System Design and Verification of the Precession Electron Diffraction Technique Christopher S. Own Thesis defense · 2005.07.13
Acknowledgements � People � L.D. Marks � Wharton Sinkler � Marks Group • Arun Subramanian, Jim Ciston, Bin Deng � Hitachi and JEOL support • Ken Eberly, Jim Poulos, Mike Kersker � Winfried Hill and Vasant Ramasubramanian � Shi-Hau Own � Funding � Fannie and John Hertz Foundation � UOP LLC, STCS, US DOE (Grant DE-FG02-03ER 15457)
Overview Background I. Motivation � Precession Electron Diffraction (PED) � System Design II. Instrumentation � Verification III. Simulation � Theoretical models � Examples IV. Conclusions / Future Work V.
I. Background
Motivation: Routine Structural Crystallography Direct Starting Methods Diffraction structure Intensities model True Refinement Structure
Direct Methods (DM) � In diffraction experiment we measure intensities Real space FT � (phase information lost) constraints (S 1 ) Φ = − φ Fourier space ( k ) F ( k ) exp( i ( k )) constraints (S 2 ) = 2 I ( k ) F ( k ) FT -1 Recovery Criterion � Recover phases to generate NO feasible scattering potential YES maps Observed Intensities Observed Intensities � Need good intensities to Feasible (assigned phases) recover correct phases Solution (Genetic Algorithm) � Else get false structure!
Motivation (cont’d) � The crystallography workhorse: X-ray diffraction � Limitations for nanoscale characterization: • Too low S/N for small crystals, need synchrotron • Synchrotron: Cost / time restriction • Ring overlap (powder) • No imaging � Solution: Electron Diffraction (ED) � Simultaneous imaging/diffraction � EDX, EFTEM, etc… � Readily available / inexpensive
Problem: Multiple Scattering � Terminology: X-rays: Kinematical Electrons: Dynamical λ = θ 2 d sin � Direct Methods requires good quality intensities (<15% error) z � ED is often too dynamical: � Want kinematical, but even thin specimens dynamical • Ultra-thin specimens Multiple scattering: impossible to make (except surfaces) � Error can be 1,000’s of %! Thickness matters! • Hindered routine electron crystallography.
Electron Direct Methods can work! � Data can be kinematical � Thin specimens (surfaces) � Some dynamical data can work � Channeling (good projection) • Phase relationships preserved statistically � Pseudo-kinematical EDM • Also called intensity mapping • Assumes deviation from kinematical • Intensity relationships preserved • Powder, texture patterns � Precession
Vincent-Midgley Precession Technique (PED) † � In theory: � Reduces multiple scattering (always off- φ zone) • Lower sensitivity to thickness � Reduces sensitivity to misorientation � “Quasi-kinematical” intensities result • May need correction factors (requires known structure factors) (Vincent & Midgley, Ultramicroscopy 1994.)
Scan Specimen Non-precessed De-scan (Ga,In) 2 SnO 5 Intensities 412Å crystal thickness Conventional Precession Precession… Diffraction Pattern Diffraction Pattern Precessed (Diffracted amplitudes)
(Excitation Error) Ewald Sphere Construction
Problems and Questions � Previous studies: †(J. Gjonnes, et al., Acta Cryst A, 1998. K. Gjonnes, et al., Acta Cryst A, 1998. � R-factors ~ 0.3-0.4 † M. Gemmi, et al., Acta Cryst A, 2003.) � Precession was not well-understood � Can one just use intensities? � How to use correction factors if F g not known? • Are they correct? • Is geometry-only valid? � Our early experiments gave mixed results too � Why didn’t it work? � How can we make it work?
II. System Design
US patent application: “A hollow-cone electron diffraction system”. Application serial number 60/531,641, Dec 2004. The Design
Generation II hardware
= A ⋅ θ = s ⋅ θ x cos x cos 1 1 2 Optical Aberration = A ⋅ θ = − ⋅ θ y sin y s sin 1 1 2 [ ] ( ( ) ) = A ⋅ ⋅ θ + φ ⋅ θ Compensation x cos 3 cos 3 3 3 [ ] ( ( ) ) = A ⋅ ⋅ θ + φ ⋅ θ y cos 3 sin 3 3 3 = + ⋅ φ + + ⋅ φ + x out [( x x ) cos ( y y ) sin ] x 1 2 2 1 2 2 3 For forming = − + ⋅ φ + + ⋅ φ + y out [ ( x x ) sin ( y y ) cos ] y fine probe 1 2 2 1 2 2 3 2 1.5 1 0.5 0 -2 -1 0 1 2 -0.5 -1 2-fold 45° -1.5 rotation -2 2 1.5 1 0.5 0 -2 -1 0 1 2 -0.5 -1 -1.5 -2 3-fold, no rotation
III. Verification Section Outline: � Investigate models � Multislice simulation � Comparison of correction factors (old and new) � Compare to experimental data � Suggested approach for novel structures
Simulation parameters � φ = cone semi-angle 2 φ � 0 – 50 mrad typical � t = thickness t � ~20 – 50 nm typical � Explore: 4 – 150 nm � g = reflection vector � | g | = 0.25 – 1 Å -1 are structure-defining
Multislice Simulation: A Correct Model
Error analysis: F sim (t) – F kin (normalized) 10mrad 24mrad 75mrad 50mrad 0mrad Error Experimental dataset thickness g (Own, Sinkler, & Marks, in preparation.)
