Prospects for bright field and dark field electron tomography on a discrete grid J.R. Jinschek,* K.J. Batenburg,** H.A. Calderon,*** D. Van Dyck,**** F.-R. Chen,***** Ch. Kisielowski,* and V. Radmilovic * * Ernest Orlando Lawrence Berkeley National Laboratory, National Center for Electron Microscopy, 1 Cyclotron Road MS 72R0150, Berkeley, CA 94720, U.S.A. ** Leiden University, Mathematical Institute, Leiden & CWI, Amsterdam, The Netherlands *** ESFM-IPN, Dept. de Ciencia de Materiales, 07730 Mexico D.F., Mexico **** EMAT, University of Antwerp (RUCA), 2020 Antwerp, Belgium ***** Center of Electron Microscopy, National Tsing Hua University, HsinChu, Taiwan In recent years the improvement of field emission high-resolution transmission electron microscopes (HRTEM) including e.g. the introduction of aberration correctors extended their resolution to sub- Ångstrom values. The associated increasing sensitivity (signal-to-noise ratio) led to the ability to detect single atoms by measuring discrete intensity steps per contributing atom in an atomic column: by high-angle annular dark field (HAADF)-STEM (“Z-contrast”) shown in [1] and by phase contrast microscopy (e.g. exit wave reconstruction) shown in [2]. While in Z-contrast there is a direct relationship between the signal intensity and the crystal thickness as well as the atomic number Z at the same thickness [1], in phase contrast a linearization process is need to relate the oscillating data to the number of atoms in a column and to distinguish between different atomic species at the same specimen thickness. There are currently two approaches addressing this problem: the channeling theory [3] and reversed multi-slice calculations [4]. Using the channeling theory for thin crystals the discrete nature of the channeling map directly reveals the distinguishable number of atoms in each column [2]. The reversed multi-slice algorithm with a non-linear optimization scheme calculates an optimum phase grating by using two constraints: the entrance wave (=1) and the experimentally measured exit wave (EW). From the consequential calculation of the mean inner potential, the position of and the composition in each atomic column can be determined [3]. In low-resolution tomography it is required to tilt the sample, recording images every 1-2 degrees. However using so many projections (> 100) will often degrade the sample. In contrast, the knowledge of the position of the atomic columns and the number of atoms in each of it in a few zone axes (discrete grid) reduces drastically the required input data for a (tomographic) 3D reconstruction. In the discrete tomography approach data from less then 10 zone axis orientations are sufficient [5]. To prove this concept multi-slice calculations of through-focus series (MacTempas) and subsequent exit-wave reconstructions (FEI TrueImage) on a cuboctahedron shaped nanocrystal in 6 different zone axes ([111], [11 1], [001], [110], [1 10], [011] - see Fig. 1) were performed, applying the parameters of an aberration-corrected microscope (200kV, Cs = 0mm, resolution = 0.5Å). The discrete grid data were determined using the channeling map from the reconstructed EW images (details in [2], see two examples in Fig. 2 and 3). In our special case only three projections [001], [110], [1 10] were sufficient to find a unique reconstruction, illustrating the potential of the method. The other projections were used for checking the solution. The comparison between the projected potentials in <001> (Fig. 4a) and the final result (Fig. 4b) shows that discrete tomography reconstructs the exact position of all 309 atoms and the 3D shape of the nanocrystal. Results and limitations of the method as well as requirements for performing the real experiment, like the need of a double-tilt tomography holder to reach all these zone axis orientations, will be discussed.