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## Precession Diffraction: The Philosphers Stone of Electron Crystallography Focus What

Louvion, Christophe, Contributor has reference to this Academic Journal, PHwiki organized this Journal Precession Diffraction: The Philosphers Stone of Electron CrystallographyFocusMany methods exist as long as obtaining diffraction in as long as mationSelected AreaNanodiffraction in addition to variantsCBEDAll are complicated to interpretReciprocal space is right, but intensities depend upon thickness, tilt etcWhat PED can doWe would like a method where not just the positions of the spots, but also the intensities could be used.Not rigorously equivalent to simple kinematical diffraction, but has many similaritiesIf the structure factor is large Intensity is largeUseful as long as fingerprinting structuresOften does not need calculations to interpret

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History Electron Precession (1993)Advantages:SpecimenConventional Diffraction PatternPrecession Precession Diffraction Pattern(Ga,In)2SnO5 Intensities412Å crystal thickness(Diffracted amplitudes)Precession SystemUS patent application:A hollow-cone electron diffraction system. Application serial number 60/531,641, Dec 2004.

Can be easily retrofitable to any TEM 100- 300 KV precession is possible as long as any beam size 300 – 50 nm Precession is possible as long as a parallel or convergent beam precession eliminates false spots to ED pattern that belong to dynamical contributions precession angle can vary continuously (0°-3°) to observe true crystallographic symmetry variation Software ELD as long as easy quantification of ED intensities in addition to automatic symmetry ( point, space group ) researchSPINNING STAR : UNIVERSAL INTERFASE FOR PRECESSION ELECTRON DIFFRACTION FOR ANY TEM ( 120 -200 -300 KV ) Easily interfaced to electron diffractometer as long as automatic 3D structure determinationExamples:Complicated StructuresHard to interpret SAEDSimple to interpret PEDEDSElemental ratios depend upon orientation in st in addition to ard modeWeak to no dependence with PEDAPPLICATION : FIND TRUE CRYSTAL SYMMETRY PRECESSION OFF IDEAL KINEMATICAL (111)UVAROVITE (111) PRECESSION ONCourtesy M.Gemmi Univ of Milano

APPLICATION : PERFECT CRYSTAL ORIENTATION PRECESSION OFFPRECESSION ONCrystals specially minerals -usually grow in platelet or fiber shape in addition to results dificult to orient perfectly in a particular zone axis; in this example olivine crystals are perfectly oriented after precession is on.OLIVINECourtesy X.Zou, S.Hovmoller Univ StockholmCarbideEDS, on zone (SrTiO3)RepeatMeasurements

Practical UseTwo commercial systems (one hardware, another software) are availableNot complicated, in addition to could probably be written in scripting languageAlignment can be tricky it always isNot rocket science, to useBi-polar push-pull circuit (H9000)Projector Spiral Distortions (60 mRad tilt)Some Practical Issues Block DiagramAberrations

SampleObjective PostfieldObjective PrefieldIdealized DiagramDescanScanRemember the opticsSampleObjective PostfieldObjective PrefieldDescanScanCorrect DiagramBoth MisalignedIdealized DiagramRemember the opticsAlignment can be tricky

WhyAlthough PED has been around since 1992, in addition to very actively used as long as ~10 years (mainly in Europe), there is no simple explanation (many have tried in addition to failed)Explanation is a bit rocket scienceWhyWhat, if any generalizations can be madeRole of Precession AngleSystematic Row LimitImportance of integration Phase insensitivityImportant as long as which reflections are usedFast Integration OptionsEwald Sphere Constructionz

Levels of theoryPrecession integrates each beam over szFull dynamical theoryAll reciprocal lattice vectors are coupled in addition to not seperablePartial dynamical theory (2-beam) Consider each reciprocal lattice vector dynamically coupled to transmitted beam onlyKinematical theoryConsider only role of sz assuming weak scatteringBraggs LawI = F(g)2Early Models Iobs depends upon F(g), g, f (precession angle) which we correct to the true resultOptions:0) No correction at all, I=F(g)2 1) Geometry only (Lorentz, by analogy to x-ray diffraction) corresponds to angular integration2) Geometry plus multiplicative term as long as F(g)Braggs Law fails badly (Ga,In)2SnO5

Kinematical Lorentz Correction I(g) =ò F(g) sin(ptsz)/(psz) 2 dsz sz taken appropriately over the Precession Circuit t is crystal thickness (column approximation) f is total precession angle I(g) = F(g)2L(g,t,f) K. Gjønnes, Ultramicroscopy, 1997.Kinematical Lorentz correction: Geometry in as long as mation is insufficientNeed structure factors to apply the correction!FkinFcorr2-Beam (Blackman) as long as mLimits:Ag small; Idyn(k) µ Ikin(k)Ag large; Idyn(k) µ ÖIkin(k) = Fkin(k)But This assumes integration over all angles, which is not correct as long as precession (correct as long as powder diffraction)

Blackman FormBlackman+LorentzAlas, little better than kinematicalComparison with full calculation, 24 mRadAngstromsTwo-Beam Form I(g) = ò F(g) sin(ptseffz)/(pseffz) 2 dsz sz taken appropriately over the Precession Circuit szeff = (sz2 + 1/xg2)1/2 Do the proper integration over sz (not rocket science)

Why is works – Intensity mappingIff Iobs(k1)>Iobs(k2) when Fkin(k1) > Fkin(k2)Structure should be invertible (symbolic logic, triplets, flipping )SummaryPED isApproximately InvertablePseudo Braggs LawApproximately 2-beam, but not greatProperly Explained by Dynamical TheoryPED is notPseudo-Kinematical (this is different!)Fully Understood by Dummies, yetQuestions

## Louvion, Christophe Contributor

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