford STFC ISIS Facility, Rutherford Appleton Laboratory, Didcot, UK China Spallation Neutron Source Institute of High Energy Physics, Dongguan, China 7 th November 2016

2 Local and Average Viewpoints Average viewpoint: Local viewpoint:

3 Diffraction as a Structural Probe Intensity (a.u.) d-spacing (Å) Information contained in a diffraction pattern: - Size and shape of unit cell (peak positions) - Symmetry within the unit cell (absences) - Contents of the unit cell (relative intensities) - Thermal motion - Particle size - Strain - Texture Diffraction angle ( 2 )

4 Introduction to Total Scattering What is total scattering? A powder diffraction based technique in which the Bragg and diffuse scattering are measured and analysed simultaneously. F(Q) [SiO 2 ] Q (Å -1 )

5 Introduction to Total Scattering What is total scattering? A powder diffraction based technique in which the Bragg and diffuse scattering are measured and analysed simultaneously. F(Q) [SiO 2 ] Q (Å -1 )

6 Introduction to Total Scattering What is total scattering? A powder diffraction based technique in which the Bragg and diffuse scattering are measured and analysed simultaneously. 0.4 F(Q) [SiO 2 ] Q (Å -1 )

7 Introduction to Total Scattering What is total scattering? A powder diffraction based technique in which the Bragg and diffuse scattering are measured and analysed simultaneously. 0.4 F(Q) [SiO 2 ] Q (Å -1 )

8 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r r

9 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

10 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

11 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

12 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

13 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

14 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

15 Introduction to Total Scattering The pair distribution function (PDF) A histogram of pairwise interatomic distances produced by Fourier transformation of the total scattering function. G(r) r

16 Introduction to Total Scattering The pair distribution function (PDF) 4 PDF [SiO 2 ] 3 2 This is the neutron PDF for quartz type SiO r (Å)

17 Introduction to Total Scattering The pair distribution function (PDF) PDF [SiO 2 ] Si-O O-O Si-Si Visual inspection can provide information about: - bond lengths - coordination numbers - level of disorder - identities of species involved more detail comes from modelling! r (Å)

18

19 Introduction to total scattering Modelling techniques There are two main ways in which detailed structural information can be extracted from total scattering data: small box and big box modelling. D(r) 14 Data 12 Calculated 10 Difference r (Å) Small box modelling: - Crystal structure refined to fit the PDF: real-space Rietveld. - Limited to crystallographic descriptions of structural parameters. - Identify discrepancies between average and local structure.

20 Introduction to total scattering Modelling techniques There are two main ways in which detailed structural information can be extracted from total scattering data: small box and big box modelling. 5 Initial RMC Data RMC ~1,400,000 moves 5 Refined RMC Data Big box modelling: - Reverse Monte Carlo (RMC). - Supercell of >10,000 atoms, moved at random to obtain best possible agreement with all data. - Atomistic model that is consistent with average and local structure. - Not constrained by symmetry. D(r) D(r) r (Å) r (Å)

21 The Reverse Monte Carlo Technique Atomic configuration Calculate scattering functions and compare with data Calculate goodness-of-fit parameters Move a random atom a random amount Recalculate scattering functions Calculate change to goodness-of-fit Move accepted Improves Worsens Move rejected or accepted (dependent on probability)

22

23 RMCProfile Implementation of the RMC algorithm particularly suited to crystalline materials. Profile refers to the Bragg profile a very important constraint for average structure. Based on the original RMCA code of McGreevy and Puzstai, extended by Matt Tucker (now at ORNL). Developers: Dave Keen (ISIS), Martin Dove (QMUL), Andrew Goodwin (Oxford), Helen Playford (ISIS), Wojciech Slawinski (ISIS), and many others. The program is available online at It can fit multiple datasets (X-ray and neutron PDF, F(Q), Bragg) and use chemical sense in the application of appropriate constraints.

24 RMCProfile Adapted from: S. J. L. Billinge and I. Levin, Science, 2007, 316,

25 RMCProfile PDF Bragg profile F(Q) Hard sphere cutoff Distance window Polyhedral constraints Molecular potentials EXAFS Bond valence sum Single crystal diffuse

26 RMCProfile Requirements for successful RMCProfile refinement: Quality data Multiple datasets Single phase sample* Good powder average** Average structure well-characterised Understanding of structural chemistry Targeted analysis of refined configurations

27 RMCProfile RMCProfile developed at ISIS by Wojciech Slawinski - arbitrary scattering length inputs - multiple atom swapping - bugfixes - usability improvements - release date: ASAP RMCProfile 7.0 * - being developed at ISIS by Wojciech Slawinski - big news: multiphase RMC (multiple boxes of atoms) - currently in need of input from users and colleagues - (beta) release date: February 2017 RMCProfile 7.1 and later ** - incorporation of small-box modelling (with colleagues at SNS) - developments for nanoparticles, low-dimensional systems & networks (with QMUL and University of Oxford) - release date: future

