Quantitative analysis of Electron Diffraction Ring Patterns using the MAUD program

Transcription

1 Quantitative analysis of Electron Diffraction Ring Patterns using the MAUD program P. Boullay 1, L. Lutterotti 2 and D. Chateigner 1 1 CRISMAT, CNRS UMR 6508, 6 Bd du Maréchal JUIN CAEN Cedex, France 2 Department of Materials Engineering and Industrial Technologies, university of Trento, TRENTO, Italy [001] fit E-WIMV 82 Å data 38 Å Q (Å -1 ) E-MRS 2012 Spring Meeting Strasbourg Symposium X

2 Outline Quantitative analysis of electron diffraction ring patterns Phase identification, structure and microstructure characterization with quantitative and reliable approaches of nanosized polycrystalline samples? From the diffraction point of view! Extraction of integrated intensities from electron diffraction ring patterns (ED-RP) for quantitative (or semi-quantitative) analysis Vainshtein (1964), PCED 2.0 : X.Z. Li, Ultramicroscopy 110 (2010) ProcessDiffraction : J.L. Labar, Microsc. Microanal. 15 (2009) TextPat : P. Oleynikov, S. Hovmoller and X.D. Zou in Electron Crystallography The MAUD program : L. Lutterotti

3 MAUD L. Lutterotti Nuclear Inst. and Methods in Physics Res. B268, , Indexing (COD phase search procedure) MAUD Rietveld pattern fitting Evolutionary Simulated Annealing Marquardt (Least squares) Metadynamics optimization Simplex (Nelder-Mead) Genetic Materials Analysis Using Diffraction Size-Strain Delft size-strain (PV) Popa anisotropic Size/Strain distributions Planar faulting (Warren) Turbostratic (Ufer) Peak location Peak fitting Structure refinement X-ray Neutron Electron Texture Residual stresses Geometric Voigt, Reuss, Hill Triaxial Stress March-Dollase Harmonic (E)WIMV Standard Functions

4 MAUD Materials Analysis Using Diffraction download at Toolbar for common command shortcuts Tab panel to manage data sets, phases and sample. Plot panel, drag and drop a data file here to load a spectrum The MAUD program is written in JAVA and can run on various platforms Toolbar to stop/resume/slow down computation Output panel for the refinement process Full parameters list, to change the value, set refinable, fix or bound

5 MAUD Materials Analysis Using Diffraction Intensity extraction along the rings by segments using an ImageJ plugin center position and correction for a small elliptical distortion are refinable parameters pixel size pixels to mm rough estimation of the center position using a reference circle on the screen 120 patterns 3 CAKING chi=phi=0 / omega=90 / eta: 0 to 360 Calibrate the distance specimen/detector mm to 2θ

6 MAUD Materials Analysis Using Diffraction 1D XRPD-like pattern (360 summed intensity) peak location and intensities peak broadening vs. d hkl b(x): background => pic at 0 + polynomial function 2θ ( ) => Q (Å -1 ) measured profile h(x) = f(x) g(x) + b(x)

7 Structure Phase search and indexing The whole pattern representing the summed intensity along the rings can be used for an automatic phase search procedure in the Crystallography Open Database* using the program S_FPM (L. Lutterotti). Database Pattern Rietveld fit (for each phase in the database) - 1D XRPD-like experimental profile Add new phases - list of elements (synthesis condition, EDX, EELS, ) Ranking Best phase > threshold - instrumental parameters (pixels to scattering angle, peak shape function, ) Y N End: Rietveld * S. Grazulis, D. Chateigner, R.T. Downs, A.F.T. Yokochi, M. Quirós, L. Lutterotti, E. Manakova, J. Butkus, P. Moeck and A. Le Bail, J. Appl. Crystallogr. 42, , 2009.

