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Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils

  • A. Thesing and H. Kohl EMAIL logo
Published/Copyright: February 12, 2022
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 97 Issue 7

Abstract

In this study we analyse diffractograms of elastically filtered images of thin amorphous foils of carbon, silicon and germanium using the weak object approximation. The use of this approximation leads to a contrast transfer function containing a phase η(u) depending on the spatial frequency u. Furthermore, the derivative of this phase is included in the envelope function of the contrast transfer function. The phase can be attributed to the breakdown of the first-order Born approximation leading to complex scattering amplitudes characterized by this phase η(u).

We analyse contrast transfer characteristics to determine the phase of complex scattering amplitudes of carbon, silicon and germanium as a function of spatial frequency and to measure the two-particle structure factor of the corresponding amorphous specimens. The contrast transfer characteristics were calculated from diffractograms of focal series of elastically filtered images.

The phases measured show a decay with increasing spatial frequency and additional oscillations. The results for the two-particle structure factor also decay with increasing spatial frequency and contain low local maxima. Both can be attributed to voids or inhomogeneities within the amorphous structure.

Keywords: Complex scattering amplitudes; Two-particle structure factor; Weak object approximation; Contrast transfer function

Dedicated to Professor Dr. Knut Urban on the occasion of his 65th birthday

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 33640 Fax: +49 251 33602

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Received: 2006-02-08
Accepted: 2006-04-09
Published Online: 2022-02-12

© 2006 Carl Hanser Verlag, München

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Professor Dr. Knut Urban 65 Years
  4. Basic
  5. Ordering processes and atomic defects in FeCo
  6. Atomic resolution electron tomography: a dream?
  7. Electron tomography of microelectronic device interconnects
  8. Aberration correction in electron microscopy
  9. Off-axis electron holography: Materials analysis at atomic resolution
  10. Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils
  11. Prospects of the multislice method for CBED pattern calculation
  12. Electron energy-loss spectrometry for metals:some thoughts beyond microanalysis
  13. Quantitative assessment of nanoparticle size distributions from HRTEM images
  14. Quantitative microstructural and spectroscopic investigation of inversion domain boundaries in sintered zinc oxide ceramics doped with iron oxide
  15. Structural domains in antiferromagnetic LaFeO3 thin films
  16. Short-range order of liquid Ti72.3Fe27.7 investigated by a combination of neutron scattering and X-ray diffraction
  17. Extended interfacial structure between two asymmetrical facets of a Σ = 9 grain boundary in copper
  18. Dislocation imaging in fcc colloidal single crystals
  19. Applied
  20. Omega phase transformation – morphologies and mechanisms
  21. Mixed (Sr1 − xCax)33Bi24Al48O141 fullerenoids: the defect structure analysed by (S)TEM techniques
  22. Wetting of aluminium-based complex metallic alloys
  23. Annealing-induced phase transitions in a Zr–Ti–Nb–Cu–Ni–Al bulk metallic glass matrix composite containing quasicrystalline precipitates
  24. Special planar defects in the structural complex metallic alloys of Al–Pd–Mn and Al–Ni–Rh
  25. On the formation of Si nanowires by molecular beam epitaxy
  26. Self-induced oscillations in Si and other semiconductors
  27. Growth, interface structure, and magnetic properties of Fe/GaAs and Fe3Si/GaAs hybrid systems
  28. An investigation of improved titanium/titanium nitride barriers for submicron aluminum-filled contacts by energy-filtered transmission electron microscopy
  29. Radiation damage during HRTEM studies in pure Al and Al alloys
  30. Cross-sectional high-resolution transmission electron microscopy at Mo/Si multilayer stacks
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  33. Notifications
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https://doi.org/10.1515/ijmr-2006-0145
Keywords for this article
Complex scattering amplitudes; Two-particle structure factor; Weak object approximation; Contrast transfer function

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Professor Dr. Knut Urban 65 Years
  4. Basic
  5. Ordering processes and atomic defects in FeCo
  6. Atomic resolution electron tomography: a dream?
  7. Electron tomography of microelectronic device interconnects
  8. Aberration correction in electron microscopy
  9. Off-axis electron holography: Materials analysis at atomic resolution
  10. Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils
  11. Prospects of the multislice method for CBED pattern calculation
  12. Electron energy-loss spectrometry for metals:some thoughts beyond microanalysis
  13. Quantitative assessment of nanoparticle size distributions from HRTEM images
  14. Quantitative microstructural and spectroscopic investigation of inversion domain boundaries in sintered zinc oxide ceramics doped with iron oxide
  15. Structural domains in antiferromagnetic LaFeO3 thin films
  16. Short-range order of liquid Ti72.3Fe27.7 investigated by a combination of neutron scattering and X-ray diffraction
  17. Extended interfacial structure between two asymmetrical facets of a Σ = 9 grain boundary in copper
  18. Dislocation imaging in fcc colloidal single crystals
  19. Applied
  20. Omega phase transformation – morphologies and mechanisms
  21. Mixed (Sr1 − xCax)33Bi24Al48O141 fullerenoids: the defect structure analysed by (S)TEM techniques
  22. Wetting of aluminium-based complex metallic alloys
  23. Annealing-induced phase transitions in a Zr–Ti–Nb–Cu–Ni–Al bulk metallic glass matrix composite containing quasicrystalline precipitates
  24. Special planar defects in the structural complex metallic alloys of Al–Pd–Mn and Al–Ni–Rh
  25. On the formation of Si nanowires by molecular beam epitaxy
  26. Self-induced oscillations in Si and other semiconductors
  27. Growth, interface structure, and magnetic properties of Fe/GaAs and Fe3Si/GaAs hybrid systems
  28. An investigation of improved titanium/titanium nitride barriers for submicron aluminum-filled contacts by energy-filtered transmission electron microscopy
  29. Radiation damage during HRTEM studies in pure Al and Al alloys
  30. Cross-sectional high-resolution transmission electron microscopy at Mo/Si multilayer stacks
  31. Structural properties of the fiber –matrix interface in carbon-fiber/carbon-matrix composites and interfaces between carbon layers and planar substrates
  32. Microstructure and properties of surface-treated Timetal 834
  33. Notifications
  34. Personal
  35. Conferences
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