28

29 Case Study: Gallium Oxide A disordered polymorph of Ga 2 O 3 d-spacing / Å Diffracted intensity / a.u R wp = 1.36% d-spacing / Å - Potential photocatalyst and catalyst support - Structure poorly understood - Cubic spinel structure - Rietveld refinement reveals four partially occupied Ga sites - Nanocrystalline H. Y. Playford, A. C. Hannon, E. R. Barney, and R. I. Walton, Chem. Eur. J., 2013, 19,

30 Case Study: Gallium Oxide D(r) / barns Å -2 D(r) / barns Å r / Å r / Å D(r) / barns Å Observed Calculated Difference r / Å - Small-box modelling of the PDF - Medium-to-high r agrees well with average crystal structure - Large discrepancies in local structure - Improved fit when lower symmetry model is used, but it is a purely local effect H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

31 Case Study: Gallium Oxide D(r) / barns Å -2 r / Å D(r) / barns Å r / Å - Small-box modelling of the PDF - Medium-to-high r agrees well with average crystal structure - Large discrepancies in local structure - Improved fit when lower symmetry model is used, but it is a purely local effect H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

32 Case Study: Gallium Oxide Random starting model: Ga-Ga < 1Å Intensity / a.u. Handmade 2x2x2 cell with reasonable distances: supercell with artificial superstructure Neutron TOF / ms Re-randomised supercell using atom swapping & fit to Bragg pattern Physically and chemically sound starting model(s) for full RMC refinement Green = octahedral Ga Blue = tetrahedral Ga H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

33 Case Study: Gallium Oxide Random starting model: Ga-Ga < 1Å Handmade 2x2x2 cell with reasonable distances: supercell with artificial superstructure Re-randomised supercell using atom swapping & fit to Bragg pattern Green = octahedral Ga Blue = tetrahedral Ga Intensity / a.u Neutron TOF / ms Physically and chemically sound starting model(s) for full RMC refinement H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

34 Case Study: Gallium Oxide 5 Data RMC Difference RMC refinement using 6x6x6 supercell - vastly improved fit to local structure D(r) r / Å T(r) 5 0 Data RMC Ideal cubic model r / Å H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

35 Case Study: Gallium Oxide RMC refinement using 6x6x6 supercell - vastly improved fit to local structure - maintains correct average Collapsed RMC box H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118, Unit cell

36 Case Study: Gallium Oxide Spinel T d site Weighted Ga-O partials Ga 8a -O Ga 16d -O Ga 48f -O Ga 16c -O RMC provides bond length and angle distributions: G(r) Sum Data - these distributions are the sum of 200 refined boxes of atoms Non-spinel T d site r / Å Non-weighted Ga-O partials - the O h sites are highly distorted 10 8 Ga 8a -O Ga 16d -O Ga 48f -O - the crystal structure defines two very different T d sites G(r) 6 4 Ga 16c -O - but locally these sites are very similar r / Å H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

37 Case Study: Gallium Oxide Starting Refined Spinel T d site Weighted Ga-O partials Non-weighted Ga-O partials RMC provides bond length and angle distributions: - these distributions are the sum of 200 refined boxes of atoms - the O h sites are highly distorted - the crystal structure defines two very different T d sites B( )/sin( ) B( )/sin( ) O-Ga-O bond angle ( ) Non-spinel T d site Starting Refined - but locally these sites are very similar O-Ga-O bond angle ( ) H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

38 Case Study: Gallium Oxide A disordered polymorph of Ga 2 O 3 G(r) Ga 8a -O Ga 16d -O Data [4+2] [3+3] The data clearly show the octahedra are distorted, but what do they actually look like? - multiple RMC runs provide ensemble of >700,000 polyhedra to analyse! - 50% all 6 bonds shorter than the mean bond length - 40% [3+3] type r / Å H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

39 Case Study: Gallium Oxide A disordered polymorph of Ga 2 O 3 G(r) Ga 8a -O Ga 16d -O Data [4+2] [3+3] The data clearly show the octahedra are distorted, but what do they actually look like? - multiple RMC runs provide ensemble of >700,000 polyhedra to analyse! - 50% all 6 bonds shorter than the mean bond length - 40% [3+3] type Thermodynamically stable b-ga 2 O 3 has [3+3] type r / Å Locally, cubic g-ga 2 O 3 = monoclinic b-ga 2 O 3 H. Y. Playford, et al., J. Phys. Chem. C, 2014, 118,

40 Why was the Case Study successful? Requirements for successful RMCProfile refinement: Quality data ü Multiple datasets ü Single phase sample* Good powder average** ü ü Average structure well-characterised Understanding of structural chemistry ü ü Targeted analysis of refined configurations ü

41

42 Conclusions Total scattering is an extension of powder diffraction that changes the viewpoint from average to local. Reverse Monte Carlo refinements using RMCProfile produce atomistic models that are consistent with all available data Requirements for success include prior characterisation and an understanding of what you want to know about your structure! The program is always being developed and we always want to hear from you!

43 Thank you!