What does the diffraction pattern from a single atom look like? How does it differ from the scattering from long-range potential? With the development of new high-dynamic range pixel array detectors to measure the complete momentum distribution, these questions have immediate relevance for designing and understanding momentumresolved imaging modes. We explore the asymptotic limits of long-range and shortrange potentials. We use a simple quantum mechanical model to explain the general and asymptotic limits for the probability distribution in both real and reciprocal space. Features in the scattering potential much larger than the probe size cause the bright field (BF) disk to deflect uniformly, while features much smaller than the probe size, instead of a deflection, cause a redistribution of intensity within the BF disk. Because long-range and short-range features are encoded differently in the diffraction pattern, it is possible to separate their contributions in differential phase-contrast (DPC) or center-of-mass (CoM) imaging. The shape profiles for atomic resolution CoM imaging are dominated by the shape of the probe gradient and not the highly singular atomic potentials or their local fields. Instead, only the peak height shows an atomic number sensitivity, whose precise dependence is determined by the convergence angle. At lower convergence angles, the contrast oscillates with increasing atomic number, similar to BF imaging. The range of collection angles impacts DPC and CoM imaging differently, with CoM being more sensitive to the upper cutoff limit, while DPC is more sensitive to the lower cutoff.
|Original language||English (US)|
|Number of pages||1|
|State||Published - Dec 29 2017|
Bibliographical noteKAUST Repository Item: Exported on 2022-06-09
Acknowledgements: The authors acknowledge microscopy support from John Grazul and Mariena Silvestry Ramos. The WSe2 sample was provided by Ming-Yang Li from the Lain-Jong Li group at King Abdullah University of Science and Technology. We thank Mark Tate, Prafull Purohit, and Sol Gruner for help with the pixel array detector. This work was supported by the Air Force Office of Scientific Research through the 2D Electronics Multidisciplinary University Research Initiative (MURI) grant FA9550-16-1-0031 (MC) and the National Science Foundation (NSF) through the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM; DMR-1539918) (ZC). Support for the Mixed Mode Pixel Array Detector (MM-PAD) development was provided by the U.S. Department of Energy (grant DE-FG02- 10ER46693). The adaptation to the STEM was supported by the Kavli Institute at Cornell for Nanoscale Science. Electron microscope and facility support from the Cornell Center for Materials Research, through the National Science Foundation MRSEC program, award #DMR 1719875.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
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