It is widely accepted that the physical properties of nanostructures depend on the type of surface facets. For Au nanorods, the surface facets have a major influence on crucial effects such as reactivity and ligand adsorption and there has been controversy regarding facet indexing. Aberration-corrected electron microscopy is the ideal technique to study the atomic structure of nanomaterials. However, these images correspond to two-dimensional (2D) projections of 3D nano-objects, leading to an incomplete characterization. Recently, much progress was achieved in the field of atomic-resolution electron tomography, but it is still far from being a routinely used technique. Here we propose a methodology to measure the 3D atomic structure of free-standing nanoparticles, which we apply to characterize the surface facets of Au nanorods. This methodology is applicable to a broad range of nanocrystals, leading to unique insights concerning the connection between the structure and properties of nanostructures.

An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighbouring columns, enabling the analysis of a large field of view. For this algorithm, the accuracy and precision with which measurements for the atomic column positions and scattering cross-sections from annular dark field (ADF) STEM images can be estimated, has been investigated. The highest attainable precision is reached even for low dose images. Furthermore, the advantages of the model-based approach taking into account overlap between neighbouring columns are highlighted. This is done for the estimation of the distance between two neighbouring columns as a function of their distance and for the estimation of the scattering cross-section which is compared to the integrated intensity from a Voronoi cell. To provide end-users this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license.

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Recent progress in the field of topological states of matter has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs; refs ,,,), followed by closely related ternary compounds and predictions of several weak TIs (refs ,,). However, both the conceptual richness of Z2 classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z2 topological insulator is theoretically predicted and experimentally confirmed in the β-phase of quasi-one-dimensional bismuth iodide Bi4I4. The electronic structure of β-Bi4I4, characterized by Z2 invariants (1;110), is in proximity of both the weak TI phase (0;001) and the trivial insulator phase (0;000). Our angle-resolved photoemission spectroscopy measurements performed on the (001) surface reveal a highly anisotropic band-crossing feature located at the  point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.

Structural engineering of topological bulk materials is systematically explored with regard to the incorporation of the buckled bismuth layer [Bi 2 ], which is a 2D topological insulator per se, into the layered BiTeI host structure. The previously known bismuth telluride iodides, BiTeI and Bi 2 TeI, offer physical properties relevant for spintronics. Herewith a new cousin, Bi 3 TeI (sp.gr. R3m, a = 440.12(2) pm, c = 3223.1(2) pm), joins the ranks and expands this structural family. Bi 3 TeI = [Bi 2 ][BiTeI] represents a stack with strictly alternating building blocks. Conditions for reproducible synthesis and crystal-growth of Bi 2 TeI and Bi 3 TeI are ascertained, thus yielding platelet-like crystals on the millimeter size scale and enabling direct measurements. The crystal structures of Bi 2 TeI and Bi 3 TeI are examined by X-ray diffraction and electron microscopy. DFT calculations predict metallic properties of Bi 3 TeI and an unconventional surface state residing on various surface terminations. This state emerges as a result of complex hybridization of atomic states due to their strong intermixing. Our study does not support the existence of new stacking variants Bi x TeI with x > 3; instead, it indicates a possible homogeneity range of Bi 3 TeI. The series BiTeI−Bi 2 TeI−Bi 3 TeI illustrates the influence of structural modifications on topological properties.

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Powder X-ray diffraction patterns Figure S1. Powder X-ray diffraction pattern of a Bi-Rh-BiI 3 -mixture (11:3:3) tempered for 1h at 370 °C.

Dynamical scattering of fast electrons can be inverted by recasting the multislice algorithm as an artificial neural network, enabling the iterative retrieval of the three-dimensional object potential. This allows a nonheuristic treatment of the modulation transfer function of the CCD, partial spatial and temporal coherence, and inelastic scattering through an absorptive potential. Furthermore, prior knowledge about the atomic potential shape and the sparseness and positivity of the object can be used. The method is demonstrated on simulated bright field images recorded at 40 kV.