@article{ muller_atomic_2014,
  title = {Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction},
  volume = {5},
  copyright = {© 2014 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  url = {http://www.nature.com/ncomms/2014/141215/ncomms6653/abs/ncomms6653.html},
  doi = {10.1038/ncomms6653},
  abstract = {By focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary ​GaN as an ideal model system. We then present a detailed experimental study of ​SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.
View full text},
  language = {en},
  urldate = {2015-01-29TZ},
  journal = {Nature Communications},
  author = {Müller, Knut and Krause, Florian F. and Béché, Armand and Schowalter, Marco and Galioit, Vincent and Löffler, Stefan and Verbeeck, Johan and Zweck, Josef and Schattschneider, Peter and Rosenauer, Andreas},
  year = {2014},
  keywords = {Applied physics, Biological sciences, Materials science, Optical physics}
}

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A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary ​GaN as an ideal model system. We then present a detailed experimental study of ​SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. 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