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Structure of thin films by electron diffraction

Structure of thin films by electron diffraction. János L. Lábár. Usage of diffraction data in structure determination. Identifying known structures Solving unknown structures Structure determination Unit cell dimensions Space group symmetry

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Structure of thin films by electron diffraction

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  1. Structure of thin films by electron diffraction János L. Lábár

  2. Usage of diffraction data in structure determination • Identifying known structures • Solving unknown structures • Structure determination • Unit cell dimensions • Space group symmetry • Unit cell content (atoms and their appr. coordinates) • Structure refinement • More accurate atomic coordinates • Validation of the structure (attainable match)

  3. Structure determination • Periodic functions  Fourier coefficients • Amplitude : diffraction the phase problem • Phase : real space (HRTEM, fragment) reciprocal space (Direct methods) • Single crystal diffraction • X-rays, neutrons  electrons • Powder diffraction • X-rays, neutrons  electrons

  4. Single crystal diffraction • Tilting experiments • Identification of reflections: indexing • Unit cell dimensions • Space group symmetry (XRD, SAED, CBED) • Integration of individual intensities • Background • Phases (real  reciprocal space) • Dynamic intensities in SAED

  5. Single crystal diffraction • XRD: • Up to 2000 atoms in the asymmetric unit • Up to 100 atoms: guaranteed success • Rule of thumb: # refl > 10 * # atoms • SAED: • CRISP, ELD  Direct methods (EDM) • Dynamic intensities in SIR97 • Up to 30 atoms in the asymmetric unit • Size, image

  6. Powder diffraction • Collapse of 3D into 1D • Types: • Equivalent reflections, multiplicity • Exact overlap: e.g. (43l)  (50l) in tetragonal • Accidental: within instrumental resolution • Indexing programs • Peak decomposition • La Bail • Pawley

  7. Powder diffraction • Degree of overlap: Resolution • Background • Instability: negative peaks / oscillating int. • XRD (+ refinement from neutrons) : • Synchrotron: 60 atoms in asymmetric unit • Laboratory:  30 atoms in asymmetric unit • Neutron: better for refinement • SAED: instrumental resolution limit, BKG

  8. Powder diffraction: SAED resolution (peak width) • Beam convergence • Elliptical distortion • OL spherical aberration  size of selected area

  9. Powder diffraction: SAED elliptical distortion

  10. Powder diffraction: SAED spherical aberration

  11. Powder diffraction: Pattern decomposition with ProcessDiffraction • Background • Normal, log-Normal • Polynomial, Spline • Peak shapes • Gaussian, Lorentzian • Pseudo-Voigt • Global minimum • Downhill SIMPLEX • Manual control • Example: Al + Ge: SAED on film • Large crystal Al: Gaussian • Small crystal Ge: Lorentzian

  12. Pattern decomposition with ProcessDiffraction

  13. Structure refinement: The Rietveld method • Start from assumed structure • Least-square fitting of whole-pattern • Fitting parameters: • Scale-factor • Atomic positions • Temperature factors • Cell parameters • Peak shape parameters (instrumenal  sample) • Background • Additional peaks (phase)

  14. The Rietveld method • Most known structures from Rietveld refinement • Scaling factors  Quantitative phase analysis (volume fractions) • Neutrons: no angle dependence  best for refinement • Resolution (peak width) is less important  SAED can also be used efficiently for refinement • SAED: Cell parameters  camera length

  15. Quantitative phase analysis for nanocrystalline thin films from SAED • Example: 100 Å Al + 100Å NiO • Measured volume fraction by ProcessDiffraction: 51% Al + 49% NiO • Fitted parameters: peak parameters, L, scaling factors, DW

  16. Structure refinement from SAED • Integrated intensities: • ELD • ProcessDiffraction • Refinement: • FullProf • ProcessDiffraction • Simple example: TiO2 – Anatase • Selection of origin  transform „z” before compare

  17. Structure refinement with ProcessDiffraction • Structure definition modul • Checks: coordinates  site symmetry • Options modul checks • if selected site is „refinable” (variation of coordinate value does not change site symmetry) • If selected options are reasonable • Cross-checking for nanocrystalline samples • Pair correlation function (differentmodels  measured)

  18. ProcessDiffraction: Options for refinement

  19. Structure refinement with ProcessDiffraction • Example: Anatase 4 nm powder • Acceptable match • Refined position of oxygen: z=0.217 • Compare to z=0.2064 (Pearson’s) z=0.2094 (Weirich transformed)

  20. Is the example result acceptable?Independent test • Pair correlation function • Measured • Calculated for both structures • Refined result is in agreement with g(r)

  21. Remarks to refinement • Nanocrystalline films are strained • Exact shape and size of the background is ambiguous in electron diffraction • Refined position is also a function of refined cell dimensions (accurate calibration of camera length)

  22. Conclusions: structure of thin films by electron diffraction • Phase identification from both single crystal and powder patterns • Quantitative phase analysis from nanocrystalline powder patterns • Structure determination from single crystal patterns (SAED, CBED) • Structure refinement from nanocrystalline powder patterns • Limits are still to be examined

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