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Determination of the contrast transfer function by analysing diffractograms of thin amorphous foils

  • Rainer Knippelmeyer , Andreas Thesing and Helmut Kohl EMAIL logo
Published/Copyright: January 11, 2022
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 94 Issue 3

Abstract

We have analysed diffractograms of elastically filtered phase contrast images of thin evaporated amorphous silicon and carbon foils. For this analysis the two-particle structure factor was taken into account. It was determined from diffractograms of inelastically filtered images using calculated inelastic transfer functions. Due to the high accuracy of this new method, we were able to explain and reproduce quantitatively the intensity profile in the low spatial frequency range of the elastically filtered diffractograms. We could show that the weak-phase object approximation, which is normally used for the evaluation of such diffractograms is not adequate in this region. Instead, one has to use the weak-object approximation, which allows for a small imaginary part of the atomic scattering factor. In spite of the latter being only 3–10 % of the real part for the analysed materials it is observable, because the two-particle structure factor increases steeply for low spatial frequencies (in the direction of decreasing spatial frequencies).

Keywords: Contrast transfer function; Weak object approximation; Two-particle structure factor; Inelastic transfer function
Prof. Dr. Helmut Kohl Physikalisches Institut und Interdisziplinäres Centrum für Elektronenmikroskopie und Mikroanalyse (ICEM) Wilhelm-Klemm-Str. 10, D-48149 Münster, Germany Tel.:+49 251 83 33640 Fax: +49 251 83 33602
Dedicated to Professor Dr. Dr. h. c. Manfred Rühle on the occasion of his 65th birthday

Funding statement: This work is part of a Ph. D. dissertation and a diploma thesis at the Mathematisch-Naturwissenschaftliche Fakultät of the Westfälische Wilhelms-Universität Münster. Financial support by the Deutsche Forschungsgemeinschaft (Ko 885/7-1 and 7-2) is gratefully acknowledged. R. K. would like to thank G. Möbus for fruitful discussions.

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Received: 2002-10-14
Published Online: 2022-01-11

© 2003 Carl Hanser Verlag, München

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Editorial
  4. Articles/Aufsätze
  5. The role of oxidation-induced cavities on the failure of the thermally grown oxide on binary β-NiAl alloys
  6. Phase stability of Y + Gd co-doped zirconia
  7. Mechanisms governing the distortion of alumina-forming alloys upon cyclic oxidation
  8. High-temperature oxidation of FeCrAl alloys: the effect of Mg incorporation into the alumina scale
  9. Nonlinear dielectric properties at oxide grain boundaries
  10. TEM observations of singular grain boundaries and their roughening transition in TiO2-excess BaTiO3
  11. Processing of dense MgO substrates for high-temperature superconductors
  12. Microwave-induced crystallization of polysilazane-derived silicon carbonitride
  13. Schottky barrier formation in liquid-phase-sintered silicon carbide
  14. SrTiO3: a model electroceramic
  15. Optical properties and electronic structure of oxidized and reduced single-crystal strontium titanate
  16. Spreading of liquid Ag and Ag–Mo alloys on molybdenum substrates
  17. Nanoalloying in mixed AgmAun nanowires
  18. Never ending saga of a simple boundary
  19. Comparison of interfacial chemistry at Cu/α-alumina and Cu/γ-alumina interfaces
  20. Microstructure of Cu2O/Si interfaces, made by epitaxial electrodeposition
  21. Metal/oxide interfaces and their reaction with hydrogen
  22. Amorphous films at metal/ceramic interfaces
  23. Some thoughts on source monochromation and the implications for electron energy loss spectroscopy
  24. Determination of the contrast transfer function by analysing diffractograms of thin amorphous foils
  25. Progress in the preparation of cross-sectional TEM specimens by ion-beam thinning
  26. Quantification of interfacial segregation by analytical electron microscopy
  27. Quantification of elemental segregation to lath and grain boundaries in low-alloy steel by STEM X-ray mapping combined with the ζ-factor method
  28. Microstructure of Al/Ti metallization layers
  29. Connectivity of CSL grain boundaries and the role of deviations from exact coincidence
  30. Effect of laser shock processing on the microstructure and mechanical properties of pure Cu
  31. Growth and microstructure of iron nitride layers and pore formation in ε-Fe3N
  32. Phase diagram of the Al–Cu–Fe quasicrystal-forming alloy system
  33. Notifications/Mitteilungen
  34. Personal/Personelles
  35. Gesellschaftsnachricht
  36. International Conferences
https://doi.org/10.3139/ijmr-2003-0053
Keywords for this article
Contrast transfer function; Weak object approximation; Two-particle structure factor; Inelastic transfer function

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Editorial
  4. Articles/Aufsätze
  5. The role of oxidation-induced cavities on the failure of the thermally grown oxide on binary β-NiAl alloys
  6. Phase stability of Y + Gd co-doped zirconia
  7. Mechanisms governing the distortion of alumina-forming alloys upon cyclic oxidation
  8. High-temperature oxidation of FeCrAl alloys: the effect of Mg incorporation into the alumina scale
  9. Nonlinear dielectric properties at oxide grain boundaries
  10. TEM observations of singular grain boundaries and their roughening transition in TiO2-excess BaTiO3
  11. Processing of dense MgO substrates for high-temperature superconductors
  12. Microwave-induced crystallization of polysilazane-derived silicon carbonitride
  13. Schottky barrier formation in liquid-phase-sintered silicon carbide
  14. SrTiO3: a model electroceramic
  15. Optical properties and electronic structure of oxidized and reduced single-crystal strontium titanate
  16. Spreading of liquid Ag and Ag–Mo alloys on molybdenum substrates
  17. Nanoalloying in mixed AgmAun nanowires
  18. Never ending saga of a simple boundary
  19. Comparison of interfacial chemistry at Cu/α-alumina and Cu/γ-alumina interfaces
  20. Microstructure of Cu2O/Si interfaces, made by epitaxial electrodeposition
  21. Metal/oxide interfaces and their reaction with hydrogen
  22. Amorphous films at metal/ceramic interfaces
  23. Some thoughts on source monochromation and the implications for electron energy loss spectroscopy
  24. Determination of the contrast transfer function by analysing diffractograms of thin amorphous foils
  25. Progress in the preparation of cross-sectional TEM specimens by ion-beam thinning
  26. Quantification of interfacial segregation by analytical electron microscopy
  27. Quantification of elemental segregation to lath and grain boundaries in low-alloy steel by STEM X-ray mapping combined with the ζ-factor method
  28. Microstructure of Al/Ti metallization layers
  29. Connectivity of CSL grain boundaries and the role of deviations from exact coincidence
  30. Effect of laser shock processing on the microstructure and mechanical properties of pure Cu
  31. Growth and microstructure of iron nitride layers and pore formation in ε-Fe3N
  32. Phase diagram of the Al–Cu–Fe quasicrystal-forming alloy system
  33. Notifications/Mitteilungen
  34. Personal/Personelles
  35. Gesellschaftsnachricht
  36. International Conferences
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