Theory and practice of electron diffraction from single atoms and extended objects using an EMPAD. (29th December 2017) - Cao, Michael C; Han, Yimo; Chen, Zhen; Jiang, Yi; Nguyen, Kayla X; Turgut, Emrah; Fuchs, Gregory D; Muller, David A
Abstract : A new generation of high-dynamic range pixel array detectors that collect the full scattering distribution let us record diffraction patterns from features as small as a single atom to large domains. By understanding these asymptotic limits of diffraction pattern formation, we can separate short from long-range features in center-of-mass imaging. Abstract: 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 momentum-resolved imaging modes. We explore the asymptotic limits of long-range and short-range 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.