8 Structure Phase search and indexing The pattern representing the summed intensity along the rings can be used for an automatic phase search procedure in the Crystallographic Open Database using the program S_FPM (L. Lutterotti). Test on nanopowders (TiO 2 rutile, Mn 3 O 4 hausmannite, CoFe 2 O 4 spinel) and textured thin films (MgO on Pt) low texture : one single ED-RP is sufficient strong texture : more tricky need more than one ED-RP Kinematic approximation is used to calculate the whole pattern profile Automatic indexing and phase ID is possible! TiO 2 rutile nanoparticules see M. Reddy et al., ElectroChem. Com. 8 (2006) for details Electron atomic scattering factors from the tables of L.M. Peng et al

9 Microstructure Line broadening causes h(x) = f(x) g(x) + b(x) ED-RP vs XRPD instrumental broadening sample contribution instrumental broadening finite size of the crystals (acts like a Fourier truncation: size broadening) imperfection of the periodicity (due to d h variations inside crystals: microstrain effect) generally: 0D, 1D, 2D, 3D defects All quantities are average values over the probed volume electrons, x-rays, neutrons: complementary distributions: mean values depend on distributions shapes Extraction of f(x) can be obtained by a whole-pattern (Rietveld) analysis Need to know g(x) the instrumental broadening! L. Lutterotti The and instrumental P. Scardi, J. of Appl. Peak Crystallogr. Shape Function 23, is (1990) obtained by analysing nanoparticules of known sizes and shapes as obtained from X-ray analyses

10 Microstructure ED-RP vs XRPD Mn 3 O 4 hausmanite (L. Sicard - ITODYS - UMR 7086 CNRS / Univ. Paris 7) Reflection mode acq. time:3h30 > 100mg powder Bruker D8 / Lynx Eye 1D λ= Å (Cu Kα 1 ) Transmission mode acq. time:6h powder in a capillary TOPCON 2B / CCD ORIUS λ=0.0251å Transmission mode acq. time: few seconds! very small amount of powder

11 Microstructure ED-RP vs XRPD Mn 3 O 4 hausmannite (L. Sicard et al, J. Magn. Magn. Mater. 322 (2010) ) g(x) f(x) structure Bruker D8 / Lynx Eye 1D λ= Å (Cu Kα 1 ) SG: I 4 1 /a m d a=5.764(2)å and c=9.448(4)å 53 Å 64 Å POPA anisotropic shape f(x) g(x) pattern matching TOPCON 2B / CCD ORIUS λ=0.0251å a=5.7757(2)å and c=9.4425(4)å

12 Microstructure Size and texture effects Microstructure of nanocrystalline materials: TiO 2 rutile (1) from phase search: TiO2 rutile P4 2 /mnm a= 4.592Å a=2.957å (COD database ID n ) 72 patterns 5 20nm FEI Tecnai / CCD USC1000 / λ=0.0197å (1) M. Reddy et al., ElectroChem. Com. 8 (2006)

13 Microstructure Size and texture effects 4-circles diffract. / INEL CPS λ= CuKα structure 47 Å RX 76 Å [001] average anisotropic crystallite size pattern matching 38 Å ED-RP 82 Å

14 Microstructure Size and texture effects The features available in MAUD allow a full quantitative texture analysis for 6μm 0.5μm general cases (not only fiber textures!) from electron diffraction data with the obtention of accurate pole figures. decreasing the selected area application on textured thin film see M. Gemmi et al., J. Appl. Cryst. 44 (2011) Texture :: intensity variation along the rings fit no texture local texture analysis fit E-WIMV data data Q (Å -1 ) reconstructed pole figure (from the Orientation Distribution Function) Q (Å -1 )

15 Microstructure Pattern matching mode? 85 Å 39 Å RX: a=4.583(1)å c=2.949(1)å x(o 1 )=y(o 1 )=0.3062(5) 79 Å 47 Å pattern matching a=4.571(1)å c=2.938(1)å RX structure kinematic approximation 105 Å 27 Å a=4.584(1)å c=2.936(1)å x(o 1 )=y(o 1 )=0.3006(2) Blackman 2-beams correction x(o 1 )=y(o 1 )=0.3064(2)

16 Conclusion Quantitative analysis of electron diffraction ring patterns Quantitative analysis of nanosized polycrystalline samples using MAUD automatic phase search procedure (COD database, multi-phases) average lattice cell parameters and crystallite size (anisotropic shapes) accurate texture analysis (general cases, ODF, ) can be obtained in the Pattern matching mode structure determination and refinement are possible within MAUD would need some adaptation (2-beams and/or multi beams dynamical corrections) Acknowledgments: V. Pralong and V. Caignaert (TiO 2 CRISMAT Caen L. Sicard and S. Ammar (Mn 3 O 4 ITODYS Paris 7 N. Ballot and S. Mercone (CoFe 2 O 4 LSPM Paris 13 S. Gascoin (XRD CRISMAT Caen ANR FURNACE