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 14050 CAEN Cedex, France 2 Department of Materials Engineering and Industrial Technologies, university of Trento, 38123 TRENTO, Italy [001] fit E-WIMV 82 Å data 38 Å Q (Å -1 ) E-MRS 2012 Spring Meeting – Strasbourg Symposium X
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) 297-304 � ProcessDiffraction : J.L. Labar, Microsc. Microanal. 15 (2009) 20-29 � TextPat : P. Oleynikov, S. Hovmoller and X.D. Zou in Electron Crystallography � The MAUD program : L. Lutterotti E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
MAUD Materials Analysis Using Diffraction http://www.ing.unitn.it/~maud/ MAUD Rietveld pattern fitting L. Lutterotti Delft size-strain (PV) Nuclear Inst. and Methods Popa anisotropic in Physics Res. B268, Evolutionary Size/Strain distributions 334-340, 2010. Simulated Annealing Planar faulting (Warren) Marquardt (Least squares) Turbostratic (Ufer) Metadynamics optimization Size-Strain Indexing Simplex (Nelder-Mead) Genetic (COD phase search procedure) March-Dollase Peak location X-ray Harmonic Texture Neutron (E)WIMV Standard Functions Electron Peak fitting Residual stresses Geometric Structure refinement Voigt, Reuss, Hill Triaxial Stress E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
MAUD Materials Analysis Using Diffraction download at http://www.ing.unitn.it/~maud/ Toolbar for common command shortcuts Tab panel to manage data sets, phases and Plot panel, drag and drop a sample. data file here to load a spectrum Toolbar to The MAUD stop/resume/slow down computation program is written in JAVA and can Output panel for the run on various refinement process platforms Full parameters list, to change the value, set refinable, fix or bound E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
MAUD Materials Analysis Using Diffraction Intensity extraction along the rings by segments using an ImageJ plugin center position and correction for a small elliptical pixel size ► pixels to mm distortion are 120 patterns refinable parameters rough estimation of the center position using a reference circle 3° on the screen CAKING chi=phi=0° / omega=90° / eta: 0° to 360° Calibrate the distance specimen/detector ► mm to 2 θ E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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 2 θ (°) => Q (Å -1 ) measured profile h(x) = f(x) ⊗ g(x) + b(x) E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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) Add new Ranking phases - 1D XRPD-like experimental profile - list of elements ( synthesis condition, EDX, EELS, … ) Best phase End: Y N - instrumental parameters ( pixels to scattering angle, peak shape function, … ) > threshold 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 , 726-729, 2009. E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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 Automatic indexing and phase ID is possible ! calculate the whole pattern profile TiO 2 rutile nanoparticules … see M. Reddy et al., ElectroChem. Com. 8 (2006) 1299-1303 for details Electron atomic scattering factors from the tables of L.M. Peng et al E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure ED-RP vs XRPD h(x) = f(x) ⊗ g(x) + b(x) Line broadening causes sample contribution instrumental broadening • 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 and P. Scardi, J. of Appl. Crystallogr. 23, 246-252 (1990) The instrumental Peak Shape Function is obtained by analysing nanoparticules of known sizes and shapes as obtained from X-ray analyses E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure ED-RP vs XRPD Mn 3 O 4 hausmanite ( L. Sicard - ITODYS - UMR 7086 CNRS / Univ. Paris 7 ) Reflection mode Bruker D8 / Lynx Eye 1D acq. time:3h30 λ =1.54056 Å (Cu K α 1 ) > 100mg powder 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 E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure ED-RP vs XRPD Mn 3 O 4 hausmannite ( L. Sicard et al, J. Magn. Magn. Mater. 322 (2010) 2634-2640 ) Bruker D8 / Lynx Eye 1D structure g(x) ► f(x) λ =1.54056 Å (Cu K α 1 ) SG: I 4 1 /a m d a=5.764(2)Å and c=9.448(4)Å 64 Å POPA anisotropic 53 Å shape TOPCON 2B / CCD ORIUS pattern matching f(x) ► g(x) λ =0.0251Å a=5.7757(2)Å and c=9.4425(4)Å E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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°9001681) 72 patterns 5° 20nm FEI Tecnai / CCD USC1000 / λ =0.0197Å (1) M. Reddy et al., ElectroChem. Com. 8 (2006) 1299-1303 E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure Size and texture effects 4-circles diffract. / INEL CPS structure RX λ = CuK α 47 Å [001] 76 Å average anisotropic crystallite size pattern matching ED-RP 38 Å 82 Å E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure Size and texture effects The features available in MAUD allow a full quantitative texture analysis for 0.5 μ m 6 μ m general cases (not only fiber textures!) from electron diffraction data with the decreasing the obtention of accurate pole figures. selected area ► application on textured thin film see M. Gemmi et al., J. Appl. Cryst. 44 (2011) Texture :: intensity variation along the rings local texture analysis fit fit no texture E-WIMV data data reconstructed pole figure (from the Orientation Q (Å -1 ) Q (Å -1 ) Distribution Function) E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
Microstructure Pattern matching mode? 39 Å 47 Å RX: a=4.583(1)Å c=2.949(1)Å x(O 1 )=y(O 1 )=0.3062(5) 85 Å 79 Å RX a=4.571(1)Å c=2.938(1)Å pattern matching 27 Å a=4.584(1)Å c=2.936(1)Å x(O 1 )=y(O 1 )=0.3006(2) 105 Å Blackman 2-beams correction x(O 1 )=y(O 1 )=0.3064(2) structure – kinematic approximation E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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 nanoparticules) @ CRISMAT – Caen L. Sicard and S. Ammar (Mn 3 O 4 nanoparticules) @ ITODYS – Paris 7 N. Ballot and S. Mercone (CoFe 2 O 4 nanoparticules) @ LSPM – Paris 13 S. Gascoin (XRD measurements) @ CRISMAT – Caen ANR FURNACE E-MRS 2012 Spring Meeting – Symposium X P. Boullay - CRISMAT Caen France
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