Resolution Quality and Atom Positions in Sub-Angstrom Electron Microscopy

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Ability to determine whether an image peak represents one single atom or several depends on resolution of the HR-(S)TEM. Rayleigh's resolution criterion, an accepted standard in optics, was derived as a means for judging when two image intensity peaks from two sources of light (stars) are distinguishable from a single source. Atom spacings closer than the Rayleigh limit have been resolved in HR-TEM, suggesting that it may be useful to consider other limits, such as the Sparrow resolution criterion. From the viewpoint of the materials scientist, it is important to be able to use the image to determine whether an ... continued below

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O'Keefe, Michael A.; Allard, Lawrence F. & Blom, Douglas A. February 15, 2005.

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Ability to determine whether an image peak represents one single atom or several depends on resolution of the HR-(S)TEM. Rayleigh's resolution criterion, an accepted standard in optics, was derived as a means for judging when two image intensity peaks from two sources of light (stars) are distinguishable from a single source. Atom spacings closer than the Rayleigh limit have been resolved in HR-TEM, suggesting that it may be useful to consider other limits, such as the Sparrow resolution criterion. From the viewpoint of the materials scientist, it is important to be able to use the image to determine whether an image feature represents one or more atoms (resolution), and where the atoms (or atom columns) are positioned relative to one another (resolution quality). When atoms and the corresponding image peaks are separated by more than the Rayleigh limit of the HR-(S)TEM, it is possible to adjust imaging parameters so that relative peak positions in the image correspond to relative atom positions in the specimen. When atoms are closer than the Rayleigh limit, we must find the relationship of the peak position to the atom position by peak fitting or, if we have a suitable model, by image simulation. Our Rayleigh-Sparrow parameter QRS reveals the ''resolution quality'' of a microscope image. QRS values greater than 1 indicate a clearly resolved twin peak, while values between 1 and 0 mean a lower-quality resolution and an image with peaks displaced from the relative atom positions. The depth of the twin-peak minimum can be used to determine the value of QRS and the true separation of the atom peaks that sum to produce the twin peak in the image. The Rayleigh-Sparrow parameter can be used to refine relative atom positions in defect images where atoms are closer than the Rayleigh limit of the HR-(S)TEM, reducing the necessity for full image simulations from large defect models.

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OSTI as DE00842050

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  • Microscopy & Microanalysis 2005, Honolulu, HI (US), 07/31/2005--08/04/2005

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  • Report No.: LBNL--57524
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 842050
  • Archival Resource Key: ark:/67531/metadc782723

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  • February 15, 2005

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  • Dec. 3, 2015, 9:30 a.m.

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  • Sept. 21, 2017, 6:04 p.m.

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O'Keefe, Michael A.; Allard, Lawrence F. & Blom, Douglas A. Resolution Quality and Atom Positions in Sub-Angstrom Electron Microscopy, article, February 15, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc782723/: accessed December 15, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.