(Ga,In) 2 SnO 4 data Kinematical Amplitudes Precession Intensities
(Ga,In) 2 SnO 4 precession data: High-pass filtered amplitudes (Real Space) ∆ R (Å) Displacement (R neutron – R precession ): Sn1 0.00E+00 Sn2 0.00E+00 Sn3 6.55E-03 ∆ R mean < 4 pm In/Ga1 5.17E-02 In/Ga2 2.37E-03 Ga1 6.85E-02 (Sinkler, et al. J. Solid State Chem, 1998. Ga2 1.22E-01 Own, Sinkler, & Marks, in press.)
(Own, Sinkler, & Marks, in preparation.) Global error metric: R 1 R-factor, (Ga,In) 2 SnO 4 0.8 0.7 0.6 ( ) 0.5 ∑ R-factor − F F 0.4 = exp sim R ∑ 0.3 1 F exp 0.2 Dynamical 0.1 Precession 0 0 250 500 750 1000 1250 1500 t (Å) Broad clear global minimum � R-factor = 0.118 � Experiment matches simulated known structure � Compare to > 0.3 from previous precession studies (unrefined!) � Accurate thickness determination: � Average t ~ 41nm (very thick crystal for studying this material) �
t > 50 nm: needs correction How to use PED intensities � Treat like powder diffraction � Apply Lorentz-type dynamical correction factor to get true intensity: † ≈ = × true corrected exp I I C I g g Blackman g ⎛ ⎞ ⎜ ⎟ π ⎜ ⎟ ⎛ ⎞ t A ( ) g = ⎜ ⎟ , φ = − × g ⎜ ⎟ A C g t , g 1 ⎜ ⎟ ξ Blackman g A 2 ⎝ ⎠ 2 R ⎜ ⎟ g ( ) ∫ 0 g J 2 x dx ⎜ ⎟ 0 ⎝ ⎠ 0 *An approximation* † (K. Gjønnes, Ultramic, 1997. Geometry Dynamical M. Blackman, Proc. Roy. Soc., 1939.) correction correction
Lorentz-only correction: Geometry information is insufficient F corr F kin Need structure factors to apply the correction!
New Dynamical Two-beam Correction Factor ( ) − 1 ⎛ ⎞ π π 2 2 sin ts ( ) 1 ⎜ ⎟ ∫ φ = θ 2 eff ( ) C g , t , F d ⎜ ⎟ 2 beam g ξ 2 2 s ⎝ ⎠ g 0 eff � Sinc function altered by ξ g 1 = + 2 s s ξ eff 2 g � A function of structure factor F g π θ V cos ξ = c B � Some F g must be λ g F g known to use!
t = 20 nm, ξ g = 25 nm
C Blackman v. C 2beam ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ A ( ) g ⎜ ⎟ , φ = − × g ⎜ ⎟ C g t , g 1 ⎜ ⎟ Blackman A ⎝ ⎠ 2 R ⎜ ⎟ g ( ) ∫ 0 J 2 x dx ⎜ ⎟ 0 ⎝ ⎠ 0 C Blackman approximates C 2beam ( ) − when |sinc| 2 is sufficiently integrated 1 ⎛ ⎞ π π 2 2 sin ts ( ) 1 ⎜ ⎟ ∫ φ = θ 2 eff ( ) C g , t , F d ⎜ ⎟ 2 beam g ξ 2 2 s ⎝ ⎠ g 0 eff
C 2beam correction: t = 127 nm, φ = 75 mrad (No apparent g-preference)
a priori correction: GITO ( 41 nm) Consider the limits of the Blackman formula Correction ⎛ ⎞ factor ⎜ ⎟ ⎜ ⎟ A = × g ⎜ ⎟ C Geom Blackman A ⎜ ⎟ g ( ) ∫ J 0 2 x dx ⎜ ⎟ ⎝ ⎠ 0 π t = A g ξ 2 g Corrected Intensities
Try GITO Using intensities ( F g 2 ) w/ DM (Real Space) ∆ R (Å) Displacement (R neutron – R precession ): Sn1 0.00E+00 Sn2 0.00E+00 Sn3 6.55E-03 ∆ R mean < 4 pm In/Ga1 5.17E-02 In/Ga2 2.37E-03 Ga1 6.85E-02 (Sinkler, et al. J. Solid State Chem, 1998. Ga2 1.22E-01 Own, Sinkler, & Marks, in press.)
Suggested PED flowchart
IV. Examples La 4 Cu 3 MoO 12 Al 8 Si 40 O 96 Al 2 SiO 5 1. 2. 3.
La 4 Cu 3 MoO 12 [001] I ntensities comparison Kinematical Intensities Conventional Diffraction PED intensities Intensities
Proposed structure: highly ordered b = 10.98 Å � Homeotype of YAlO 3 � Rare earth hexagonal phase � Frustrated structure: a = 6.46Å doubling of cell along a-axis † � Maintains stoichiometry � Better R-factor if twinning model introduced in refinement † (Griend et al., JACS 1999.)
PED solutions: disorder 5 Å Amplitude solution Intensity solution (high-pass filtered) (high-pass filtered)
Al 8 Si 40 O 96 [001] (Mordenite): Thick (50 nm), poor projection characteristics Kinematical amplitudes PED intensities
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